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+[
+    {
+        "url": "http://arxiv.org/abs/2404.16302v1",
+        "title": "CFMW: Cross-modality Fusion Mamba for Multispectral Object Detection under Adverse Weather Conditions",
+        "abstract": "Cross-modality images that integrate visible-infrared spectra cues can\nprovide richer complementary information for object detection. Despite this,\nexisting visible-infrared object detection methods severely degrade in severe\nweather conditions. This failure stems from the pronounced sensitivity of\nvisible images to environmental perturbations, such as rain, haze, and snow,\nwhich frequently cause false negatives and false positives in detection. To\naddress this issue, we introduce a novel and challenging task, termed\nvisible-infrared object detection under adverse weather conditions. To foster\nthis task, we have constructed a new Severe Weather Visible-Infrared Dataset\n(SWVID) with diverse severe weather scenes. Furthermore, we introduce the\nCross-modality Fusion Mamba with Weather-removal (CFMW) to augment detection\naccuracy in adverse weather conditions. Thanks to the proposed Weather Removal\nDiffusion Model (WRDM) and Cross-modality Fusion Mamba (CFM) modules, CFMW is\nable to mine more essential information of pedestrian features in\ncross-modality fusion, thus could transfer to other rarer scenarios with high\nefficiency and has adequate availability on those platforms with low computing\npower. To the best of our knowledge, this is the first study that targeted\nimprovement and integrated both Diffusion and Mamba modules in cross-modality\nobject detection, successfully expanding the practical application of this type\nof model with its higher accuracy and more advanced architecture. Extensive\nexperiments on both well-recognized and self-created datasets conclusively\ndemonstrate that our CFMW achieves state-of-the-art detection performance,\nsurpassing existing benchmarks. The dataset and source code will be made\npublicly available at https://github.com/lhy-zjut/CFMW.",
+        "authors": "Haoyuan Li, Qi Hu, You Yao, Kailun Yang, Peng Chen",
+        "published": "2024-04-25",
+        "updated": "2024-04-25",
+        "primary_cat": "cs.CV",
+        "cats": [
+            "cs.CV",
+            "cs.MM",
+            "cs.RO",
+            "eess.IV"
+        ],
+        "label": "Original Paper",
+        "paper_cat": "Diffusion AND Model",
+        "gt": "In this section, we briefly review previous related works about crossmodality object detection, state space model, and multi-weather image restoration. Cross-modality Object Detection The existing cross-modality object detection methods can be divided into two categories: feature level and pixel level fusion, distinguished through feature fusion methods and timing. Recently, dual stream object detection models based on convolutional neural networks have made great progress in improving recognition performance [4, 34, 37, 54, 55], while pixel level fusion methods have also achieved good performance [5, 44, 59]. Other works employing methods such as GAN to effective integration also have achieved good results [51, 58, 59]. Those works can be integrated into downstream tasks such as object detection. Traditional convolutional neural networks have limited receptive fields that the information is only integrated into a local area when using the convolution operator, where the self-attention operator of the transformer can learn long-range dependencies [43]. Thus, a transformer-based method, named Cross-Modality Fusion Transformer (CFT) [34], was presented and achieved state-of-theart detection performance. Differing from these works, we first introduce Mamba into cross-modality object detection to learn long-range dependencies with gating mechanisms, achieving high accuracy and low computation overhead simultaneously. State Space Model The concept of the State Space Model was initially introduced in the S4 model [11], presenting a distinctive architecture capable of effectively modeling global information, compared with traditional convolutional neural networks and transformers. Based on S4, the S5 model [38] reduces complexity to a linear level, with H3 [31] introducing it into language model tasks. Mamba [10] introduced an input-activate mechanism to enhance the State Space model, achieving higher inference speed and overall metrics compared with equivalent-scale transformers. With the introduction of Vision Mamba [61] and Vmamba [30], the application of the State Space Model has been extended into visual tasks. Currently, existing research does not consider effectively generalizing the State Space Model to cross-modality object detection. Multi-Weather Image Restoration Recently, some attempts have been made to unity multiple recovery tasks in a single deep learning framework, including generating modeling solutions to recover superimposed noise types [9], recovering superimposed noise or weather damage with unknown test time, or especially unfavorable multi-weather image fading [3, 22, 42]. All in One [23] unified a weather restoration method with a multi-encoder and decoder architecture. It is worth noting that diffusion-based conditional generative models have shown state-of-the-art performance in various tasks such as class-conditional data synthesis with classifier guidance [7], image super-resolution [14], image deblurring [48]. Denosing diffusion restoration models (DDRM) [21] were proposed for general linear inverse image restoration problems, exploiting pro-trained denoising diffusion models for unsupervised posterior sampling. Generally, diffusion models were so far not considered to be generalized to adverse weather scenes in the cross-modality image fusion field. Unlike existing works, we expand the multiweather restoration to the field of cross-modality fusion.",
+        "pre_questions": [],
+        "main_content": "INTRODUCTION In an open and dynamic environment, object detection faces challenging weather conditions such as rain, haze, and snow. The rapid advancement of deep-learning-based object detection methods has significantly improved the ability to identify and classify objects. Benefiting from the advanced feature extraction and fusion strategies, cross-modality object detection methods have achieved high accuracy, e.g., CFT [34], GAFF [56], and CFR_3 [54]. However, as shown in Fig. 1, the performance of these methods is often challenged by adverse weather conditions, which can severely impact the visibility and quality of visual data. Although the infrared image \u2217Equal contribution. \u2020Corresponding authors (e-mail: chenpeng@zjut.edu.cn, kailun.yang@kit.edu). Figure 1: The proposed method can achieve high-precision cross-modality object detection under adverse weather conditions. The top two examples are results from CFT [34], while the bottom two examples are results from CFMW (ours). could provide complementary cues to some extent, it cannot repair the appearance distortion or information loss of visual images. Thus, traditional cross-modality object detection methods still face severe performance degradation under adverse weather. Existing methods cannot be directly applied to adverse weather conditions, since the color gamut of visible images is weakened by environmental disturbance and the existing fusion methods are difficult to fully fuse visible and infrared spectra, nor have they made sufficient training under corresponding datasets. To make up the blank in this research area, we construct and release a new dataset, named Severe Weather Visible-Infrared Dataset (SWVID), as well as propose a novel framework named Cross-modality Fusion Mamba with Weather-removal (CFMW). To facilitate research in this area, we propose a new visibleinfrared dataset, named SWVID, which is designed to encompass diverse severe weather scenarios by mathematically formalizing the impact of various weather phenomena on images. Specifically, SWVID comprises 20, 000 aligned visible-infrared image pairs, spanning three weather conditions and two scenes, with each condition and scene evenly distributed. Motivated by the critical research gap highlighted in Fig. 1, where current methods falter in adverse weather, we introduce CFMW for multispectral object detection under adverse weather conditions. Our CFMW leverages a Weather Removal Diffusion Model (WRDM) and Cross-modality Fusion Mamba (CFM) to enhance detection accuracy amid adverse weather arXiv:2404.16302v1  [cs.CV]  25 Apr 2024 conditions while minimizing computational burden. Specifically, WRDM is employed to restore affected visible images before fusion with infrared counterparts, offering plug-and-play compatibility with image fusion networks. Based on learning reversal to increase the order of noise and disrupt the process of data samples, the WRDM model is advantageous to minimize the impact of adverse weather conditions. Additionally, CFM can be integrated into the feature extraction backbone, effectively integrating global contextual information from diverse modalities. Recent research shows that Mamba [10] achieves higher inference speed and overall metrics than the equivalent-scale transformer. To our knowledge, this study represents the first endeavor to employ Diffusion models and Mamba for multispectral object detection. Extensive experiments on both well-established and self-created datasets demonstrate that our CFMW method achieves superior detection performance compared to existing benchmarks. Specifically, we achieved about 17% performance improvement compared with the current state-of-the-art image restoration methods. The proposed method achieves about 8% accuracy improvement while saving 51.2% GPU memory compared with CFT [34], a state-of-theart cross-modality object detection method. At a glance, we summarize the main contributions as follows: \u2022 We introduce a novel task focusing on visible-infrared object detection under adverse weather conditions and develop a new dataset called the Severe Weather Visible-Infrared Dataset (SWVID), which simulates real-world conditions. SWVID comprises 60, 000 paired visible-infrared images and labels, encompassing weather conditions such as rain, haze, and snow;  We propose a novel approach, Cross-modality Fusion Mamba and snow; \u2022 We propose a novel approach, Cross-modality Fusion Mamba with Weather-removal (CFMW) for multispectral object detection under adverse weather conditions;  We introduce a novel Weather Removal Diffusion Model tection under adverse weather conditions; \u2022 We introduce a novel Weather Removal Diffusion Model (WRDM) and Cross-modality Fusion Mamba (CFM) modules to tackle image de-weathering and visible-infrared object detection tasks simultaneously;  Extensive experiments demonstrate that this integration detection tasks simultaneously; \u2022 Extensive experiments demonstrate that this integration achieves the best task migration capacity, resulting in stateof-the-art performance for both tasks. As shown in Fig. 2, CFMW comprises two main stages. In the multi-weather image restoration stage, we aim to achieve image restoration of three types of adverse weather conditions (rain, snow, and haze) and implement it using a unified framework with only one pre-trained weight. In the cross-modality fusion stage, we aim to integrate unique features of different modalities. Inspired by CFT [34], to show the effectiveness of our proposed CFM fusion model, we extend the framework of YOLOv5 to enable multispectral object detection. We present our carefully designed loss functions and training procedure for WRDM and CFM in the last subsection. 3.2 Weather Removal Diffusion Model (WRDM) Denoising diffusion models [13, 39] are a class of generative models, that learn a Markov chain that gradually transforms a Gaussian Figure 2: Framework of Cross-Modality Fusion Mamba backbone. It has three parts: a Weather Removal Diffusion Model (WRDM), a two-stream feature extraction network (our baseline), and three Cross-Modality Fusion Mamba (CFM) modules. \u00c9 represents element-wise add, \u00cb represents element-wise multiply, and C1 is short of 1-dimension convolutions. noise distribution into the data distribution trained by the models. The original denoising diffusion probabilistic models (DDPMs)[13] diffusion process (data to noise) and generative process (noise to data) are based on a Markov chain process, resulting in a large number of steps and huge time consumption. Thus, denoising diffusion implicit models (DDIMs) [40] were presented to accelerate sampling, providing a more efficient class of iterative implicit probabilistic models. DDIMs define the generative process via a class of non-Markovian diffusion processes that lead to the same training objective as DDPMs but can produce deterministic generative processes, thus speeding up sample generation. In DDIMs, implicit sampling refers to the generation of samples from the latent space of the model in a deterministic manner. Implicit sampling using a noise estimator network can be performed by: \ud835\udc4b\ud835\udc61\u22121 = \u221a\u00af \ud835\udefc\ud835\udc61\u22121 \u00b7 (\ud835\udc4b\ud835\udc61\u2212\u221a1 \u2212\u00af \ud835\udefc\ud835\udc61\u00b7 \ud835\udf16\ud835\udf03(\ud835\udc4b\ud835\udc61,\ud835\udc61) \u221a\u00af \ud835\udefc\ud835\udc61 ) +\u221a1 \u2212 \u00af \ud835\udefc\ud835\udc61\u22121 \u00b7 \ud835\udf16\ud835\udf03(\ud835\udc4b\ud835\udc61,\ud835\udc61). (1) where \ud835\udc4b\ud835\udc61and \ud835\udc4b\ud835\udc61\u22121 represent the data \ud835\udc4b0 \u223c\ud835\udc5e(\ud835\udc4b0)) in different diffusion time steps, \ud835\udefc\ud835\udc61= 1 \u2212\ud835\udefd\ud835\udc61, \u00af \ud835\udefc\ud835\udc61= \ud835\udc61 \u00ce \ud835\udc56=1 \ud835\udefc\ud835\udc56, and \ud835\udf16\ud835\udf03(\ud835\udc4b\ud835\udc61,\ud835\udc61) can be optimized as: E\ud835\udc4b0,\ud835\udc61,\ud835\udf16\ud835\udc61\u223c\ud835\udc41(0, \ud835\udc70), [\u2225\ud835\udf16\ud835\udc61\u2212\ud835\udf16\ud835\udf03(\u221a\u00af \ud835\udefc\ud835\udc61\ud835\udc4b0+\u221a1 \u2212\u00af \ud835\udefc\ud835\udc61\ud835\udf16\ud835\udc61,\ud835\udc61\u22252]. Conditional diffusion models have shown state-of-the-art imageconditional data synthesis and editing capabilities [6, 7]. The core idea is to learn a conditional reverse process without changing the diffusion process. Our proposed WRDM is a conditional diffusion model, adding reference images (clear images) in the process of sampling to guide the reconstructed image to be similar to reference images. As shown in Fig. 3, we introduce a new parameter e \ud835\udc4b, which represents the weather-degraded observation. A Markov chain is defined as a diffusion process, and Gaussian noise is gradually added to simulate the gradual degradation of data samples until reaching time point \ud835\udc47. We ground our model hyper-parameters via a U-Net architecture based on WideResNet [52]. For the input images conditional reflection, we connect patch \ud835\udc65\ud835\udc47and e \ud835\udc65, to obtain the six-dimensional input image channel. Conditioning the reverse process on e \ud835\udc4bcan maintain its compatibility with implicit sampling, so we could expand Eq. (1) as: \ud835\udc4b\ud835\udc61\u22121 = \u221a\u00af \ud835\udefc\ud835\udc61\u22121 \u00b7 (\ud835\udc4b\ud835\udc61\u2212\u221a1 \u2212\u00af \ud835\udefc\ud835\udc61\u00b7 \ud835\udf16\ud835\udf03(\ud835\udc4b\ud835\udc61, e \ud835\udc4b,\ud835\udc61) \u221a\u00af \ud835\udefc\ud835\udc61 ) +\u221a1 \u2212 \u00af \ud835\udefc\ud835\udc61\u22121 \u00b7 \ud835\udf16\ud835\udf03(\ud835\udc4b\ud835\udc61, e \ud835\udc4b,\ud835\udc61). (2) The sampling process starts from \ud835\udc4b\ud835\udc47\u223c\ud835\udc41(0, \ud835\udc70), following a deterministic reverse path towards \ud835\udc4b0 with fidelity. See more derivation details in the supplementary material. Our proposed WRDM is a patch-based conditional diffusion model, guiding the reverse sampling process toward smoothness across neighboring patches. During training, we randomly sample the \ud835\udc5d\ud835\udc65\ud835\udc5dpatch location for \ud835\udc43\ud835\udc56within the compute of image dimensions. Under any given time step \ud835\udc47, we reverse-sample the average estimated noise of each pixel in the overlapping patch area according to Fig. 3, which effectively controls the reverse sampling process to ensure that all adjacent patches have higher fidelity. Furthermore, WRDM can be regarded as a plug-in, embedded into other works such as visible-infrared image fusion to remove the influence of multi-weather conditions, which is demonstrated experimentally in Fig. 5. 3.3 Cross-modality Fusion Mamba (CFM) The goal of Cross-modality Fusion Mamba (CFM) is to introduce the advanced state space model (SSM), or Mamba [10], to crossmodality object detection. Structured state space sequence models (S4) and Mamba are inspired by the continuous system, mapping a 1-D function or sequence \ud835\udc65(\ud835\udc61) \u2208R \u2192\ud835\udc66(\ud835\udc61) through a hidden Figure 3: Schematic diagram of WRDM training and reasoning process. The left side is the framework of WRDM. We use a paired data distribution (e \ud835\udc4b,\ud835\udc4b\ud835\udc61), splitting into (e \ud835\udc4b(\ud835\udc51),\ud835\udc4b(\ud835\udc51) \ud835\udc61 ) for model-training. The right side is the illustration of the patch-based diffusive image restoration pipeline (4 patches for example here). state \u210e(\ud835\udc61) \u2208R\ud835\udc41. This system uses \ud835\udc68\u2208R\ud835\udc41\u00d7\ud835\udc41as the evolution parameter and \ud835\udc69\u2208R\ud835\udc41\u00d71, \ud835\udc6a\u2208R1\u00d7\ud835\udc41as the projection parameters, so that \ud835\udc66(\ud835\udc61) could evolve as follows: \u210e\u2032(\ud835\udc61) = \ud835\udc68\u210e(\ud835\udc61) + \ud835\udc69\ud835\udc65(\ud835\udc61), \ud835\udc66(\ud835\udc61) = \ud835\udc6a\u210e\u2032(\ud835\udc61). (3) Notice that S4 and Mamba are the discrete versions of the continuous system, including a timescale parameter \u0394 to transform the continuous parameters \ud835\udc34, \ud835\udc35to discrete parameters \u00af \ud835\udc68, \u00af \ud835\udc69as follows: \u00af \ud835\udc68= \ud835\udc52\ud835\udc65\ud835\udc5d(\u0394\ud835\udc68), \u00af \ud835\udc69= (\u0394\ud835\udc68)\u22121(\ud835\udc52\ud835\udc65\ud835\udc5d(\u0394\ud835\udc68) \u2212\ud835\udc70) \u00b7 \u0394\ud835\udc69. (4) After that, Eq. (3) could be rewritten as: \u210e\ud835\udc61= \u00af \ud835\udc68\u210e\ud835\udc61\u22121 + \u00af \ud835\udc69\ud835\udc65\ud835\udc61, \ud835\udc66\ud835\udc61= \ud835\udc6a\u210e\ud835\udc61. (5) Finally, the models compute output through a global convolution as follows: \u00af \ud835\udc72= \ud835\udc6a\u00af \ud835\udc69, \ud835\udc6a\u00af \ud835\udc68\u00af \ud835\udc69, ..., \ud835\udc6a\u00af \ud835\udc68\ud835\udc74\u22121 \u00af \ud835\udc69, \ud835\udc66= \ud835\udc65\u2217\u00af \ud835\udc72. (6) where \ud835\udc74is the length of the input sequence x, and \u00af \ud835\udc72\u2208R\ud835\udc40is a structured convolution kernel. Standard Mamba is designed for the 1-D sequence. As shown in Vision Mamba (Vim), 2-D multispectral images \ud835\udc61\u2208R\ud835\udc3b\u00d7\ud835\udc4a\u00d7\ud835\udc36 could be transformed into the flattened 2-D patches \ud835\udc65\ud835\udc5d\u2208R\ud835\udc3d\u00d7(\ud835\udc432\u00b7\ud835\udc36), where (\ud835\udc3b,\ud835\udc4a) represents the size of input images, \ud835\udc36is the channels, and \ud835\udc43is the size of image patches. Similarly, we linearly project the \ud835\udc65\ud835\udc5dto the vector with size \ud835\udc37and add position embeddings \ud835\udc6c\ud835\udc5d\ud835\udc5c\ud835\udc60\u2208R(\ud835\udc3d+1)\u00d7\ud835\udc37as follows: \ud835\udc7b0 = [\ud835\udc61\ud835\udc50\ud835\udc59\ud835\udc60;\ud835\udc611 \ud835\udc5d\ud835\udc7e;\ud835\udc612 \ud835\udc5d\ud835\udc7e; ...;\ud835\udc61\ud835\udc3d \ud835\udc5d\ud835\udc7e] + \ud835\udc6c\ud835\udc5d\ud835\udc5c\ud835\udc60. (7) where \ud835\udc61\ud835\udc57 \ud835\udc43is the \ud835\udc57\u2212\ud835\udc61\u210epath of \ud835\udc95, \ud835\udc7e\u2208R(\ud835\udc432\u00b7\ud835\udc36)\u00d7\ud835\udc37is the learnable projection matrix. Here are more details of the proposed CFM. As mentioned in the introduction section, the RGB modality and the Thermal modality show different features under different lighting and weather conditions, which are complementary and redundant. Therefore, we aim to design a block to suppress redundant features and fuse complementary to efficiently harvest essential cross-modal cues for object detection against adverse weather conditions. Motivated by the concept of Cross-Attention [1], we introduce a new crossmodality Mamba block to fuse features from different modalities. As shown in Fig. 2, to encourage feature interaction between RGB and Thermal modalities, we use a Channel Swapping Mamba block (CS) [12], which incorporates information from different channels and enhances cross-modality correlations. Given RGB features \ud835\udc39\ud835\udc45\ud835\udc56 and Thermal features \ud835\udc39\ud835\udc47\ud835\udc56, the first half of channels from \ud835\udc39\ud835\udc45\ud835\udc56will be concatenated with the latter half of \ud835\udc39\ud835\udc47\ud835\udc56and processed through the Mamba block for feature extraction. The obtained features are added to \ud835\udc39\ud835\udc45\ud835\udc56, creating a new feature \ud835\udc39\ud835\udc45\ud835\udc56 \u2032. Meanwhile, the first half of \ud835\udc39\ud835\udc47\ud835\udc56is concatenated with the latter half of \ud835\udc39\ud835\udc45\ud835\udc56, then passes through the Mamba block. The obtained features are added to \ud835\udc39\ud835\udc47\ud835\udc56, creating a new feature \ud835\udc39\ud835\udc47\ud835\udc56 \u2032. Subsequently, we project the features: \ud835\udc39\ud835\udc45\ud835\udc56 \u2032 and \ud835\udc39\ud835\udc47\ud835\udc56 \u2032 into the shared space during the feature fusion process, using the gating mechanism to encourage complementary feature learning while restraining redundant features. As shown in Fig. 2, we first normalize every token sequence in \ud835\udc39\ud835\udc45\ud835\udc56 \u2032 and \ud835\udc39\ud835\udc47\ud835\udc56 \u2032 with Norm block, which helps to improve the convergence speed and performance of the model. Then project the input sequence through linear layers and apply SiLu as the activation function. \u00af \ud835\udc68\ud835\udc90, \u00af \ud835\udc69\ud835\udc90, and \ud835\udc6a\ud835\udc90can be generated by the Parameters Function: \u00af \ud835\udc68\ud835\udc90, \u00af \ud835\udc69\ud835\udc90, \ud835\udc6a\ud835\udc90= \ud835\udc43\ud835\udc4e\ud835\udc5f\ud835\udc4e\ud835\udc5a\ud835\udc52\ud835\udc61\ud835\udc52\ud835\udc5f\ud835\udc60\ud835\udc39\ud835\udc62\ud835\udc5b\ud835\udc50\ud835\udc61\ud835\udc56\ud835\udc5c\ud835\udc5b(\ud835\udc65\ud835\udc5c\u2032), (8) where \ud835\udc65\u2032 \ud835\udc5c= \ud835\udc73\ud835\udc8a\ud835\udc8f\ud835\udc86\ud835\udc82\ud835\udc93(\ud835\udc65\ud835\udc65 \ud835\udc5c\ud835\udc75\ud835\udc90\ud835\udc93\ud835\udc8e(\ud835\udc39\ud835\udc5c\u2032 \ud835\udc56)). After that, we apply State Space Model (SSM): \ud835\udc66\ud835\udc5c= \ud835\udc7a\ud835\udc7a\ud835\udc74( \u00af \ud835\udc68\ud835\udc90, \u00af \ud835\udc69\ud835\udc90, \ud835\udc6a\ud835\udc90)(\ud835\udc65\ud835\udc5c\u2032), (9) Figure 4: Overview of the established SWVID benchmarks. The dataset includes three weather conditions (i.e., Rain, Foggy, and Snow), and two scenarios (i.e., Daylight and Night), providing 60, 000 images in total. Then we apply the gating operation, followed by residual connection: \ud835\udc67= \ud835\udc73\ud835\udc8a\ud835\udc8f\ud835\udc86\ud835\udc82\ud835\udc93\ud835\udc9b(\ud835\udc39\ud835\udc47\ud835\udc56 \u2032), (10) \ud835\udc66\ud835\udc45\u2032 = \ud835\udc66\ud835\udc45\u2299\ud835\udc7a\ud835\udc8a\ud835\udc73\ud835\udc7c(\ud835\udc67), (11) \ud835\udc66\ud835\udc47\u2032 = \ud835\udc66\ud835\udc47\u2299\ud835\udc7a\ud835\udc8a\ud835\udc73\ud835\udc7c(\ud835\udc67), (12) \ud835\udc39\ud835\udc56= \ud835\udc79\ud835\udc86\ud835\udc94\ud835\udc89\ud835\udc82\ud835\udc91\ud835\udc86(\ud835\udc73\ud835\udc8a\ud835\udc8f\ud835\udc86\ud835\udc82\ud835\udc93\ud835\udc47(\ud835\udc66\ud835\udc45\u2032 + \ud835\udc66\ud835\udc47\u2032) + \ud835\udc39\ud835\udc56\u2032). (13) Finally, we get the fused 2-D feature \ud835\udc39\ud835\udc56successfully. Different from CFT [34], our fusion block improves computational efficiency while inheriting the components of global receptive field and dynamic weight. Comparing the state space model (SSM) in our CFM block with the self-attention mechanism of transformers in CFT [34], both of them play an important role in providing global context adaptively, but self-attention is quadratic to sequence length while SSM is linear to sequence length [61]. To achieve lower memory usage when dealing with long-sequence works, CFM chooses the recomputation method as the same as Mamba. Experiment on the SWVID and LLVIP dataset, whose resolution is 1080 \u00d7 720, shows that CFT requires 21.88GB GPU memory while CFM only requires 10.72GB, saving 11.16GB in the same configuration. 3.4 Loss Functions As a two-stage pre-training model, we carefully design the training loss functions to produce enhanced results with minimum blurriness and the closest details to ground-truth images and to extract the differences between RGB and thermal modalities. For training WRDM, the goal of the loss function in this stage is to maximize the data log-likelihood \ud835\udc59\ud835\udc5c\ud835\udc54\ud835\udc5d\ud835\udf03(\ud835\udc650). Since maximizing this target directly is very challenging, we use variational inference to approximate this target. Variational inference approximates the true posterior distribution \ud835\udc5d\ud835\udf03(\ud835\udc650 : \ud835\udc47) by introducing a variational Table 1: Comparisons of SWVID benchmark with existing visible-infrared datasets. !means available while %denotes the opposite. Dataset Year Resolution Publication Scene Daylight Night Weather KAIST [16] 2015 640 \u00d7 512 CVPR \" \" % FLIR [8] 2018 640 \u00d7 512 \" \" % RoadScene [50] 2020 640 \u00d7 512 AAAI \" \" % LLVIP [18] 2021 1080 \u00d7 720 ICCV \" \" % MSRS [41] 2022 640 \u00d7 480 Info. Fusion \" \" % M3FD [27] 2022 640 \u00d7 512 CVPR \" \" % VTUAV [32] 2022 1920 \u00d7 1080 CVPR \" \" % SWVID 2024 1080 \u00d7 720 Proposed \" \" \" distribution\ud835\udc5e(\ud835\udc651 : \ud835\udc47|\ud835\udc650) and then minimizes the difference between these two distributions. Here we define L\ud835\udf03= \u2212\ud835\udc59\ud835\udc5c\ud835\udc54\ud835\udc5d\ud835\udf03(\ud835\udc650), we have: L\ud835\udf03= \ud835\udc47 \u2211\ufe01 \ud835\udc61=1 E\ud835\udc5e[\ud835\udc59\ud835\udc5c\ud835\udc54\ud835\udc5d\ud835\udf03(\ud835\udc650|\ud835\udc65\ud835\udc47)] \u2212 \ud835\udc47\u22121 \u2211\ufe01 \ud835\udc61=1 E\ud835\udc5e(\ud835\udc65\ud835\udc61\u22121|\ud835\udc65\ud835\udc61) [\ud835\udc37\ud835\udc3e\ud835\udc3f(\ud835\udc5e(\ud835\udc65\ud835\udc61\u22121|\ud835\udc65\ud835\udc61,\ud835\udc650))||\ud835\udc5d\ud835\udf03(\ud835\udc65\ud835\udc61\u22121|\ud835\udc65\ud835\udc61)]. (14) where the second term is the expected value of the Kullback-Leibler divergence between \ud835\udc5e(\ud835\udc65\ud835\udc61\u22121|\ud835\udc65\ud835\udc61) and \ud835\udc5d\ud835\udf03(\ud835\udc65\ud835\udc61\u22121|\ud835\udc65\ud835\udc61). In alignment with the prevalent practices in this field, the overall loss function (L\ud835\udc61\ud835\udc5c\ud835\udc61\ud835\udc4e\ud835\udc59) is a sum of the bounding-box regression loss (L\ud835\udc4f\ud835\udc5c\ud835\udc65), the classification loss (L\ud835\udc50\ud835\udc59\ud835\udc60), and the confidence loss (L\ud835\udc50\ud835\udc5c\ud835\udc5b\ud835\udc53= L\ud835\udc5b\ud835\udc5c\ud835\udc5c\ud835\udc4f\ud835\udc57+ L\ud835\udc5c\ud835\udc4f\ud835\udc57). L\ud835\udc61\ud835\udc5c\ud835\udc61\ud835\udc4e\ud835\udc59= L\ud835\udc4f\ud835\udc5c\ud835\udc65+ L\ud835\udc50\ud835\udc59\ud835\udc60+ L\ud835\udc5b\ud835\udc5c\ud835\udc5c\ud835\udc4f\ud835\udc57+ L\ud835\udc5c\ud835\udc4f\ud835\udc57, (15) Details of the loss function for CFMW are elucidated in the supplementary material. 4 EXPERIMENTS 4.1 Established SWVID benchmark Dataset. The color gamut of visible images is weakened by environmental disturbance in dynamic environments, and the existing fusion methods make it difficult to fully fuse visible and infrared spectra because of a deficiency of sufficient training under corresponding datasets. As shown in Fig. 4, we established the benchmark, SWVID, which is constructed from the public datasets (i.e. LLVIP [18], M3FD [27], MSRS [41]) collected in the real scene. It contains a variety of uniformly distributed scenes (daylight, night, rain, foggy, and snow), simulating real environments through the combination of different scenes. Furthermore, we provide the corresponding ground-truth images for each visible image affected by adverse weather conditions for image fusion and image restoration network training. As shown in Table 1, compared with previous visible-infrared datasets, SWVID is the first one that considers weather conditions. Specifically, we have constructed the dataset from public visible-infrared datasets as follows: D\ud835\udc5f\ud835\udc4e\ud835\udc56\ud835\udc5b(\ud835\udc3d(\ud835\udc65)) = \ud835\udc3d(\ud835\udc65)(1 \u2212\ud835\udc40\ud835\udc5f(\ud835\udc65)) + \ud835\udc45(\ud835\udc65)\ud835\udc40\ud835\udc5f(\ud835\udc65), (16) D\ud835\udc60\ud835\udc5b\ud835\udc5c\ud835\udc64(\ud835\udc3d(\ud835\udc65)) = \ud835\udc3d(\ud835\udc65)(1 \u2212\ud835\udc40\ud835\udc60(\ud835\udc65)) + \ud835\udc46(\ud835\udc65)\ud835\udc40\ud835\udc60(\ud835\udc65), (17) D\ud835\udc53\ud835\udc5c\ud835\udc54\ud835\udc54\ud835\udc66(\ud835\udc3d(\ud835\udc65)) = \ud835\udc3d(\ud835\udc65)\ud835\udc52\u2212 \u222b\ud835\udc51(\ud835\udc65) 0 \ud835\udefd\ud835\udc51\ud835\udc59+ \u222b\ud835\udc51(\ud835\udc65) 0 \ud835\udc3f\u221e\ud835\udefd\ud835\udc52\u2212\ud835\udefd\ud835\udc59\ud835\udc51\ud835\udc59. (18) Figure 5: Examples of daylight and night scenes for multimodal fusion and object detection visualization, including three kinds of adverse weather conditions (rain, haze, and snow). We embed WRDM into two state-of-the-art visible-infrared fusion methods (i.e., CDDFuse [59] and DeFusion [25]) to mitigate the adverse impact of weather conditions. where \ud835\udc65represents the spatial location in an image, D\ud835\udc5f\ud835\udc4e\ud835\udc56\ud835\udc5b(\ud835\udc3d(\ud835\udc65)), D\ud835\udc60\ud835\udc5b\ud835\udc5c\ud835\udc64(\ud835\udc3d(\ud835\udc65)) and D\ud835\udc53\ud835\udc5c\ud835\udc54\ud835\udc54\ud835\udc66(\ud835\udc3d(\ud835\udc65)) represent a function that maps a clear image to one with rain, snow, and fog particle effects, \ud835\udc3d(\ud835\udc65) represents the clear image with no weather effects, \ud835\udc40\ud835\udc5f(\ud835\udc65) and \ud835\udc40\ud835\udc60(\ud835\udc65) represent rain and snow equivalents, \ud835\udc45(\ud835\udc65) represents a map of the rain masks, \ud835\udc46(\ud835\udc65) represents a chromatic aberration map of the snow particles. Considering scattering effects, \ud835\udc51(\ud835\udc65) represents the distance from the observer at a pixel location \ud835\udc65, \ud835\udefdis an atmospheric attenuation coefficient, and \ud835\udc3f\u221eis the radiance of light. We divide SWVID into the training set (34, 280 images), validation set (17, 140 images), and test set (8, 570 images), each folder contains three parts: pairs of visible-infrared images and corresponding weather-influenced visible images. Notice that weather-influenced visible images contain three kinds of weather conditions, classified as SWVID-snow, SWVID-rain, and SWVID-foggy. During the training period, we use the pairs of images (weather-influenced and ground-truth) to train WRDM in the first stage, then use the pairs of images (ground-truth and infrared) with corresponding labels to train CFM in the second stage. During the validating and testing period, we use the pairs of images (weather-influenced and infrared) directly, verifying and testing the performance of CFMW under real conditions. Also, we use the same way when evaluating other networks in comparative experiments. Evaluation metrics. We adopt the conventional peak signalto-noise ratio (PSNR) [15] and structural similarity (SSIM) [47] for quantitative evaluations between ground truth and restored images. PSNR is mainly used to evaluate the degree of distortion after image processing, while SSIM pays more attention to the Table 2: Quantitative comparisons in terms of PSNR and SSIM (higher is better) with state-of-the-art image deraining, dehazing, and desnowing methods. For the sake of fairness, we uniformly use the visible light part of the established SWVID dataset as the evaluation dataset. Image-Deraining Task SWVID-rain (RGB) Image-Dehazing Task SWVID-foggy (RGB) Image-Desnowing Task SWVID-snow (RGB) PSNR\u2191 SSIM\u2191 PSNR\u2191 SSIM\u2191 PSNR\u2191 SSIM\u2191 pix2pix [17] 19.95 0.7270 pix2pix [17] 25.12 0.8359 SPANet [46] 29.92 0.8260 CycleGAN [60] 17.65 0.6452 DuRN [29] 31.44 0.9256 DDMSNet [57] 34.87 0.9462 PCNet [19] 27.13 0.8546 AttentiveGAN [33] 32.56 0.9331 DesnowNet [2] 32.15 0.9416 MPRNet [53] 29.14 0.9022 IDT [49] 34.14 0.9412 RESCAN [24] 30.57 0.9003 de-rain (ours) 36.78 0.9464 de-haze (ours) 36.53 0.9795 de-snow (ours) 42.23 0.9821 All-in-One [23] 25.13 0.8856 All-in-One [23] 31.24 0.9122 All-in-One [23] 28.12 0.8815 TransWeather [42] 29.77 0.9107 TransWeather [42] 33.85 0.9388 TransWeather [42] 35.15 0.9417 WRDM (ours) 35.02 0.9322 WRDM (ours) 35.88 0.9602 WRDM (ours) 40.98 0.9578 Table 3: Comparison of performances with other networks on the SWVID-snow dataset. Model Data Backbone mAP50\u2191 mAP75\u2191 mAP\u2191 mono-modaltiy networks Faster R-CNN [36] RGB ResNet50 82.3 34.6 30.7 Faster R-CNN [36] Thermal ResNet50 90.6 63.7 55.4 SDD [28] RGB VGG16 73.6 37.8 38.6 SDD [28] Thermal VGG16 88.6 55.6 50.2 YOLOv3 [35] RGB Darknet53 78.3 29.4 24.4 YOLOv3 [35] Thermal Darknet53 84.6 50.7 47.4 YOLOv5 [20] RGB CSPD53 80.7 38.2 30.7 YOLOv5 [20] Thermal CSPD53 90.5 65.2 57.6 YOLOv7 [45] RGB CSPD53 85.3 41.8 34.9 YOLOv7 [45] Thermal CSPD53 91.8 67.6 60.4 multi-modality networks Baseline RGB+T CSPD53 92.2 68.4 59.3 CFT [34] RGB+T CFB 92.4 71.1 58.4 CFMW (ours) RGB+T CFM 97.2 76.9 63.4 structural information and visual quality of the images. \ud835\udc43\ud835\udc46\ud835\udc41\ud835\udc45= 10 \u00d7 \ud835\udc59\ud835\udc54( (2\ud835\udc5b\u22121)2 \ud835\udc40\ud835\udc46\ud835\udc38 ), (19) \ud835\udc46\ud835\udc46\ud835\udc3c\ud835\udc40= [\ud835\udc59(\ud835\udc65,\ud835\udc66)]\ud835\udefc\u00b7 [\ud835\udc50(\ud835\udc65,\ud835\udc66)]\ud835\udefd\u00b7 [\ud835\udc60(\ud835\udc65,\ud835\udc66)]\ud835\udefe, (20) As for object detection quantitative experiments, we introduced three object detection metrics: mean Average Precision (mAP, mAP50, and mAP75) to evaluate the accuracy of the object detection models. For more calculation details, please refer to the supplementary material. 4.2 Implantation Details As for WRDM, we performed experiments both in specific-weather conditions and multi-weather conditions image restoration settings. We denote our specific-weather restoration models as de-rain, desnow, and de-foggy to verify the general WRDM model under specific weather conditions. We trained the 128 \u00d7 128 patch size version of all models. We use NVIDIA RTX 4090 cards to perform all the experiments. We use Adam as an optimizer while training all the models we compare. During the training process, we trained WRDM for 3 \u00d7 106 iterations. As for CFM, we did not perform Table 4: Comparison of performances with other networks on the LLVIP [18] dataset. Model Data Backbone mAP50\u2191 mAP75\u2191 mAP\u2191 mono-modaltiy networks Faster R-CNN [36] RGB ResNet50 91.4 48.0 49.2 Faster R-CNN [36] Thermal ResNet50 96.1 68.5 61.1 SDD [28] RGB VGG16 82.6 31.8 39.8 SDD [28] Thermal VGG16 90.2 57.9 53.5 YOLOv3 [35] RGB Darknet53 85.9 37.9 43.3 YOLOv3 [35] Thermal Darknet53 89.7 53.4 52.8 YOLOv5 [20] RGB CSPD53 90.8 51.9 50.0 YOLOv5 [20] Thermal CSPD53 94.6 72.2 61.9 YOLOv7 [45] RGB CSPD53 91.4 58.4 53.6 YOLOv7 [45] Thermal CSPD53 94.6 70.6 62.4 multi-modality networks Baseline RGB+T CSPD53 95.2 71.4 62.3 CFT [34] RGB+T CFB 97.5 72.9 63.6 CFMW (ours) RGB+T CFM 98.8 77.2 64.8 task-specific parameter tuning or modifications to the network architecture. For better performance, we select the YOLOv5 model\u2019s public weight initialization (yolov5s.pt), which is pre-trained on the COCO dataset [26]. 4.3 Comparative Experiments In this section, we make comparisons with several state-of-theart methods in image deweathering and cross-modality object detection separately. In Table 2, we perform comparisons with methods for image desnowing (i.e. SPANet [46], DDMSNet [57], DesnowNet [2], RESCAN [24]), deraining (i.e. pix2pix [17], CycleGAN [60], PCNet [19], MPRNet [53]), and dehazing (i.e. pix2pix [17], DuRN [29], Attentive-GAN [33], IDT [49]), as well as two state-ofthe-art multi-weather image restoration methods: All in One [23] and TransWeather [42]. In Table 3 and Table 4, to prove the consistent improvements of CFMW, we compare with several base single-modality object detection methods (i.e., Faster R-CNN [36], SDD [28], YOLOv3 [35], YOLOv5 [20], YOLOv7 [45]) and several multi-modality object detection methods (i.e., our baseline, standard two-stream YOLOv5 object detection network, and CFT [34]). Table 5: Ablation experiments on SWVID-snow dataset. To present the general effectiveness of our CFMW, we further combine the WRDM and CFM module with other classical detectors (i.e., YOLOv7, YOLOv5, Faster R-CNN). Modality Method Detector mAP50\u2191 mAP75\u2191 mAP\u2191 RGB CSPDarknet53 YOLOv7 [45] 85.3 41.8 34.9 Thermal CSPDarknet53 95.8 72.6 60.4 RGB+T +two stream 95.4 68.1 60.4 +CFM 95.5 68.6 63.3 +WRDM 96.5 70.9 63.1 +CFM&WRDM 96.6 75.1 64.1 RGB CSPDarknet53 YOLOv5 [20] 80.7 38.2 30.7 Thermal CSPDarknet53 90.5 65.2 57.6 RGB+T +two stream 92.2 68.4 59.3 +CFM 96.5 70.6 63.3 +WRDM 96.4 71.2 62.8 +CFM&WRDM 97.2 76.9 63.4 RGB Resnet53 Faster R-CNN [36] 82.3 34.6 30.7 Thermal Resnet53 90.6 63.7 55.4 RGB+T +two stream 93.7 62.8 55.4 +CFM 96.7 69.5 61.9 +WRDM 96.2 69.4 61.6 +CFM&WRDM 96.2 69.7 62.2 Comparison of image deweathering. As shown in Table 2, we use the single RGB modality of the SWVID dataset (including rain, foggy, and haze weather conditions) as a comparative dataset to measure the performance of different models under different weather conditions. The top of the table contains results from specific-weather image restoration, where we show \ud835\udc46= 50 sampling time steps. For image-deraining, image-dehazing, and image-desnowing tasks, the proposed solution consistently achieves the best results (36.78/0.9464 on SWVID-rain, 36.53/0.9795 on SWVID-foggy, and 42.23/0.9821 on SWVID-snow). Especially, in the image de-rain task, the performance improvement is about 24% compared with the current state-of-the-art method (MPRNet [53]). For multi-weather image restoration, although the results are not as good as the specific-weather model due to the complexity of the task, the proposed method also reaches the best results ( 35.02/0.9322 on SWVID-rain, 35.88/0.9602 on SWVID-foggy, and 40.98/0.9578 on SWVID-snow) compared with All in One [23] and TransWeather [42], with about 17% performance improvement compared against TransWeather [42] and about 25% performance improvement compared against All in One [23]. Comparison of cross-modality object detection. As shown in Table 3 and Table 4, we use LLVIP [18] and SWVID-snow as the comparative datasets. Compared with SWVID-rain and SWVIDfoggy, the size of pedestrians in these two datasets is more in line with the general object detection standards. There are more complex cases of pedestrian overlap in these two datasets, which can better measure the accuracy of the object detection networks. The top of the table contains results from single-modality networks, each network uses the RGB modality or the thermal modality for detection. The bottom of the table shows results from multi-modality networks, including our baseline, CFT [34] and the proposed CFMW. According to Table 3, it can be observed that with the integration of WRDM and CFM, CFMW achieves an overwhelming performance improvement on each metric (mAP50:2.3\u2191, mAP75:4.3\u2191, mAP:3.0\u2191) on SWVID-snow compared with the best existing network on each metric, which shows that it has preferable adaptability under adverse weather conditions. Also, CFMW can achieve a more accurate detection (mAP50:98.8, mAP75:77.2, mAP:64.8) with lower computational consumption, as shown in Table 4, which demonstrates the commonality of CFWM. 4.4 Ablation Study In this section, we analyze the effectiveness of CFMW. We first validate the importance of WRDM and CFM modules in performance improvement in a parametric form through detailed ablation experiments, then visually show the role of WRDM in cross-modality fusion and object detection tasks to highlight its versatility as a weather-restoration plug-in. Ablation experiments To understand the impact of each component in our method, we have performed a comprehensive set of ablation experiments. As shown in Table 5, we further combine the CFM and WRDM with other classical detectors, i.e. YOLOv7 [45], YOLOv5 [20] and Faster R-CNN [36] to present the general effectiveness of our CFMW. The proposed CFMW improves the performance of cross-modality object detection using either a one-stage or twostage detector under complex weather conditions. Specifically, CFM achieves an 11.3% gain on mAP50, an 81.6% gain on mAP75, and a 78.3% gain on mAP (on YOLOv5 [20] ). After adding WRDM, we achieved a 12.1% gain on mAP50, an 88.2% gain on mAP75, and an 80.4% gain on mAP. CFM and WRDM provide non-negligible gains for all the considered evaluation metrics. Visual interpretation To verify the applicability of WRDM as a plug-in intuitively, we visually show the application scenario of WRDM in the field of visible-infrared image fusion and object detection. As shown in Fig. 5, we perform comparisons with methods of visible-infrared image fusion methods (i.e. CDDFuse [59], DeFusion [25]). It can be seen from the figure that compared with the original images, the image fusion effects of the two methods before and after using WRDM are quite different, more people at the far end of images could be detected successfully after deweathering. In cross-modality object detection, rich image details can provide great assistance for feature extraction and fusion, with direct fusion without removing the weather influence causing the loss and interference of image details. 5 CONCLUSION In this work, we introduce a novel approach to visible-infrared object detection under severe weather conditions, namely the Severe Weather Visible-Infrared Dataset (SWVID). We have provided a valuable resource for training and evaluating models in realistic and challenging environments. The Cross-modality Fusion Mamba with Weather-removal (CFMW) model, has proven to be highly effective in enhancing detection accuracy while managing computational efficiency. Our extensive experiments have shown that CFMW outperforms existing benchmarks, achieving state-of-the-art on both tasks: multi-weather image restoration and cross-modality object detection. This work opens up new possibilities for cross-modality object detection in adverse weather.",
+        "additional_info": [
+            [
+                {
+                    "url": "http://arxiv.org/abs/2404.14743v1",
+                    "title": "Gradient Guidance for Diffusion Models: An Optimization Perspective",
+                    "abstract": "Diffusion models have demonstrated empirical successes in various\napplications and can be adapted to task-specific needs via guidance. This paper\nintroduces a form of gradient guidance for adapting or fine-tuning diffusion\nmodels towards user-specified optimization objectives. We study the theoretic\naspects of a guided score-based sampling process, linking the gradient-guided\ndiffusion model to first-order optimization. We show that adding gradient\nguidance to the sampling process of a pre-trained diffusion model is\nessentially equivalent to solving a regularized optimization problem, where the\nregularization term acts as a prior determined by the pre-training data.\nDiffusion models are able to learn data's latent subspace, however, explicitly\nadding the gradient of an external objective function to the sample process\nwould jeopardize the structure in generated samples. To remedy this issue, we\nconsider a modified form of gradient guidance based on a forward prediction\nloss, which leverages the pre-trained score function to preserve the latent\nstructure in generated samples. We further consider an iteratively fine-tuned\nversion of gradient-guided diffusion where one can query gradients at newly\ngenerated data points and update the score network using new samples. This\nprocess mimics a first-order optimization iteration in expectation, for which\nwe proved O(1/K) convergence rate to the global optimum when the objective\nfunction is concave.",
+                    "authors": "Yingqing Guo, Hui Yuan, Yukang Yang, Minshuo Chen, Mengdi Wang",
+                    "published": "2024-04-23",
+                    "updated": "2024-04-23",
+                    "primary_cat": "stat.ML",
+                    "cats": [
+                        "stat.ML",
+                        "cs.LG"
+                    ],
+                    "label": "Original Paper",
+                    "paper_cat": "Diffusion AND Model",
+                    "gt": "Our study is motivated by recent empirical progress of guidance-based diffusion model fine-tuning for steering sample generation towards specific needs (Dhariwal and Nichol, 2021; Bansal et al., 2023). Upon modeling the specific needs as a reward function, the relevant methods can be summarized into two categories in the sequel. 3 Guided Generation and Fine-tuning Given an auxiliary reward function judging the sample property of interests, existing research explored diverse mechanisms to guide generation from diffusion models. There are mainly two types of methods. The first type of method incorporates an additive so-called \u201cguidance\u201d term into the score function of pre-trained diffusion models at inference time. For example, classifier guidance (Song et al., 2020a; Dhariwal and Nichol, 2021) defines the guidance term as the gradient of an externally trained classifier on noise corrupted data. Classifier-free guidance (Ho and Salimans, 2022) simultaneously trains conditional and unconditional diffusion models, circumventing the training of an external classifier. After the training, the score functions of the conditional and unconditional models are combined together to achieve guided generation. Bansal et al. (2023) draw motivation from classifier guidance and generalize the idea to a \u201cuniversal guidance\u201d for adapting unconditioned score functions to various external rewards. The second type of method attempts to directly fine-tune the weight parameters in a pretrained diffusion model by interacting with the target reward function. For example, Clark et al. (2023) fine-tune diffusion models by directly backpropagating the gradient of the reward function. Recently, a line of works utilizes Reinforcement Learning (RL) techniques for fine-tuning diffusion models (Black et al., 2023; Fan et al., 2023). They formulate the sample generation process of diffusion models as a finite-horizon Markov chain. The score function can be viewed as a policy, the generated samples are the state of the Markov chain, and the target reward function defines the terminal reward. In this way, fine-tuning diffusion models is equivalent to policy optimization and allows the use of policy gradient methods. Sampling and Statistical Theory of Diffusion Model In contrast to the fruitful empirical advances, the theory of diffusion models is still limited. To the best of our knowledge, a theoretical understanding of fine-tuning diffusion models is absent. Existing results mainly focus on the sampling ability and statistical properties of unconditional diffusion models. In particular, for sampling ability, a line of works shows that the distribution generated by a diffusion model is close to the data distribution, as long as the score function is accurately estimated (De Bortoli et al., 2021; Albergo et al., 2023; Block et al., 2020; Lee et al., 2022a; Chen et al., 2022; Lee et al., 2022b,a; Chen et al., 2022; Lee et al., 2022b). The accuracy of the estimated score function is measured in terms of an L\u221eor L2-norm distance. More recently, Chen et al. (2023c,b); Benton et al. (2023) develop refined and tighter analyses using Taylor expansions of the discretized backward process and localization method. It is worth mentioning that the analysis in Chen et al. (2023c,b); Benton et al. (2023) extends to broader sample generation processes such as deterministic ones based on probabilistic ODEs. Going beyond distributions in Euclidean spaces, De Bortoli (2022) analyzes diffusion models for sampling distribution supported on a low-dimensional manifold. Moreover, Montanari and Wu (2023) consider sampling from symmetric spiked models, and El Alaoui et al. (2023) study sampling from Gibbs distributions using diffusion processes. Turning towards the statistical theory of diffusion models, Song et al. (2020b) and Liu et al. (2022) provide asymptotic analyses, assuming a parametric form of the score function. Unfortunately, asymptotic analysis does not lead to concrete sample complexities. Later, concurrent works, Oko et al. (2023) and Chen et al. (2023a), establish sample complexity bounds of diffusion models for estimating nonparametric data distributions. In high dimensions, their results highlight a curse of dimensionality issue without further assumptions, which also appears in Wibisono et al. (2024) considering kernel methods. More interestingly, these works demonstrate that diffusion models can 4 circumvent the curse of dimensionality issue if the data has low-dimensional structures. In the same spirit, Mei and Wu (2023) investigate learning high-dimensional graphical models using diffusion models, without the curse of dimensionality. For conditional diffusion models, Yuan et al. (2023); Fu et al. (2024) establish sample complexity bounds for learning generic conditional distributions. We refer readers to Chen et al. (2024) for an overview of contemporary theoretical progress. Novelty of This Paper Despite the existing theoretical underpinnings of diffusion models, our paper provides the first rigorous study of adapting and fine-tuning diffusion models using gradient guidance from an optimization perspective. Specifically, we first understand why naive gradient guidance does not lead to meaningful optimization performance. Built upon the insights gained from the analysis, we propose gradient guidance that is proven to preserve generated data structures and simultaneously achieve strong optimization guarantees on adapted variants of diffusion models. We are aware of two recent works (Uehara et al., 2024; Marion et al., 2024) studying adapting the output distribution of diffusion models to a target reward function. In particular, they define a reward function with respect to the output distribution of the diffusion model. Given a pre-trained diffusion model, for instance, Uehara et al. (2024) utilizes a KL-divergence regularizer penalizing the deviation to the pre-trained model for preventing overfitting in fine-tuning. Through some explicit computation, Uehara et al. (2024); Marion et al. (2024) identify the proper guidance term to adapt the pre-trained model. Yet a sophisticated estimation procedure is needed to find the guidance term in Uehara et al. (2024); our gradient guidance enjoys much simplicity and efficacy, as we demonstrated in both theory and experiments.",
+                    "pre_questions": [],
+                    "main_content": "Introduction Diffusion models have emerged as a significant advancement in the field of generative artificial intelligence, offering state-of-the-art performance in image generation (Song and Ermon, 2019; Song et al., 2020a; Dhariwal and Nichol, 2021). These models operate by gradually transforming a random noise distribution into a structured output, by using a score function trained from large amounts of data. Such a transforming process is typically modeled as a stochastic differential equation, offering a mathematically grounded approach for sampling. One of the key advantages of diffusion models is their ability to be guided or fine-tuned for specific tasks, which allows them to excel in a wide range of applications (Kong et al., 2020; Ajay et al., 2022; Gruver et al., 2023). Guidance-based diffusion, a nuanced extension of diffusion models, stands at the forefront of controlled generation in generative AI. This approach involves steering the noise transformation process of a diffusion model towards desired outcomes by incorporating additional \u201cguidance signals\u201d. This guidance can manifest in various forms, such as text prompts, class labels, or even \u2217\u2020 Equal contribution. Emails: {yg6736, huiyuan, yy1325, minshuochen, mengdiw}@princeton.edu. 1 arXiv:2404.14743v1  [stat.ML]  23 Apr 2024 conditioning on specific attributes and rewards. The core principle behind this technique is to influence the probabilistic pathway of the noise transformation process at each time step, thereby steering the final output towards predefined criteria or objectives. This controlled generation capability opens up opportunities for generative AI in a broad range of tasks, such as in targeted image synthesis, content creation with specific themes, or even in drug design where molecular structures need to meet specifications. A notable example is the classifier-based diffusion model introduced by Song et al. (2020c); Dhariwal and Nichol (2021), which generates data conditioned on a class label, via guidance signals that are computed from conditional likelihoods from a classifier. Building on this concept, Bansal et al. (2023) extend the classifier-guidance method to a form of \u201cuniversal guidance\u201d. Such guidance allows the generation process to be influenced by gradient obtained from some external loss function, effectively tailoring the diffusion process to meet specific objectives (Chung et al., 2022a,b; Graikos et al., 2022; Kawar et al., 2022; Lugmayr et al., 2022; Wang et al., 2022). Despite of numerous empirical successes, there remain significant gaps in the theoretical understanding and guarantees associated with guided diffusion models. Problem and Challenges Suppose we have a pre-trained diffusion model that can generate new samples faithfully from the pre-training data\u2019s distribution and maintain the data\u2019s latent structure. The goal is to adapt this diffusion model to generate new samples that optimize task-specific objectives, while maintaining the learned structure in new samples. Compared to classic optimization, the guided diffusion model offers new possibilities to optimize complex design variables such as images, videos, proteins, and genomes (Black et al., 2023; Watson et al., 2023; Liu et al., 2024). Interested readers may refer to recent surveys for a more comprehensive exposure (Yang et al., 2023; Chen et al., 2024; Guo et al., 2023). To adapt pre-trained diffusion models, existing practical methods largely rely on empirical heuristics and hyperparameter tuning. There remain critical theoretical questions: (i) Why does naively guiding diffusion models using gradient never work in practice? (ii) How to add a guidance signal to improve the target objective without compromising the quality of the generated output? (iii) Can one guarantee the properties of new samples generated by guided diffusion? (iv) What are the limits of adaptability in these guided models? This paper aims to answer these questions from an optimization perspective. Scope of This Paper We investigate the role of guidance in diffusion models from an optimization perspective. The goal is to generate samples that optimize a given objective function f. Drawing inspiration from gradient-based optimization methods, we construct a guidance signal based on the gradient vector, \u2207f. Then we use the gradient signal, in addition to the pre-trained score function, to guide the sampling process towards generating structured output with higher function values. See Figure 1 for illustration our algorithmic framework. Our main results are summarized as follows: \u2022 We focus on structured data. Assume that pre-trained data belongs to a latent low-dimensional subspace, thus the trained score function is capable of discerning and maintaining the latent subspace structure of data during (unguided) generation. To guide the generation, we introduce a gradient-like guidance based on a forward prediction loss (Definition 1). 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A pre-trained diffusion model is guided with an additional gradient signal from an external objectives function towards generating near-optimal solutions. \u2022 We formalize a mathematical framework of using a gradient-guided diffusion model for generative optimization. While retaining the pre-trained score function, the generation process is iteratively refined and guided using new gradient queries (Algorithm 1; Figure 1 without fine-tuning). Under proper assumptions, we demonstrate that this adapted model generates novel samples whose expectation converges to a solution that is regularized with respect to the original problem (Theorem 2). The regularization ensures that the generated samples remain proximal to the training data. In other words, gradient guidance cannot shift data distribution unboundedly towards higher objective values, revealing a fundamental limit for adapting pre-trained diffusion models. \u2022 Furthermore, we explore an adaptive variant of gradient-guided diffusion, where both the score function and gradient guidance are iteratively fine-tuned using self-generated samples (Algorithm 2; Figure 1 with fine-tuning). Although slightly increasing the computational demand, we provide evidence that this approach generates new samples whose expectation converges to global optima, within the latent subspace, at a rate of O(1/K) (Theorems 3 and 4), where K denotes the number of iterations and gradient evaluations, matching classical convergence theory of convex optimization. Our findings suggest that this novel gradient guidance not only preserves the latent subspace structure of the data but also ensures fast convergence towards the optimal solution. Numerical experiments with a pre-trained U-network score function are provided in Section 7 to support these theoretical findings. Score-based diffusion models capture the distribution of pre-training data by learning a sequence of transformations to generate new samples from noise (Song et al., 2020c). A forward stochastic process progressively adds noise to data, whose sample trajectories are used to train the score function. To generate new samples, a backward denoising process starts from sampling pure noise and gradually transforms the noise guided by the learned score function. Forward Process The forward process of diffusion models initializes with X0 \u2208RD, a random variable drawn from the pre-training data D. It introduces noise to via an Ornstein-Uhlenbeck process, i.e., 1 \ufffd dXt = \u22121 2 1 2q(t)Xt dt + \ufffd q ener process, an \ufffd q(t) dWt for q(t) > 0, (1) \ufffd where (Wt)t\u22650 is a standard Wiener process, and q(t) is a non-decreasing weighting function. Xt represents the noise-corrupted data distribution at time t. Given X0 = x0, the conditional distribution Xt|X0 = x0 is Gaussian, i.e., N(\u03b1(t)x0, h(t)ID) with \u03b1(t) = exp(\u2212 \ufffdt 0 1 2q(s)ds) and h(t) = 1 \u2212\u03b12(t). In practice, the forward process will terminate at a large time T so that the marginal distribution of XT is close to N(0, ID). In our analysis, we take q(t) \u22611 without loss of generality, where \u03b1(t) := exp(\u2212t/2) and h(t) := 1 \u2212exp(\u2212t). Backward Process If reversing the time of the forward process, we can reconstruct the original distribution of the data from pure noise. With (W t)t\u22650 being another independent Wiener process, 5 the backward SDE below (Anderson, 1982) reverses the time in the forward SDE (1), dX\u2190 t = \uf8ee \uf8f01 2X\u2190 t + \u2207log pT\u2212t(X\u2190 t ) | {z } score \uf8f9 \uf8fbdt + dW t. (2) Here pt(\u00b7) denotes the marginal density of Xt in the forward process. In the forward SDE (2), the score function \u2207log pt(\u00b7) plays a crucial role, but it has to be estimated from data. Score Matching To learn the unknown score function \u2207log pt(\u00b7), it is common to train a score network s\u03b8(x, t) using samples generated by the forward process. Let D denote the data for training. Then the score network is learned by minimizing the following loss: mins\u2208S Z T 0 Ex0\u2208DExt|x0 h \u2225\u2207xt log \u03d5t(xt|x0) \u2212s(xt, t)\u22252i dt, (3) where S is a given function class, ED denotes the empirical expectation over training data D and Ext|x0 denotes condition expectation over the forward process, \u03d5t(xt|x0) is the Gaussian transition kernel, i.e., 1 (2\u03c0h(t))D/2 exp(\u2212\u2225xt\u2212\u03b1(t)x0\u22252 2h(t) ). Generation and Guided Generation Given a pre-trained score function s\u03b8, one generates new samples by simulating the backward process (2) with the true score replaced by s\u03b8. Further, one can add additional guidance to the backward SDE to steer its output distribution towards specific properties of interest. Module 1 formalizes the generation process and guided generation process using a pre-trained diffusion model. Module 1 Guided BackwardSample(s\u03b8, G) 1: Input: Score s\u03b8, guidance G default to be zero for unguided generation. 2: Hyper-parameter: T. 3: Initialized at X\u2190 t \u223cN(0, I), simulate the following SDE till time T: dX\u2190 t = \u00141 2X\u2190 t + s\u03b8 (X\u2190 t , T \u2212t) + G (X\u2190 t , T \u2212t) \u0015 dt + dW t. 4: Output: Sample X\u2190 T . Conditional Generation Suppose the goal is to generate X with a desired property Y = y from the distribution P(X|Y = y). To this end, one needs the conditional score function \u2207xt log pt(xt | y), as a replacement of the unconditioned score \u2207xt log pt(xt). The Bayes rule gives \u2207xt log pt(xt | y) = \u2207log pt(xt) | {z } est. by s\u03b8(xt,t) + \u2207xt log pt(y | xt) | {z } to be est. by guidance . (4) When a pre-trained score network s\u03b8(xt, t) \u2248\u2207log pt(xt), the remaining task is to estimate \u2207xt log pt(y | xt) and add it as a \u201cguidance\u201d G to the backward process (Module 1). 6 Classifier and Classifier-Free Guidance Classifier guidance (Song et al., 2020c; Dhariwal and Nichol, 2021) is a approach for sampling from P(X|Y = y) when Y is a discrete label. This method estimates \u2207xt log pt(y | xt) by training auxiliary classifiers, denoted as \u02c6 p(y | xt, t), and then computing the gradient of the classifier logits as the guidance, i.e., G(xt, t) = \u2207xt log \u02c6 p(y | xt, t). An alternative is the classifier-free guidance method (Ho and Salimans, 2022), which jointly trains a conditional and an unconditional diffusion model, and combine the two score estimates via a form of guidance to generate samples. Notations For a random variable X, Px represents its distribution, and p(x) denotes its density function. For X, Y jointly distributed, P(X | Y = y) denotes the conditional distribution, and p(x | y) denotes its density function. We use the notation E[x | y] for the conditional expectation. Let D be the pre-training data, and let ED be the empirical expectation over D. Let \u00af \u00b5 and \u00af \u03a3 denote the data\u2019s empirical mean and covariance matrix, i.e., \u00af \u00b5 := Ex\u2208D[x] and \u00af \u03a3 := Ex\u2208D \u0002 (x \u2212\u00af \u00b5)(x \u2212\u00af \u00b5)\u22a4\u0003 . For a matrix A, we denote by Span(A) the subspace spanned by its column vectors. For a square matrix A, we denote by A\u22121 its inverse or Moore\u2013Penrose inverse. For any differentiable function f : Rn \u2192Rm, \u2207f \u2208Rm\u00d7n denotes Jacobian matrix, i.e., (\u2207f)ij = \u2202fi(x) \u2202xj . 4 A Primer on Gradient Guidance Suppose we have a pre-trained diffusion model where the score network s\u03b8(xt, t) provides a good approximation to the true score function log p(xt). Then this diffusion model is viewed as an implicit density estimator of the pre-training data\u2019s distribution. Its backward process (2) generates samples from this estimated distribution (Oko et al., 2023; Chen et al., 2023a). Now suppose we want to generate novel samples with desired properties that can be measured by a differentiable function f. We will refer to f as a reward or objective function later on, and it is often user-specified. Motivated by the gradient methodology in optimization, a natural, intuitive way for adding guidance is to steer the generated samples towards the steepest ascent direction of f (Bansal et al., 2023; Clark et al., 2023). This motivates the following guided backward process (Module 1): dX\u2190 t = \u00141 2X\u2190 t + s\u03b8(X\u2190 t , T \u2212t)+G(X\u2190 t , t) \u0015 dt + dW t. Here the guidance term G is what we focus on and wish to design. Specifically, we want to construct this guidance term G based on the gradient \u2207f of a general objective f. 4.1 Subspace Data and Score Decomposition Real-world data often has rich intrinsic structures. These structures can be induced by local regularities, global symmetries, and repetitive patterns (Tenenbaum et al., 2000; Roweis and Saul, 2000) and are often low-dimensional (Pope et al., 2021). The power of diffusion models is to model the latent distribution and generate novel samples that preserve important characteristics of real-world data. If we blindly improve f at the cost of losing these characteristics, the quality of new samples would degrade dramatically. This quality degradation, also known as \u201creward overoptimization\u201d, is a common challenge for adapting diffusion models towards an external reward (Yuan et al., 2023; Uehara et al., 2024). 7 We aim to design gradient guidance to improve objective function while mitigating the risk of over-optimization. To this end, we focus on data that admits a low-dimensional latent subspace. Let us make the following assumption. Assumption 1 (Subspace Data). Data X \u2208RD can be represented as X = AU, where A \u2208RD\u00d7d is an unknown matrix and the latent variable U \u2208Rd follows some distribution Pu with a density pu. Here d \u226aD. We assume the empirical covariance of U is full rank. Under Assumption 1, the score function \u2207log pt(x) decomposes to two orthogonal parts: an on-support component belonging to the subspace; and an orthogonal component. We recall this key result in Proposition 1. Proposition 1 (Score Decomposition for Subspace Data (Chen et al. (2023a) Lem. 1, Thm. 3)). Under Assumption 1, the score function \u2207log pt(x) decomposes as \u2207log pt(x) = A\u2207log pLD t (A\u22a4x) | {z } s\u2225(A\u22a4x,t): on-support score \u2212 1 h(t) \u0010 ID \u2212AA\u22a4\u0011 x | {z } s\u22a5(x,t): ortho. score . (5) where pLD t (u\u2032) = R \u03d5t(u\u2032|u)pu(u) du with \u03d5t(\u00b7|u) being the density of N(\u03b1(t)u, h(t)Id) for the same \u03b1(t) and h(t) in the forward process (1). According to Chen et al. (2023a), pre-training a score function on subspace data takes advantage of the decomposition given by (5) and learns the latent subspace. When the pre-trained score network is used to generate new samples, the backward sampling process also decomposes into two orthogonal processes due to (5). Analysis of this backward process proves that the generated output would remain proximal to the latent subspace. This explains why diffusion models can learn and preserve data\u2019s underlying characteristics. We refer interested readers to Chen et al. (2023a) for more discussions. In the rest of this section, we investigate the principles for designing a guidance based on the gradient of f that ensures generated samples (i) improve the value of f, and at the same time, (ii) adhere to the subspace structure, i.e. generated samples being close to the subspace spanned by A. 4.2 Naive Gradient Does\u2019t Work as Guidance Motivated by the gradient optimization methodology, a natural, intuitive way for adding guidance is to steer the generated samples towards the steepest ascent direction of f (Bansal et al., 2023; Clark et al., 2023). Therefore, a tempting simple choice of the guidance G is the steepest ascent direction, which we refer to as naive gradient guidance i.e., G(X\u2190 t , t) \u221d\u2207f(X\u2190 t ). (6) This naive choice of guidance signal G would steer the movement of the original backward process towards the direction that increases f. However, the naive gradient guidance (6) is never adopted in practice; existing methods have to resort to more sophisticated forms of guidance or more computationally demanding fine-tuning methods; for example Bansal et al. (2023); Uehara et al. (2024); Marion et al. (2024). Introducing gradient information indiscriminately into the backward SDE has the risk of potentially leading the 8 <latexit sha1_base64=\"bcQ/eNp79YODvDvdj6LzPoTKPj0=\">A AB/HicbVBLSgNBFHwTfzH+oi7dNAbBVZgRiS6DblwmYD6QDKGnp5M06fnQ/UYIQ7yAW72BO3HrXbyA57AnmYVJLGgoqt7jVZcXS6HRtr+tws bm1vZOcbe0t39weFQ+PmnrKFGMt1gkI9X1qOZShLyFAiXvxorTwJO8403uM7/zxJUWUfiI05i7AR2FYigYRSM1cVCu2FV7DrJOnJxUIEdjU P7p+xFLAh4ik1TrnmPH6KZUoWCSz0r9RPOYsgkd8Z6hIQ24dtN50Bm5MIpPhpEyL0QyV/9upDTQehp4ZjKgONarXib+5/USHN6qQjBHnIF oeGiSQYkezXxBeKM5RTQyhTwmQlbEwVZWi6Wbri6yzarGSKcVZrWCftq6pTq9a15X6XV5REc7gHC7BgRuowM0oAUMOLzAK7xZz9a79WF9 LkYLVr5zCkuwvn4BQqVgA=</latexit>t Pre-trained Random Noise Large  Reward  Region Gradient Direction Subspace Naive Gradient  Guidance O\ufb00 Subspace Figure 2: Directly adding the gradient of the objective function to the backward sampling process sabotages the subspace structure. Left: When gradients are pointing out of the data subspace, adding them directly to the backward SDE will make samples go off the subspace. Right: Numerical experiments show that naive gradients lead to substantially larger off-subspace error compared to our gradient guidance Gloss(Definition 1); see Section 7 for experiment details. stochastic denoising process to divergence, and compromising the data structures learned during pre-training. Let us suppose the data distribution is supported on a low-dimensional subspace as in Assumption 1. We explain why naive gradients do not work as guidance. With subspace data, the score function would steer the distribution towards concentrating onto the latent subspace, due to its special decomposition form given by Proposition 1. We refer interested readers to Chen et al. (2023a) for detailed analysis of this phenomenon. However, naive gradient vectors can be pointing towards any direction, not limited to within the latent subspace. Thus directly adding gradient guidance to the backward process could jeopardize the decomposition form of the score function, and it would also jeopardize the latent structure in the generated output. See Figure 2 for illustration and experiment results. The failure of naive gradient motivates us to seek robust alternatives. 4.3 Motivating Gradient Guidance from Conditional Score Function We want to study how to add guidance to the sampling process utilizing the gradient of f. To motivate our design of guidance, we start with the most elementary Gaussian probabilistic model. Later we will drop this assumption and consider general data distributions and general f. Assumption 2 (Gaussian model). Let data follow a Gaussian distribution, i.e., X \u223cN(\u00b5, \u03a3), and let f(x) = g\u22a4x be a linear function for some g \u2208RD. Let Y = f(X) + \u03f5 with independent, identically distributed noise \u03f5 \u223cN(0, \u03c32) for some \u03c3 > 0. To generate samples from P(X|Y = y), we need to train a diffusion model with a conditional score function. By the Bayes\u2019 rule, the conditional score function takes the form of a sum given by \u2207xt log pt(xt | y) = \u2207log pt(xt) | {z } est. by s\u03b8(xt,t) + \u2207xt log pt(y | xt) | {z } to be est. by guidance . (recall (4)) Now if we already have a pre-trained score function s\u03b8, the remaining task is to estimate the second 9 term log pt(y | xt). Under the Gaussian assumption, we derive the following closed-form conditional score. The proof is provided in Appendix B.1. Lemma 1 (Conditional score gives a gradient-like guidance). Under Assumption 2, we have \u2207xt log pt(y|xt) = \u03b2(t) h y \u2212g\u22a4E[x0|xt] i \u00b7 \u0000\u03b12(t)\u03a3 + h(t)ID \u0001\u22121 \u03a3g, (7) where E[x0|xt] denotes the conditional expectation of x0 given xt in the forward process (1), \u03b1(t) = e\u2212t/2, h(t) = 1 \u2212e\u2212t as in (1), and \u03b2(t) = \u03b1(t)/(\u03c32 + g\u22a4\u03a3\u22121 \u0000ID + \u03b12(t)/h(t) \u00b7 \u03a3 \u0001\u22121 g). Observe that, when \u03a3 = I, (7) suggests the following form of guidance that is aligned with the naive gradient, i.e., the steepest ascent direction: G(xt, t) \u221d h y \u2212g\u22a4E[x0|xt] i \u00b7 g. However, even for Gaussian distributions, as long as \u03a3 \u0338= I, the term of (7) is no longer proportional to g but becomes a pre-conditioned version of the gradient. Figure 3: Plot of \u03b2(t), \u03b1(t), h(t) for t \u2208[0, 10] when \u03a3 = I. Another observation is that this guidance scales with a residual term y \u2212g\u22a4E[x0 | xt]. In particular, the residual term y \u2212g\u22a4E[x0 | xt] tunes the strength of guidance. Recall E[x0 | xt] denotes the posterior expectation of clean data x0 given xt in the forward process. Thus, in a backward view, E[x0 | xt] coincides with the expected sample to be generated conditioned on xt. In this sense, the quantity y \u2212g\u22a4E[x0 | xt] measures a look-ahead gap between the expected reward of generated samples and the target value. A larger absolute value of the residual means stronger guidance in the backward generation process. We plot the theoretical choice of \u03b2(t) and \u03b1(t), h(t) to t in Figure 3. In practice, the choice of \u03b1(t), h(t) can vary and they are determined by the forward process used for pre-training; and \u03b2(t) can be treated as a tuning parameter to adjust the strength of guidance. 4.4 Construct Gradient Guidance to Preserve Latent Subspace When the data distribution is supported on a latent subspace, directly adding gradient guidance to the backward sampling process could jeopardize the data\u2019s latent structure. We saw that this would lead to over-optimization, as illustrated in Figure 2. To remedy such an issue, we propose the following modification to the gradient guidance. This modified gradient guidance takes advantage of a given score function. Definition 1 (Gradient Guidance of Look-Ahead Loss). Given a gradient vector g, define the gradient guidance of look-ahead loss as Gloss(xt, t) := \u2212\u03b2(t) \u00b7 \u2207xt \u0010 y \u2212g\u22a4E[x0|xt] \u00112 , (8) where \u03b2(t) > 0, y \u2208R are tuning parameters, and E[x0|xt] is the conditional expectation of x0 given xt in the forward process (1), i.e., dXt = \u22121 2q(t)Xt dt + p q(t) dWt. 10 The formula of (8) generalizes the intuition of a conditional score to work with any data distribution and objective function. The look-ahead loss (y \u2212g\u22a4E[x0|xt])2 resembles the proximal term commonly used in first-order proximal optimization methods. It is worth noting that Gloss coincides with the forward universal guidance \u2207xt\u2113(y, f(\u02c6 E[x0|xt])) proposed by Bansal et al. (2023) ((8) in their paper) when \u2113is the square loss and f = g\u22a4x. When the pre-training data distribution is Gaussian, the gradient guidance (8) is equivalent to Lemma 1 equation (7). This equivalence is a side-product from the proof of Lemma 1 and we provide a sketch here (see details in Appendix B.1). Given the probabilistic model Assumption 2, \u2207xt log pt(y|xt), the quantity to be estimated by guidance, is the score of a Gaussian distribution N \u0000my(xt), \u03c32 y(xt) \u0001 , with my(xt) and \u03c32 y(xt) being mean and variance of the conditional distribution Y | Xt = xt respectively, i.e., \u2207xt log pt(y | xt) = \u2212\u2207xt \" 1 2 \u0012y \u2212my(xt) \u03c3y(xt) \u00132# \u2212\u2207xt log \u03c3y(xt), (9) with my(xt) = g\u22a4E[x0 | xt] and \u03c3y(xt) not depending on xt. Thus we see Gloss is equivalent to (7). A key advantage of Gloss is that it enables preserving the subspace structure, for any data distribution under Assumption 1. This result is formally stated in the following theorem, we provide a proof sketch here and the full proof is in Appendix B.2. Theorem 1 (Faithfulness of Gloss to the Low-Dimensional Subspace of Data). Under Assumption 1, it holds for any data distribution and g \u2208RD that Gloss(xt, t) \u2208Span(A). (10) Proof Sketch We have \u2207xt \u0010 y \u2212g\u22a4E[x0|xt] \u00112 \u221d\u2207xtE[x0|xt]\u22a4g. Note here that \u2207xtE[x0|xt] is the Jacobian matrix of E[x0|xt], which is a mapping from RD to RD. We will show that the Jacobian \u2207xtE[x0|xt] maps any vector g \u2208RD to Span(A). To see this, we utilize the score decomposition result of Proposition 1 which is \u2207log pt(xt) = A\u2207log pLD t (A\u22a4xt) \u2212 1 h(t) \u0010 ID \u2212AA\u22a4\u0011 xt. (recall (5)) Plugging (5) into the equality E[x0|xt] = 1 \u03b1(t) (xt + h(t)\u2207log pt(xt)) (Tweedie\u2019s formula (Efron, 2011)), we have E[x0|xt] = 1 \u03b1(t) \u0012 xt + h(t) \u0014 Am(A\u22a4xt) \u2212 1 h(t)xt \u0015\u0013 = h(t) \u03b1(t)Am(A\u22a4xt), (11) here we denote for short m(u) := \u2207log pLD t (u) + 1 h(t)u. From (11), we see that \u2207xtE[x0|xt]\u22a4maps any vector to Span(A) because m(\u00b7) takes A\u22a4xt as input in the expression of E[x0|xt]. \u25a0 We highlight that the faithfulness of Gloss holds for arbitrary data distribution supported on the latent subspace. It takes advantage of the score function\u2019s decomposition (5), having the effect of automatically adapting g onto the latent low-dimensional subspace of data. 11 4.5 Estimation and Implementation of Gloss Theorem 1 asserts that the gradient guidance given by Definition 1 provably preserves the subspace structure of data. However, Gloss is not immediately available to compute and it involves the unknown quantity E[x0|xt]. Next, we discuss the estimation and computation of Gloss based on a pre-trained score function s\u03b8 in practice. First, we need to estimate the quantity E[x0|xt]. It is the conditional expectation of x0 given xt in the forward process, thus it depends on the pre-training data distribution. One can construct estimate E[x0|xt] based on the pre-trained score network s\u03b8, by using the Tweedie\u2019s formula (Efron, 2011): \u2207log pt(xt) = \u2212E \u0014xt \u2212\u03b1(t)x0 h(t) \f \fxt \u0015 . (12) Suppose we have a given pre-trained score network that approximates the ground truth, i.e., s\u03b8(xt, t) \u2248\u2207log pt(xt). Then a natural estimator of \u02c6 E[x0|xt] is given by \u02c6 E[x0|xt] := 1 \u03b1(t) (xt + h(t)s\u03b8(xt, t)) , (13) and we refer to it as the look-ahead estimator. The estimator (13) is widely adopted in practice (Song et al., 2020a; Bansal et al., 2023). Here \u03b1(t) and h(t) are the noise scheduling used in the forward process (1). Thus, we have obtained an implementable version of the gradient guidance Gloss, given by Gloss(xt, t) = \u2212\u03b2(t) \u00b7 \u2207xt \u0012 y \u2212g\u22a4 \u0012 1 \u03b1(t) (xt + h(t)s\u03b8(xt, t)) \u0013\u00132 , (14) With a slight abuse of notation, we use Gloss to refer to this implementable formula (14) in the remainder of this paper. \u2026\u2026 Square Loss <latexit sha1_base64=\"MCfCylmUav/6OdNRyRNfCVSfv8=\">AB/3icbVDLSsNAFJ34rPVdelmsAh1UxLxtSy6cVnBPqANZTKZNEMnkzBzI5TQhT/gVv/Anbj1U/wBv8NJm4VtPTBwOde7pnjJYJrsO1va2V1bX1js7RV3t7Z3duvHB y2dZwqylo0FrHqekQzwSVrAQfBuoliJPIE63iju9zvPDGleSwfYZwNyJDyQNOCeRSWIOzQaVq1+0p8DJxClJFBZqDyk/fj2kaMQlUEK17jp2AmxEFnAo2KfdTzRJCR2TIeoZKEjHtZtOsE3xqFB8HsTJPAp6qfzcyEmk9jwzGREI9aKXi/95vRSCGzfjMkmBSTo7FKQCQ4zj2OfK0ZBjA0hVHGTFdOQKELB1DN3xd5tEnZFOMs1rBM2ud156p+XBRbdwWFZXQMTpBNeSga9RA96iJWoiEL2gV/RmPVv1of1ORtdsYqdIzQH6+sXnImWVg=</latexit>h(t) <latexit sha1_base64=\"Ogxow3Zrphfic4L4LQYhmBz4QaU=\">ACXicbVDLSsNAFJ3UV62vqks3g0WoC0sivpZFNy4r2Ae0aZlMJu3QyYOZG6GEfIE/4Fb/wJ249Sv8Ab/DSZuFbT1w4XDOvdzDcSLBFZjmt1FYWV1b3yhulra2d3b3yv sHLRXGkrImDUoOw5RTPCANYGDYJ1IMuI7grWd8V3mt5+YVDwMHmESMdsnw4B7nBLQUr9HRDQi/eTMSqtwOihXzJo5BV4mVk4qKEdjUP7puSGNfRYAFUSprmVGYCdEAqeCpaVerFhE6JgMWVfTgPhM2ck0dYpPtOJiL5R6AsBT9e9FQnylJr6jN30CI7XoZeJ/XjcG78ZOeBDFwAI6e+TFAkOIswqwyWjICaECq5zorpiEhCQRc198VWbS0pIuxFmtYJq3zmnVu3y4qNRv84qK6Agdoyqy0DWqo3vUQE1EkUQv6BW9Gc/Gu/FhfM5WC0Z+c4jmYHz9Agzbmg=</latexit> \u21b5\u22121(t) <latexit sha1_base64=\"MXp+DKiSlYDt69Es0RlC16jzLc=\">AB/nicbVDLSsNAFL3xWeur6tJNsAiuSiK+lkU3LivaB7ShTCaTduhkEmZuxFIK/oBb/QN3 4tZf8Qf8DidtFrb1wMDhnHu5Z46fCK7Rcb6tpeWV1bX1wkZxc2t7Z7e0t9/Qcaoq9NYxKrlE80El6yOHAVrJYqRyBes6Q9uMr/5yJTmsXzAYcK8iPQkDzklaKT7py52S2Wn4kxgLxI3J2XIUeuWfjpBTNOISaSCaN12nQS9EVHIqWDjYifVLCF0QHqsbagkEdPeaBJ1bB8bJbDWJkn0Z6ofzdGJNJ6GPlmMiLY1/NeJv7ntVMr7 wRl0mKTNLpoTAVNsZ29m874IpRFENDCFXcZLVpnyhC0bQzcyXQWbRx0RTjztewSBqnFfeicn53Vq5e5xUV4BCO4ARcuIQq3EIN6kChBy/wCm/Ws/VufVif09ElK985gBlYX7+msJZq</latexit>xt Gradient  Compute <latexit sha1_base64=\"qEXaESVr1fTBbnNbrKvEPvC+E8A=\">ACGHicbVDLSsNAFJ34rPVdnNYBFclUSkuiyK4LKCfUAawmQybYdOHszcSEvMwt/wB9zqH7gTt+78Ab/DS duFbT0wcDjnXu6Z48WCKzDNb2NldW19Y7OwVdze2d3bLx0ctlSUSMqaNBKR7HhEMcFD1gQOgnViyUjgCdb2hte535gUvEovIdxzJyA9EPe45SAltxSuTsgkHYDAgPS2+yzB65Jn7EIxct1Qxq+YEeJlYM1JBMzTc0k/Xj2gSsBCoIErZlhmDkxIJnAqWFbuJYjGhQ9JntqYhCZhy0sknMnyiFR/3IqlfCHi/t1ISaDUOPD0ZJ5WLXq5+J9nJ9C7dFIexgmwkE4P9R KBIcJ5I9jnklEQY0IlVxnxXRAJKGge5u74qs8WlbUxViLNSyT1lnVqlVrd+eV+tWsogIqo2N0ix0geroFjVQE1H0hF7QK3ozno1348P4nI6uGLOdIzQH4+sXngagnw=</latexit>\u02c6 E[x0|xt] Gradient w.r.t <latexit sha1_base64=\"MXp+DKiSlYDt69Es0RlC16jzLc=\">AB/nicbVDLSsNAFL3xWeur6tJNsAiuSiK+lkU3LivaB7ShTCaTduhkEmZuxFIK/oBb/QN3 4tZf8Qf8DidtFrb1wMDhnHu5Z46fCK7Rcb6tpeWV1bX1wkZxc2t7Z7e0t9/Qcaoq9NYxKrlE80El6yOHAVrJYqRyBes6Q9uMr/5yJTmsXzAYcK8iPQkDzklaKT7py52S2Wn4kxgLxI3J2XIUeuWfjpBTNOISaSCaN12nQS9EVHIqWDjYifVLCF0QHqsbagkEdPeaBJ1bB8bJbDWJkn0Z6ofzdGJNJ6GPlmMiLY1/NeJv7ntVMr7 wRl0mKTNLpoTAVNsZ29m874IpRFENDCFXcZLVpnyhC0bQzcyXQWbRx0RTjztewSBqnFfeicn53Vq5e5xUV4BCO4ARcuIQq3EIN6kChBy/wCm/Ws/VufVif09ElK985gBlYX7+msJZq</latexit>xt + <latexit sha1_base64=\"JjNjoy08E2STahQ+0GXQtFmlqw=\">ACDnicbVDLSsNAFJ34rPWV6tJNsAgVpCTia1l047KCfUAbwmQyaYdOHszcqCXkH/wBt/oH7sStv+A P+B1O2ixs64ELh3Pu5R6OG3MmwTS/taXldW19dJGeXNre2dXr+y1ZQIQlsk4pHoulhSzkLaAgacdmNBceBy2nFHN7nfeaBCsi8h3FM7QAPQuYzgkFJjl6RTtqHIQWc1Z4cOIFjR6+adXMCY5FYBamiAk1H/+l7EUkCGgLhWMqeZcZgp1gAI5xm5X4iaYzJCA9oT9EQB1Ta6SR6ZhwpxTP8SKgJwZiofy9SHEg5Dly1GWAYynkvF/zegn4V3bKwjgBG pLpIz/hBkRG3oPhMUEJ8LEimAimshpkiAUmoNqa+eLJPFpWVsVY8zUskvZp3bqon9+dVRvXRUldIAOUQ1Z6BI10C1qohYi6BG9oFf0pj1r79qH9jldXdKm30A+3rF54PnFQ=</latexit>s\u2713(xt, t) <latexit sha1_base64=\"8RbS92UirR97/cna4GH7idu+Q=\">AB/HicbVBLSgNBFHwTfzH+oi7dNAbBVZgRiS6DblwmYD6QDKGn503SpOdDd48QryAW72BO3HrXbyA57AnmYVJL Ggoqt7jVZeXCK60bX9bhY3Nre2d4m5pb/g8Kh8fNJWcSoZtlgsYtn1qELBI2xprgV2E4k09AR2vPF95neUCoeR496kqAb0mHEA86oNlJzOChX7Ko9B1knTk4qkKMxKP/0/ZilIUaCapUz7ET7U6p1JwJnJX6qcKEsjEdYs/QiIao3Ok86IxcGMUnQSzNizSZq383pjRUahJ6ZjKkeqRWvUz8z+ulOrh1pzxKUo0RWxwKUkF0TLJfE59LZFpMDKFMcpOVsBGVlGnTzdIVX2XRZ iVTjLNawzpX1WdWrXWvK7U7/KinAG53AJDtxAHR6gAS1gPACr/BmPVv1of1uRgtWPnOKSzB+voF8EOVcw=</latexit>g <latexit sha1_base64=\"O0NxyODe2aQyeBYzgsnxedhThE=\">ACJ3icbVDLSsNAFJ3UV62vqEs3g0VQwZKIr2VRBJcKVgtNDJPptB06eTBzI4aYf/A3/AG3+gfuRJdu/A4nt QtbPTBwOde7pnjx4IrsKwPozQxOTU9U56tzM0vLC6ZytXKkokZQ0aiUg2faKY4CFrAfBmrFkJPAFu/b7J4V/fcuk4lF4CWnM3IB0Q97hlICWPHN7M8U7uHvjQBRjp0cgcwICPd/PTvO8dedZ+B7feBu3ex6ZtWqWQPgv8Qekioa4twzv5x2RJOAhUAFUaplWzG4GZHAqWB5xUkUiwntky5raRqSgCk3G/wpxtaeNOJPULAQ/U3xsZCZRKA19PFoHVuFeI/3mtBD pHbsbDOAEW0p9DnURgiHBREG5zySiIVBNCJdZMe0RSjoGkeutFURLa/oYuzxGv6Sq92afVDbv9ir1o+HFZXRGlpHm8hGh6iOztA5aiCKHtATekYvxqPxarwZ7z+jJWO4s4pGYHx+A16DpY8=</latexit> (y \u2212g>\u02c6 E[x0|xt])2 Figure 4: Computation of Gradient Guidance Gloss. The gradient guidance (14) has a light-weighted implementation. Suppose the pre-trained score function s\u03b8 is given in the form of a neural network with pre-trained weights. Computing (14) involves calculating the squared loss \u0010 y \u2212g\u22a4\u02c6 E[x0|xt] \u00112 via a forward pass of the network s\u03b8 and a backward pass utilizing the auto-gradient feature of deep-leaning frameworks such as PyTorch and TensorFlow. See Figure 4 for illustration. Note that the value of y in Gloss is a target reward value, inherited from the conditional score analysis under a Gaussian model. In practice, we treat y as a tuning parameter. In our theoretical analysis, we will specify the choices of y, \u03b2(t) and provide guarantees for general optimization beyond the Gaussian model. So far, we have finally obtained a gradient guidance (14) that is both implementable and faithful to data\u2019s latent subspace. The next step is to apply this gradient guidance and use it to adapt the generation process of a pre-trained diffusion model. Let us find out what one can obtain using gradient-guided diffusion models. 12 5 Gradient-Guided Diffusion Model as Regularized Optimizer In this section, we study whether gradient guidance steers a pre-trained diffusion model to generate samples of near-optimal objective values. We provide a positive answer and our results are twofold: 1) We demonstrate that iteratively applying gradient guidance improves the generated samples towards higher objective values; 2) The pre-trained diffusion model acts as a form of regularization from an optimization perspective. 5.1 Gradient-Guided Generation with A Pre-trained Score Assume access to a pre-trained score network s\u03b8 and gradient information of the objective function f. Let us present our Algorithm 1 that adapts the pre-trained diffusion model and iteratively updates the gradient guidance (14). The gradient guidance is able to steer the backward sampling process towards generating new samples with higher values of f. See Figure 1 for illustration. Algorithm 1 takes as input any pre-trained score function s\u03b8(x, t) and adapts the backward sampling process with gradient guidance. In each iteration, it evaluates \u2207f(\u00b7) at samples generated from the previous iteration (Line 5(i)), and then computes the gradient guidance Gloss using the newly queried gradient (Line 5(ii)). Using the updated gradient guidance, the backward process then generate new samples with improved objective values (Module 1). At the end of iterations, the algorithm outputs an adapted version of the diffusion model, specified by (s\u03b8, GK), which generates samples with near-optimal objective values. Algorithm 1 Gradient-Guided Diffusion for Generative Optimization 1: Input: Pre-trained score network s\u03b8(\u00b7, \u00b7), differentiable objective function f. 2: Tuning Parameter: Strength parameters \u03b2(t), {yk}K\u22121 k=0 , number of iterations K, batch sizes {Bk}. 3: Initialization: G0 = NULL. 4: for k = 0, . . . , K \u22121 do 5: Generate: Sample zk,i \u223cGuided BackwardSample(s\u03b8, Gk) using Module 1, for i \u2208[Bk]. 6: Compute Guidance: (i) Compute the sample mean \u00af zk := (1/Bk) PBk i=1 zk,i. (ii) Query gradient gk = \u2207f(\u00af zk). (iii) Update gradient guidance Gk+1(\u00b7, \u00b7) = Gloss(\u00b7, \u00b7) via (8), using s\u03b8, gradient vector gk, and parameters yk and \u03b2(t). 7: end for 8: Output: (s\u03b8, GK). It is worth highlighting that Algorithm 1 works with any pre-trained score network s\u03b8(xt, t). It retains the original score network and only updates the guidance term. The gradient guidance changes the generation process by an additive term to the backward SDE, without having to re-train the score network. Therefore, the algorithm is computationally efficient and easy to implement. We experimented with Algorithm 1 using a pre-trained score network with about 15M parameters; see Section 7 for details. In our experiment, a single run of the backward sampling process (Module 1) takes 4.6s, and Algorithm 1 takes 76min overall. Thus it is a rather light-weighted algorithm to implement and run. 13 5.2 Gradient-Guided Diffusion Converges to Regularized Optima We analyze the convergence properties of Algorithm 1 and show that in final iterations, generated samples center around a regularized solution of the optimization objective f. Our theorems allow the pre-training data to have arbitrary distribution. Assumption 3 (Concave smooth objective). The objective f : RD \u2192R is concave and L-smooth with respect to the (semi-)norm \u2225\u00b7\u2225\u00af \u03a3\u22121, i.e., \u2225\u2207f(x1) \u2212\u2207f(x2)\u2225\u00af \u03a3 \u2264L \u2225x1 \u2212x2\u2225\u00af \u03a3\u22121 for any x1, x2. While Algorithm 1 works with any pre-trained score network, we study its optimization properties focusing on the class of linear score functions given by S = \b s(x, t) = Ctx + bt : Ct \u2208RD\u00d7D, bt \u2208RD\t . (15) Here (15) is a general linear function class. For comparison, a recent related paper Marion et al. (2024) assumes a more restricted class with Ct \u2261I for when studying parameter optimization in diffusion models. With a linear score function (15), pre-training a diffusion model is essentially the same as using a Gaussian model to estimate the pre-training data distribution and then sampling from this estimated Gaussian. In this case, the guidance Gloss is also linear in xt, therefore the final output of the guided diffusion model also follows a Gaussian distribution; see (27) in Appendix C. Recall we aim for an adapted diffusion model (s\u03b8, GK) to generate samples with high values of f. Thus, we focus on the mean of the generated distribution (taking T \u2192\u221ein the backward sampling process of (s\u03b8, GK)), denoted by \u00b5K, and establish its optimization guarantee. Theorem 2 (Convergence to Regularized Maxima in Mean). Let Assumption 3 hold, and let the pre-training data D have arbitrary distribution with covariance matrix \u00af \u03a3 \u227b0. Suppose the score function s\u03b8 is pre-trained via minimizing the score matching loss (3) over the linear function class (15). Let Alg. 1 take s\u03b8(\u00b7, \u00b7) and f as the input. For any \u03bb > L, there exists {\u03b2(t)}, {yk}, {Bk} such that, with probability \u22651 \u2212\u03b4 , the mean of the output distribution \u00b5K converges to be near x\u2217 \u03bb, and f (x\u2217 \u03bb) \u2212f(\u00b5K) = \u03bb \u0012L \u03bb \u0013K O \u0012 D log \u0012K \u03b4 \u0013\u0013 , (16) where D is the ambient dimension of data, and x\u2217 \u03bb is a regularized maximizer of f given by x\u2217 \u03bb = argmax x\u2208RD \u001a f(x) \u2212\u03bb 2 \u2225x \u2212\u00af \u00b5\u22252 \u00af \u03a3\u22121 \u001b , (17) where \u00af \u00b5, \u00af \u03a3 are empirical mean and covariance of pre-training data D. Proof Sketch Solving the score matching problem (3) with a linear function class (15) yields a pre-trained score as follows s\u03b8(xt, t) = \u2212 \u0000\u03b12(t)\u00af \u03a3 + h(t)ID \u0001\u22121 (xt \u2212\u03b1(t)\u00af \u00b5) . With proper choices of \u03b2(t), gradient guidance Gloss leads to the following output distribution at the end of round k: N \u0012 \u00af \u00b5 + yk \u2212g\u22a4 k \u00af \u00b5 \u03c32 + g\u22a4 k \u00af \u03a3gk \u00af \u03a3gk, \u00af \u03a3 \u2212 \u00af \u03a3gkg\u22a4 k \u00af \u03a3 \u03c32 + g\u22a4 k \u00af \u03a3gk \u0013 . 14 Thus, we obtain the mean of the above distribution, i.e., \u00b5k+1 = \u00af \u00b5 + \u03b7k \u00af \u03a3\u2207f(\u00af zk), where \u00af zk is the empirical mean of previous samples, \u03b7k is a stepsize determined by yk. By a rearrangement, we obtain a recursive formula \u00b5k+1 = \u00af zk + \u03b7k \u00af \u03a3 \u0002 \u2207f(\u00af zk) \u2212\u03b7\u22121 k \u00af \u03a3\u22121 (\u00af zk \u2212\u00af \u00b5) \u0003 . (18) We observe that (18) resembles a gradient ascent update from \u00b5k \u2248\u00af zk to \u00b5k+1 corresponding to a regularzed optimization problem (17). In this regularized objective, the original objective f(x) incorporates an additional proximal term with \u03bb := 1/\u03b7k. Therefore we can analyze the convergence of \u00b5k by following the classical argument for gradient optimization. The full proof is provided in Appendix C.1 Remarks. This view of regularized optimization gives the following insights on gradient-guided diffusion models: (i) The regularization term \u03bb 2 \u2225x \u2212\u00af \u00b5\u22252 \u00af \u03a3\u22121 in (17) is centered at the data\u2019s mean \u00af \u00b5. It penalizes samples that are far away from the pre-training data. The norm \u2225\u00b7\u2225\u00af \u03a3\u22121 suggests the regularization is strong in the direction where the original data distribution has low variance. In other words, it reveals that the pre-trained score function acts as a form of \u201cprior\u201d in the guided generation process. This prior favors samples that are proximal to its pre-training data distribution, even when additional guidance are present. (ii) The regularization term cannot be made arbitrarily small. In particular, our theorem requires that \u03bb \u2265L. This demonstrates a limit of adapting diffusion models with guidance. As long as the score function stays unchanged, one cannot extrapolate from the pre-training data unlimitedly by solely adding gradient guidance. As a consequence, we cannot simply add gradient guidance to a diffusion model in order to reach the global maxima of any objective function. If the goal is to reach global optima, one has to update the pre-trained score network and refine it with newly collected data, we explore this approach in Section 6. (iii) The linear convergence rate (16) is determined jointly by the smoothness of the objective function and strength of the regularization. We also pay a linear factor in the dimension D. In the following subsection, we will show that the gradient guidance Gloss can reduce the dimension dependence from D to d if the data admits a latent low-dimensional subspace. 5.3 Gradient Guidance for Optimization in Latent Spaces Next we focus on data with latent subspace as in Assumption 1. In the next theorem, we show that the generated distribution of our adapted model would converge, in expectation, to the maxima of a regularized version of f within the subspace Span(A). Theorem 3 (Convergence to Regularized Maxima in Latent Subspace in Mean). Let Assumptions 1 and 3 hold. Suppose we use the score function class (15) for pre-training and computing guidance. Then Alg.1 gives an adapted diffusion model that generates new samples that belong to Span(A). Further, for any \u03bb > L, there exists \u03b2(t), {yk} and batch size Bk, such that with high probability 1 \u2212\u03b4, the mean of the output distribution \u00b5K converges to be near x\u2217 A,\u03bb, and it holds f \u0000x\u2217 A,\u03bb \u0001 \u2212f(\u00b5K) = \u03bb \u0012L \u03bb \u0013K O \u0012 d log \u0012K \u03b4 \u0013\u0013 , 15 where x\u2217 A,\u03bb is an optimal solution of the regularized objective: x\u2217 A,\u03bb = argmax x\u2208Span(A) \u001a f(x) \u2212\u03bb 2 \u2225x \u2212\u00af \u00b5\u22252 \u00af \u03a3\u22121 \u001b . (19) Recall that the gradient guidance Gloss is faithful to the data\u2019s latent subspace, as proved in Theorem 1. As a result, the gradient-guided backward process maintains this latent subspace structure in the generated output. Therefore, all the generated samples and optimization iterates of Algorithm 1 belong to the latent subspace Span(A). In other words, the entire optimization process happens in the latent low-dimensional subspace. This facilitates a coherent and more efficient exploration in the solution space. Comparing to Theorem 2, the optimization gap in Theorem 3 is substantially smaller, reduced from O (D) to O (d). It means that the optimization process leverages the latent subspace and converges much faster. Finally we note that Theorem 3 only establishes convergence in mean. The final output distribution of Algorithm 1, with a linear score function, is a Gaussian distribution supported on the latent subspace; see Appendix C equation (27). 6 Gradient-Guided Diffusion with Adaptive Fine-Tuning for Global Optimization In the previous section, we have seen that adding guidance to a pre-trained diffusion model cannot improve the objective function unlimitedly. The pre-trained score function would act as a form of prior to keep the generated output proximal to the original data\u2019s distribution. This leads to a regularization term in the optimization formulation. Further, we consider adaptively fine-tuning the pre-trained diffusion model for generating samples to attain the unregularized global optima. The idea is not only to update the guidance in the backward sampling process but also to use generated samples to fine-tune the pre-trained score network. Empirically, fine-tuning diffusion models utilizing self-generated samples has been explored by Black et al. (2023); Clark et al. (2023). 6.1 Adaptive Fine-Tuning Algorithm with Gradient Guidance We propose an adaptive version of the gradient-guided diffusion, where both the gradient guidance and the score networks are iteratively updated utilizing self-generated samples. The full algorithm is given in Algorithm 2. We introduce a weighting scheme to fine-tune the score network using a mixture of pre-training data and newly generated samples. In Round k, let D1, . . . , Dk be sample batches generated from the previous rounds. Let {wk,i}k i=0 be a set of weights. Conceptually, at Round k, we update the model by minimizing the weighted score matching loss: min s\u2208S Z T 0 k X i=0 wk,iEx0\u2208DiExt|x0 h \u2225\u2207xt log \u03d5t(xt|x0) \u2212s(xt, t)\u22252 2 i dt, (20) where D0 := D is the pre-training data. For illustration of this algorithm, please see also Figure 1. In practice, to update the score network incorporating newly generated data, one does not have to exactly solve (20) by re-training the full model from scratch. Instead, (20) can be viewed as a 16 guideline that motivates more computationally efficient ways for updating the pre-trained score. It is a common practice to only fine-tune the weights of the old model by performing gradient descent over a few batches of newly generated data, which is similar to the spirit of (20). In our experiment, we implemented Algorithm 2 using a pre-trained U-net score function with 15M parameters and tested its performance on synthetic objectives. We implement the finetuning step by making one single Adam step over the new data. In our experiment, the iterated finetuning process of Algorithm 2 takes 91min overall, only slightly longer than the 76min taken by Algorithm 1. For details on the experiment results, please see Section 7. Algorithm 2 Gradient-Guided Diffusion with Adaptive Fine-tuning 1: Input: Pre-trained score s\u03b8(\u00b7, \u00b7), differentiable objective function f. 2: Tuning Parameter: strength parameter \u03b2(t), {yk}K\u22121 k=0 , weights {{wk,i}k i=0}K\u22121 k=0 , number of iterations K, batch sizes {Bk}. 3: Initialize: s\u03b80 = s\u03b8, G0 = NULL. 4: for k = 0, \u00b7 \u00b7 \u00b7 , K \u22121 do 5: Generate: Sample a batch Dk = {zk,i}Bk i=1 from Guided BackwardSample(s\u03b8k, Gk) (Module 1). 6: Compute Guidance: (i) Compute sample mean \u00af zk = (1/Bk) PBk i=1 zk,i, and query gradient gk = \u2207f(\u00af zk). (ii) Update s\u03b8k to s\u03b8k+1 by minimizing the re-weighted objective (20). (iii) Compute Gk+1(\u00b7, \u00b7) = Gloss(\u00b7, \u00b7) in (8), using s\u03b8k+1 and gk, with parameter yk, \u03b2(t). 7: end for 8: Output: (s\u03b8K, GK). 6.2 Guided Generation Finds Unregularized Global Optima Finally, we analyze the optimization properties for gradient-guided diffusion model with iterative finetuning. We establish that the process of Algorithm 2 yields a final output distribution whose mean, denoted by \u00b5K, converges to the global optimum of f. For simplicity of analysis, we study the following function class S\u2032 = n s(x, t) = \u02c6 Ctx + bt : bt \u2208RDo , (21) where \u02c6 Ct is set to stay the same as in the pre-trained score and only bt gets updated during iterative fine-tuning. Marion et al. (2024) studied a similar function class where \u02c6 Ct is freezed to be \u02c6 Ct \u2261I. Theorem 4 (Convergence to Unregularized Maxima in Latent Subspace in Mean). Let Assumptions 1 and 3 hold, and assume there exists M > 0 such that \r \r \rx\u2217 A,\u03bb \r \r \r < M for all \u03bb \u22650. Suppose we use the score function class (15) for pre-training s\u03b8 and the class (21) for finetuning it. Then Algorithm 2 gives an adapted diffusion model that generates new samples belonging to Span(A). Further, there exists {\u03b2(t)}, {yk} , {Bk} and {wk,i}, such that with probability 1 \u2212\u03b4, f\u2217 A \u2212f(\u00b5K) = O \u0012dL2 log K K \u00b7 log \u0012K \u03b4 \u0013\u0013 , (22) where f\u2217 A = max{f(x)|x \u2208Span(A)}. The proof idea is similar to the proof of Theorem 2. For simplicity, we analyze the case where only the most recent sample batch Dk is merged with D0 for finetuning the score function. More 17 specifically, we let wk,i = 0 for 0 < i < k and wk,0 = 1 \u2212wk,k. Similar to the proof of Theorem 2, we obtain a recurisve update rule given by \u00b5k+1 = \u00af zk + \u03b7k \u00af \u03a3 \u0002 \u2207f(\u00af zk) \u2212(1 \u2212wk,k) \u03b7\u22121 k \u00b7 \u00af \u03a3\u22121 (\u00af zk \u2212\u00af \u00b5) \u0003 , (23) where \u00af zk \u2248\u00b5k is the empirical mean of previous samples. This update rule also closely resembles the gradient ascent iteration for maximizing a regularized objective. A key difference here is that we can control the weights wk,i to reduce the impact of D0 and make the regularization term vanish to zero. Thus the mean \u00b5k eventually converges to the global maxima. For the detailed arguments and proof of convergence, we refer readers to Appendix C.3. Theorem 4 illustrates the effect of finetuning a diffusion model using self-generated data. For comparison, Theorem 3 showed that without finetuning the diffusion model can only generate new samples proximal to the pre-training distribution. Now if we allow finetuning using self-generated samples, the diffusion model can iteratively refines itself and reaches global optima, while preserving the latent subspace structure in its generated output. Now let us we take on an optimization view. The convergence rate suggested by Theorem 4 matches with that of standard convex optimization, in terms of their dependence on K the number of gradient evaluations. Further, if we compare the guided diffusion model with a standard gradient solver, the optimality gap of our algorithm scales with the small intrinsic dimension O(d), while standard gradient ascent converges much more slowly due to the large ambient dimension O(D). This comparison highlights the merits of \u201cgenerative optimization\u201d. More specifically, diffusion models leverage pre-training data to learn their intrinsic characteristics. Therefore, when we add gradient guidance to the pre-trained score function and use it for generation, it means that we are solving an optimization problem in its own intrinsic low-dimensional space. This leads to substantially more efficient exploration and faster convergence. This theoretical insight explains the practical successes of guided diffusion models on complex optimization problems, such as video creation, image synthesis and protein AI, where traditional methods do not work at all. 7 Numerical Experiments We experiment with our design of the gradient guidance as well as Algorithm 1 and Algorithm 2. Going beyond our theoretical assumptions, we adopt a 15M-parameter U-Net as the score function class for training and fine-tuning our diffusion model. 7.1 Experiment Setup We set the data\u2019s ambient dimension as D = 64 and the linear subspace dimension as d = 16. The linear subspace is represented by an orthogonal matrix A \u2208RD\u00d7d. We randomly generate a matrix A and fix it once generated. After that, we sample a data point X by first randomly sampling a latent variable U \u223cN(0, Id) and computing X = AU. We independently sample a total of 65536 data points as our pre-training data set. The objective functions considered in our experiments are f1(x) = 10\u2212(\u03b8\u22a4x\u22123)2 and f2(x) = 5\u22120.5\u2225x\u2212b\u2225. Here, \u03b8 and b are randomly generated and fixed afterward. Since our data assumes a low-dimensional subspace representation, it is convenient to decompose \u03b8 into \u03b8\u22a5= (I \u2212AA\u22a4)\u03b8 and \u03b8\u2225= AA\u22a4\u03b8, representing the off-support and on-support components. We refer to \u2225\u03b8\u22a5\u2225 \u2225\u03b8\u2225\u2225as the off/on-support ratio. Analogously, for a generated sample, we can also define its off/on-support ratio. Clearly, a small off/on-support ratio indicates close vicinity to the subspace. 18 Score Network Pre-training We utilize a version of the U-Net (Ronneberger et al., 2015), with 14.8M trainable parameters. Note that this is a complicated network going beyond the linear score function class considered in our theories. Following the implementation of Denoising Diffusion Probabilistic Models (DDPM, Ho et al. (2020)), we train the U-Net o estimate the score function \u2207log pt, via minimizing the score matching loss introduced in Eqn. (3). We discretize the backward process to have 200 time steps as in Nichol and Dhariwal (2021), and the U-Net is trained using our generated data set for 20 epochs. We use Adam as the optimizer, set the batch size as 32, and set the learning rate to be 10\u22124. After the pre-training phase, we confirmed that the data subspace structure is well learned, as the generated samples using the pre-trained diffusion model have an average off/on-support ratio of 0.039. Implementation of Algorithm 1 In each iteration of Algorithm 1, we need to compute the gradient guidance Gloss. We set the targeted y value at the k-th iteration as yk = \u03b4 + g\u22a4 k zk, where \u03b4k specifies the increment per iteration. The choice on \u03b4k is instance-dependent and we set it via tuning for near-optimal in different experiments. For comparing naive gradient with gradient guidance in Figure 5, we set \u03b4 = 0.2 and 0.9, respectively for using naive gradient G and gradient guidance Gloss. In Figure 6, we choose \u03b4 to be (a) 0.05, (b) 0.2, (c) 1, and (d) 1, corresponding to each panel. We initialize Algorithm 1 with a batch of 32 samples generated by the pre-trained model. Each sample determines an optimization trajectory. We repeat Algorithm 1 for 5 times with different random seeds and report the error bars. Implementation of Algorithm 2 Algorithm 2 differs from Algorithm 1 in that it allows additional fine-tuning of the pre-trained score network. We adopt a computationally lightweight finetuning strategy: We only perform one Adam optimization step using the re-weighted loss given by Eqn. (20) with a batch of 32 generated samples. We set the learning rate as 10\u22126. This simple strategy already demonstrates good performances as shown in Figure 7. Other implementation details are kept the same as those of Algorithm 1. We run all experiments using one NVIDIA A100 GPU. Module 1 takes 4.6 seconds to generate a sample. Algorithm 1 takes 76 minutes, and Algorithm 2 takes 91 minutes. 7.2 Results We first demonstrate our gradient guidance Gloss preserves the subspace structure learned from the pre-trained model. For comparison, we also tested the naive guidance G defined following Lemma 1 (with \u03a3 = I). For a quick reference, we repeat the definition here: G(xt, t) := \u03b2(t) \u0010 y \u2212g\u22a4E[x0|xt] \u0011 g, where \u03b2(t) > 0 and y \u2208R are tuning parameters, and E[x0|xt] is the conditional expectation of x0 given noise corrupted data xt. For implementation, we replace E[x0|xt] by its look-ahead estimator \u02c6 E[x0|xt] based on the Tweedie\u2019s formular. Comparing G and Gloss on Preserving Subspace Structure Figure 5(a), (c) verify that the naive gradient G performs much worse than Gloss in preserving the linear subspace structure. It is consistent with our theoretical finding that the gradient guidance Gloss keeps the generated sample close to the latent subspace, with substantially smaller off-support errors. When allowing adaptive 19 score fine-tuning in Algorithm 2, Figure 5(b), (d) show that the off-support error increases as the model gets fine-tuned using self-generated data, due to increasing distribution shift. Even in this case, the naive gradient G leads to much more severe off-support errors as compared to Gloss. (a) Algorithm 1 (b) Algorithm 2 (c) 300-350 round of (a) (d) 1000-1200 round of (b) Figure 5: Comparison between two types of gradient guidance G and Gloss. We plot the off/on support ratio of the generated samples, denoted by roff = \u2225x\u22a5\u2225 \u2225x\u2225\u2225. The objective function is f1(x), with \u03b8 having an off/on-support ratio of 9. Algorithm 1 Converges to Regularized Optima We plot the convergence of Algorithm 1 in terms of the objective value in Figure 6. Figure 6 (a),(b) are for the objective function f1 = 10\u2212(\u03b8\u22a4x\u22123)2 as the objective function, while Figure 6(c),(d) are for the objective f2 = 5\u22120.5\u2225x\u2212b\u2225. We observe that the algorithm converges to reach some sub-optimal objective value, but there remains a gap to the maximal value. This is consistent with our theory that the pre-trained model essentially acts as a regularization in addition to the objective function. Adding gradient guidance alone cannot reach global maxima. This coincides with our theoretical findings in Theorem 3. (a) \u03b8 = A\u03b2\u2217 (b) \u2225\u03b8\u22a5\u2225 \u2225\u03b8\u2225\u2225= 9 (c) b = 4 \u00b7 1D (d) b \u223cN(4 \u00b7 1D, 9 \u00b7 ID) Figure 6: Convergence of Algorithm 1 under different objectives. Objectives are f1(x) for (a) and (b), and f2(x) for (c) and (d). Parameters \u03b8 and b are specified as (a) \u03b8 = A\u03b2\u2217with \u03b2\u2217being sampled from the unit ball in Rd; (b) the off/on-support ratio of \u03b8 being 9 (same as Figure 5); (c) and (d) choosing b as a homogeneous vector or randomly from a Gaussian distribution. All the experiments adopt the gradient guidance Gloss. Algorithm 2 Converges to Global Optima Algorithm 2 converges to the maximal value of the objective function f1 = 10 \u2212(\u03b8\u22a4x \u22123)2 as shown in Figure 7(a). In Figure 7(b), we visualize the distribution of generated samples of Algorithm 1 (blue) and 2 (red), respectively, as the iteration evolves. We see that samples from Algorithm 1 mostly stay close to the pre-training data distribution (area described by the dotted contour). In constrast, samples of Algorithm 2 move outside the contour, as the diffusion model gets finetuned using self-generated data. 20 (a) Convergence of Algorithm 2 (b) Distribution of generated samples Figure 7: Convergence of Algorithm 2. Panel (a) plots the objective values achieved by Algorithm 2 as a function of iterations. Here \u03b8 is chosen the same as in Figure 6(b) with off/on-support ratio \u2225\u03b8\u22a5\u2225 \u2225\u03b8\u2225\u2225= 9. Panel (b) visualizes the distribution of the generated samples of Algorithm 2 (red) across the iterations. For comparison, we also visualize the distribution of generated samples of Algorithm 1 (blue). 8 Conclusion In this paper, we investigate the role and design of gradient guidance for adapting and fine-tuning a pre-trained diffusion model from an optimization perspective. We propose a gradient guidance based on a lookahead loss, as well as two variants of diffusion-based generative optimization algorithm utilizing such guidance. We provide optimization guarantees for adapting/fine-tuning diffusion models towards maximizing any target concave differentiable reward function. Our analysis has also been extended to linear subspace data, where our gradient guidance and adaptive algorithms provably preserve and leverage the latent subspace, thus they achieve faster convergence to near-optimal solutions. 21"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2305.13301v4",
+                    "title": "Training Diffusion Models with Reinforcement Learning",
+                    "abstract": "Diffusion models are a class of flexible generative models trained with an\napproximation to the log-likelihood objective. However, most use cases of\ndiffusion models are not concerned with likelihoods, but instead with\ndownstream objectives such as human-perceived image quality or drug\neffectiveness. In this paper, we investigate reinforcement learning methods for\ndirectly optimizing diffusion models for such objectives. We describe how\nposing denoising as a multi-step decision-making problem enables a class of\npolicy gradient algorithms, which we refer to as denoising diffusion policy\noptimization (DDPO), that are more effective than alternative reward-weighted\nlikelihood approaches. Empirically, DDPO is able to adapt text-to-image\ndiffusion models to objectives that are difficult to express via prompting,\nsuch as image compressibility, and those derived from human feedback, such as\naesthetic quality. Finally, we show that DDPO can improve prompt-image\nalignment using feedback from a vision-language model without the need for\nadditional data collection or human annotation. The project's website can be\nfound at http://rl-diffusion.github.io .",
+                    "authors": "Kevin Black, Michael Janner, Yilun Du, Ilya Kostrikov, Sergey Levine",
+                    "published": "2023-05-22",
+                    "updated": "2024-01-04",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI",
+                        "cs.CV"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2209.11215v3",
+                    "title": "Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions",
+                    "abstract": "We provide theoretical convergence guarantees for score-based generative\nmodels (SGMs) such as denoising diffusion probabilistic models (DDPMs), which\nconstitute the backbone of large-scale real-world generative models such as\nDALL$\\cdot$E 2. Our main result is that, assuming accurate score estimates,\nsuch SGMs can efficiently sample from essentially any realistic data\ndistribution. In contrast to prior works, our results (1) hold for an\n$L^2$-accurate score estimate (rather than $L^\\infty$-accurate); (2) do not\nrequire restrictive functional inequality conditions that preclude substantial\nnon-log-concavity; (3) scale polynomially in all relevant problem parameters;\nand (4) match state-of-the-art complexity guarantees for discretization of the\nLangevin diffusion, provided that the score error is sufficiently small. We\nview this as strong theoretical justification for the empirical success of\nSGMs. We also examine SGMs based on the critically damped Langevin diffusion\n(CLD). Contrary to conventional wisdom, we provide evidence that the use of the\nCLD does not reduce the complexity of SGMs.",
+                    "authors": "Sitan Chen, Sinho Chewi, Jerry Li, Yuanzhi Li, Adil Salim, Anru R. Zhang",
+                    "published": "2022-09-22",
+                    "updated": "2023-04-15",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "math.ST",
+                        "stat.TH"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2208.14699v1",
+                    "title": "Let us Build Bridges: Understanding and Extending Diffusion Generative Models",
+                    "abstract": "Diffusion-based generative models have achieved promising results recently,\nbut raise an array of open questions in terms of conceptual understanding,\ntheoretical analysis, algorithm improvement and extensions to discrete,\nstructured, non-Euclidean domains. This work tries to re-exam the overall\nframework, in order to gain better theoretical understandings and develop\nalgorithmic extensions for data from arbitrary domains. By viewing diffusion\nmodels as latent variable models with unobserved diffusion trajectories and\napplying maximum likelihood estimation (MLE) with latent trajectories imputed\nfrom an auxiliary distribution, we show that both the model construction and\nthe imputation of latent trajectories amount to constructing diffusion bridge\nprocesses that achieve deterministic values and constraints at end point, for\nwhich we provide a systematic study and a suit of tools. Leveraging our\nframework, we present 1) a first theoretical error analysis for learning\ndiffusion generation models, and 2) a simple and unified approach to learning\non data from different discrete and constrained domains. Experiments show that\nour methods perform superbly on generating images, semantic segments and 3D\npoint clouds.",
+                    "authors": "Xingchao Liu, Lemeng Wu, Mao Ye, Qiang Liu",
+                    "published": "2022-08-31",
+                    "updated": "2022-08-31",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.CV"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2404.07771v1",
+                    "title": "An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimization",
+                    "abstract": "Diffusion models, a powerful and universal generative AI technology, have\nachieved tremendous success in computer vision, audio, reinforcement learning,\nand computational biology. In these applications, diffusion models provide\nflexible high-dimensional data modeling, and act as a sampler for generating\nnew samples under active guidance towards task-desired properties. Despite the\nsignificant empirical success, theory of diffusion models is very limited,\npotentially slowing down principled methodological innovations for further\nharnessing and improving diffusion models. In this paper, we review emerging\napplications of diffusion models, understanding their sample generation under\nvarious controls. Next, we overview the existing theories of diffusion models,\ncovering their statistical properties and sampling capabilities. We adopt a\nprogressive routine, beginning with unconditional diffusion models and\nconnecting to conditional counterparts. Further, we review a new avenue in\nhigh-dimensional structured optimization through conditional diffusion models,\nwhere searching for solutions is reformulated as a conditional sampling problem\nand solved by diffusion models. Lastly, we discuss future directions about\ndiffusion models. The purpose of this paper is to provide a well-rounded\ntheoretical exposure for stimulating forward-looking theories and methods of\ndiffusion models.",
+                    "authors": "Minshuo Chen, Song Mei, Jianqing Fan, Mengdi Wang",
+                    "published": "2024-04-11",
+                    "updated": "2024-04-11",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "math.ST",
+                        "stat.ML",
+                        "stat.TH"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2209.12381v2",
+                    "title": "Convergence of score-based generative modeling for general data distributions",
+                    "abstract": "Score-based generative modeling (SGM) has grown to be a hugely successful\nmethod for learning to generate samples from complex data distributions such as\nthat of images and audio. It is based on evolving an SDE that transforms white\nnoise into a sample from the learned distribution, using estimates of the score\nfunction, or gradient log-pdf. Previous convergence analyses for these methods\nhave suffered either from strong assumptions on the data distribution or\nexponential dependencies, and hence fail to give efficient guarantees for the\nmultimodal and non-smooth distributions that arise in practice and for which\ngood empirical performance is observed. We consider a popular kind of SGM --\ndenoising diffusion models -- and give polynomial convergence guarantees for\ngeneral data distributions, with no assumptions related to functional\ninequalities or smoothness. Assuming $L^2$-accurate score estimates, we obtain\nWasserstein distance guarantees for any distribution of bounded support or\nsufficiently decaying tails, as well as TV guarantees for distributions with\nfurther smoothness assumptions.",
+                    "authors": "Holden Lee, Jianfeng Lu, Yixin Tan",
+                    "published": "2022-09-26",
+                    "updated": "2022-10-03",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "math.PR",
+                        "math.ST",
+                        "stat.ML",
+                        "stat.TH"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2302.07121v1",
+                    "title": "Universal Guidance for Diffusion Models",
+                    "abstract": "Typical diffusion models are trained to accept a particular form of\nconditioning, most commonly text, and cannot be conditioned on other modalities\nwithout retraining. In this work, we propose a universal guidance algorithm\nthat enables diffusion models to be controlled by arbitrary guidance modalities\nwithout the need to retrain any use-specific components. We show that our\nalgorithm successfully generates quality images with guidance functions\nincluding segmentation, face recognition, object detection, and classifier\nsignals. Code is available at\nhttps://github.com/arpitbansal297/Universal-Guided-Diffusion.",
+                    "authors": "Arpit Bansal, Hong-Min Chu, Avi Schwarzschild, Soumyadip Sengupta, Micah Goldblum, Jonas Geiping, Tom Goldstein",
+                    "published": "2023-02-14",
+                    "updated": "2023-02-14",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.LG"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2309.11420v1",
+                    "title": "Deep Networks as Denoising Algorithms: Sample-Efficient Learning of Diffusion Models in High-Dimensional Graphical Models",
+                    "abstract": "We investigate the approximation efficiency of score functions by deep neural\nnetworks in diffusion-based generative modeling. While existing approximation\ntheories utilize the smoothness of score functions, they suffer from the curse\nof dimensionality for intrinsically high-dimensional data. This limitation is\npronounced in graphical models such as Markov random fields, common for image\ndistributions, where the approximation efficiency of score functions remains\nunestablished.\n  To address this, we observe score functions can often be well-approximated in\ngraphical models through variational inference denoising algorithms.\nFurthermore, these algorithms are amenable to efficient neural network\nrepresentation. We demonstrate this in examples of graphical models, including\nIsing models, conditional Ising models, restricted Boltzmann machines, and\nsparse encoding models. Combined with off-the-shelf discretization error bounds\nfor diffusion-based sampling, we provide an efficient sample complexity bound\nfor diffusion-based generative modeling when the score function is learned by\ndeep neural networks.",
+                    "authors": "Song Mei, Yuchen Wu",
+                    "published": "2023-09-20",
+                    "updated": "2023-09-20",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "math.ST",
+                        "stat.ML",
+                        "stat.TH"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2403.11968v1",
+                    "title": "Unveil Conditional Diffusion Models with Classifier-free Guidance: A Sharp Statistical Theory",
+                    "abstract": "Conditional diffusion models serve as the foundation of modern image\nsynthesis and find extensive application in fields like computational biology\nand reinforcement learning. In these applications, conditional diffusion models\nincorporate various conditional information, such as prompt input, to guide the\nsample generation towards desired properties. Despite the empirical success,\ntheory of conditional diffusion models is largely missing. This paper bridges\nthis gap by presenting a sharp statistical theory of distribution estimation\nusing conditional diffusion models. Our analysis yields a sample complexity\nbound that adapts to the smoothness of the data distribution and matches the\nminimax lower bound. The key to our theoretical development lies in an\napproximation result for the conditional score function, which relies on a\nnovel diffused Taylor approximation technique. Moreover, we demonstrate the\nutility of our statistical theory in elucidating the performance of conditional\ndiffusion models across diverse applications, including model-based transition\nkernel estimation in reinforcement learning, solving inverse problems, and\nreward conditioned sample generation.",
+                    "authors": "Hengyu Fu, Zhuoran Yang, Mengdi Wang, Minshuo Chen",
+                    "published": "2024-03-18",
+                    "updated": "2024-03-18",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "math.ST",
+                        "stat.ML",
+                        "stat.TH"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1907.05600v3",
+                    "title": "Generative Modeling by Estimating Gradients of the Data Distribution",
+                    "abstract": "We introduce a new generative model where samples are produced via Langevin\ndynamics using gradients of the data distribution estimated with score\nmatching. Because gradients can be ill-defined and hard to estimate when the\ndata resides on low-dimensional manifolds, we perturb the data with different\nlevels of Gaussian noise, and jointly estimate the corresponding scores, i.e.,\nthe vector fields of gradients of the perturbed data distribution for all noise\nlevels. For sampling, we propose an annealed Langevin dynamics where we use\ngradients corresponding to gradually decreasing noise levels as the sampling\nprocess gets closer to the data manifold. Our framework allows flexible model\narchitectures, requires no sampling during training or the use of adversarial\nmethods, and provides a learning objective that can be used for principled\nmodel comparisons. Our models produce samples comparable to GANs on MNIST,\nCelebA and CIFAR-10 datasets, achieving a new state-of-the-art inception score\nof 8.87 on CIFAR-10. Additionally, we demonstrate that our models learn\neffective representations via image inpainting experiments.",
+                    "authors": "Yang Song, Stefano Ermon",
+                    "published": "2019-07-12",
+                    "updated": "2020-10-10",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "stat.ML"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2302.07194v1",
+                    "title": "Score Approximation, Estimation and Distribution Recovery of Diffusion Models on Low-Dimensional Data",
+                    "abstract": "Diffusion models achieve state-of-the-art performance in various generation\ntasks. However, their theoretical foundations fall far behind. This paper\nstudies score approximation, estimation, and distribution recovery of diffusion\nmodels, when data are supported on an unknown low-dimensional linear subspace.\nOur result provides sample complexity bounds for distribution estimation using\ndiffusion models. We show that with a properly chosen neural network\narchitecture, the score function can be both accurately approximated and\nefficiently estimated. Furthermore, the generated distribution based on the\nestimated score function captures the data geometric structures and converges\nto a close vicinity of the data distribution. The convergence rate depends on\nthe subspace dimension, indicating that diffusion models can circumvent the\ncurse of data ambient dimensionality.",
+                    "authors": "Minshuo Chen, Kaixuan Huang, Tuo Zhao, Mengdi Wang",
+                    "published": "2023-02-14",
+                    "updated": "2023-02-14",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "stat.ML"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2310.08912v1",
+                    "title": "Sampling from Mean-Field Gibbs Measures via Diffusion Processes",
+                    "abstract": "We consider Ising mixed $p$-spin glasses at high-temperature and without\nexternal field, and study the problem of sampling from the Gibbs distribution\n$\\mu$ in polynomial time. We develop a new sampling algorithm with complexity\nof the same order as evaluating the gradient of the Hamiltonian and, in\nparticular, at most linear in the input size. We prove that, at sufficiently\nhigh-temperature, it produces samples from a distribution $\\mu^{alg}$ which is\nclose in normalized Wasserstein distance to $\\mu$. Namely, there exists a\ncoupling of $\\mu$ and $\\mu^{alg}$ such that if $({\\boldsymbol x},{\\boldsymbol\nx}^{alg})\\in\\{-1,+1\\}^n\\times \\{-1,+1\\}^n$ is a pair drawn from this coupling,\nthen $n^{-1}{\\mathbb E}\\{\\|{\\boldsymbol x}-{\\boldsymbol\nx}^{alg}\\|_2^2\\}=o_n(1)$. For the case of the Sherrington-Kirkpatrick model,\nour algorithm succeeds in the full replica-symmetric phase.\n  We complement this result with a negative one for sampling algorithms\nsatisfying a certain `stability' property, which is verified by many standard\ntechniques.\n  No stable algorithm can approximately sample at temperatures below the onset\nof shattering, even under the normalized Wasserstein metric. Further, no\nalgorithm can sample at temperatures below the onset of replica symmetry\nbreaking.\n  Our sampling method implements a discretized version of a diffusion process\nthat has become recently popular in machine learning under the name of\n`denoising diffusion.' We derive the same process from the general construction\nof stochastic localization. Implementing the diffusion process requires to\nefficiently approximate the mean of the tilted measure. To this end, we use an\napproximate message passing algorithm that, as we prove, achieves sufficiently\naccurate mean estimation.",
+                    "authors": "Ahmed El Alaoui, Andrea Montanari, Mark Sellke",
+                    "published": "2023-10-13",
+                    "updated": "2023-10-13",
+                    "primary_cat": "math.PR",
+                    "cats": [
+                        "math.PR"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2402.05468v1",
+                    "title": "Implicit Diffusion: Efficient Optimization through Stochastic Sampling",
+                    "abstract": "We present a new algorithm to optimize distributions defined implicitly by\nparameterized stochastic diffusions. Doing so allows us to modify the outcome\ndistribution of sampling processes by optimizing over their parameters. We\nintroduce a general framework for first-order optimization of these processes,\nthat performs jointly, in a single loop, optimization and sampling steps. This\napproach is inspired by recent advances in bilevel optimization and automatic\nimplicit differentiation, leveraging the point of view of sampling as\noptimization over the space of probability distributions. We provide\ntheoretical guarantees on the performance of our method, as well as\nexperimental results demonstrating its effectiveness in real-world settings.",
+                    "authors": "Pierre Marion, Anna Korba, Peter Bartlett, Mathieu Blondel, Valentin De Bortoli, Arnaud Doucet, Felipe Llinares-L\u00f3pez, Courtney Paquette, Quentin Berthet",
+                    "published": "2024-02-08",
+                    "updated": "2024-02-08",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2010.02502v4",
+                    "title": "Denoising Diffusion Implicit Models",
+                    "abstract": "Denoising diffusion probabilistic models (DDPMs) have achieved high quality\nimage generation without adversarial training, yet they require simulating a\nMarkov chain for many steps to produce a sample. To accelerate sampling, we\npresent denoising diffusion implicit models (DDIMs), a more efficient class of\niterative implicit probabilistic models with the same training procedure as\nDDPMs. In DDPMs, the generative process is defined as the reverse of a\nMarkovian diffusion process. We construct a class of non-Markovian diffusion\nprocesses that lead to the same training objective, but whose reverse process\ncan be much faster to sample from. We empirically demonstrate that DDIMs can\nproduce high quality samples $10 \\times$ to $50 \\times$ faster in terms of\nwall-clock time compared to DDPMs, allow us to trade off computation for sample\nquality, and can perform semantically meaningful image interpolation directly\nin the latent space.",
+                    "authors": "Jiaming Song, Chenlin Meng, Stefano Ermon",
+                    "published": "2020-10-06",
+                    "updated": "2022-10-05",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.CV"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2305.16381v3",
+                    "title": "DPOK: Reinforcement Learning for Fine-tuning Text-to-Image Diffusion Models",
+                    "abstract": "Learning from human feedback has been shown to improve text-to-image models.\nThese techniques first learn a reward function that captures what humans care\nabout in the task and then improve the models based on the learned reward\nfunction. Even though relatively simple approaches (e.g., rejection sampling\nbased on reward scores) have been investigated, fine-tuning text-to-image\nmodels with the reward function remains challenging. In this work, we propose\nusing online reinforcement learning (RL) to fine-tune text-to-image models. We\nfocus on diffusion models, defining the fine-tuning task as an RL problem, and\nupdating the pre-trained text-to-image diffusion models using policy gradient\nto maximize the feedback-trained reward. Our approach, coined DPOK, integrates\npolicy optimization with KL regularization. We conduct an analysis of KL\nregularization for both RL fine-tuning and supervised fine-tuning. In our\nexperiments, we show that DPOK is generally superior to supervised fine-tuning\nwith respect to both image-text alignment and image quality. Our code is\navailable at\nhttps://github.com/google-research/google-research/tree/master/dpok.",
+                    "authors": "Ying Fan, Olivia Watkins, Yuqing Du, Hao Liu, Moonkyung Ryu, Craig Boutilier, Pieter Abbeel, Mohammad Ghavamzadeh, Kangwook Lee, Kimin Lee",
+                    "published": "2023-05-25",
+                    "updated": "2023-11-01",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.CV"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2303.03384v1",
+                    "title": "Restoration-Degradation Beyond Linear Diffusions: A Non-Asymptotic Analysis For DDIM-Type Samplers",
+                    "abstract": "We develop a framework for non-asymptotic analysis of deterministic samplers\nused for diffusion generative modeling. Several recent works have analyzed\nstochastic samplers using tools like Girsanov's theorem and a chain rule\nvariant of the interpolation argument. Unfortunately, these techniques give\nvacuous bounds when applied to deterministic samplers. We give a new\noperational interpretation for deterministic sampling by showing that one step\nalong the probability flow ODE can be expressed as two steps: 1) a restoration\nstep that runs gradient ascent on the conditional log-likelihood at some\ninfinitesimally previous time, and 2) a degradation step that runs the forward\nprocess using noise pointing back towards the current iterate. This perspective\nallows us to extend denoising diffusion implicit models to general, non-linear\nforward processes. We then develop the first polynomial convergence bounds for\nthese samplers under mild conditions on the data distribution.",
+                    "authors": "Sitan Chen, Giannis Daras, Alexandros G. Dimakis",
+                    "published": "2023-03-06",
+                    "updated": "2023-03-06",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "math.ST",
+                        "stat.ML",
+                        "stat.TH"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2308.03686v3",
+                    "title": "Nearly $d$-Linear Convergence Bounds for Diffusion Models via Stochastic Localization",
+                    "abstract": "Denoising diffusions are a powerful method to generate approximate samples\nfrom high-dimensional data distributions. Recent results provide polynomial\nbounds on their convergence rate, assuming $L^2$-accurate scores. Until now,\nthe tightest bounds were either superlinear in the data dimension or required\nstrong smoothness assumptions. We provide the first convergence bounds which\nare linear in the data dimension (up to logarithmic factors) assuming only\nfinite second moments of the data distribution. We show that diffusion models\nrequire at most $\\tilde O(\\frac{d \\log^2(1/\\delta)}{\\varepsilon^2})$ steps to\napproximate an arbitrary distribution on $\\mathbb{R}^d$ corrupted with Gaussian\nnoise of variance $\\delta$ to within $\\varepsilon^2$ in KL divergence. Our\nproof extends the Girsanov-based methods of previous works. We introduce a\nrefined treatment of the error from discretizing the reverse SDE inspired by\nstochastic localization.",
+                    "authors": "Joe Benton, Valentin De Bortoli, Arnaud Doucet, George Deligiannidis",
+                    "published": "2023-08-07",
+                    "updated": "2024-03-06",
+                    "primary_cat": "stat.ML",
+                    "cats": [
+                        "stat.ML",
+                        "cs.LG"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2402.07747v1",
+                    "title": "Optimal score estimation via empirical Bayes smoothing",
+                    "abstract": "We study the problem of estimating the score function of an unknown\nprobability distribution $\\rho^*$ from $n$ independent and identically\ndistributed observations in $d$ dimensions. Assuming that $\\rho^*$ is\nsubgaussian and has a Lipschitz-continuous score function $s^*$, we establish\nthe optimal rate of $\\tilde \\Theta(n^{-\\frac{2}{d+4}})$ for this estimation\nproblem under the loss function $\\|\\hat s - s^*\\|^2_{L^2(\\rho^*)}$ that is\ncommonly used in the score matching literature, highlighting the curse of\ndimensionality where sample complexity for accurate score estimation grows\nexponentially with the dimension $d$. Leveraging key insights in empirical\nBayes theory as well as a new convergence rate of smoothed empirical\ndistribution in Hellinger distance, we show that a regularized score estimator\nbased on a Gaussian kernel attains this rate, shown optimal by a matching\nminimax lower bound. We also discuss the implication of our theory on the\nsample complexity of score-based generative models.",
+                    "authors": "Andre Wibisono, Yihong Wu, Kaylee Yingxi Yang",
+                    "published": "2024-02-12",
+                    "updated": "2024-02-12",
+                    "primary_cat": "math.ST",
+                    "cats": [
+                        "math.ST",
+                        "stat.ML",
+                        "stat.TH"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2106.01357v5",
+                    "title": "Diffusion Schr\u00f6dinger Bridge with Applications to Score-Based Generative Modeling",
+                    "abstract": "Progressively applying Gaussian noise transforms complex data distributions\nto approximately Gaussian. Reversing this dynamic defines a generative model.\nWhen the forward noising process is given by a Stochastic Differential Equation\n(SDE), Song et al. (2021) demonstrate how the time inhomogeneous drift of the\nassociated reverse-time SDE may be estimated using score-matching. A limitation\nof this approach is that the forward-time SDE must be run for a sufficiently\nlong time for the final distribution to be approximately Gaussian. In contrast,\nsolving the Schr\\\"odinger Bridge problem (SB), i.e. an entropy-regularized\noptimal transport problem on path spaces, yields diffusions which generate\nsamples from the data distribution in finite time. We present Diffusion SB\n(DSB), an original approximation of the Iterative Proportional Fitting (IPF)\nprocedure to solve the SB problem, and provide theoretical analysis along with\ngenerative modeling experiments. The first DSB iteration recovers the\nmethodology proposed by Song et al. (2021), with the flexibility of using\nshorter time intervals, as subsequent DSB iterations reduce the discrepancy\nbetween the final-time marginal of the forward (resp. backward) SDE with\nrespect to the prior (resp. data) distribution. Beyond generative modeling, DSB\noffers a widely applicable computational optimal transport tool as the\ncontinuous state-space analogue of the popular Sinkhorn algorithm (Cuturi,\n2013).",
+                    "authors": "Valentin De Bortoli, James Thornton, Jeremy Heng, Arnaud Doucet",
+                    "published": "2021-06-01",
+                    "updated": "2023-04-05",
+                    "primary_cat": "stat.ML",
+                    "cats": [
+                        "stat.ML",
+                        "cs.LG",
+                        "math.PR"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2302.07121v1",
+                    "title": "Universal Guidance for Diffusion Models",
+                    "abstract": "Typical diffusion models are trained to accept a particular form of\nconditioning, most commonly text, and cannot be conditioned on other modalities\nwithout retraining. In this work, we propose a universal guidance algorithm\nthat enables diffusion models to be controlled by arbitrary guidance modalities\nwithout the need to retrain any use-specific components. We show that our\nalgorithm successfully generates quality images with guidance functions\nincluding segmentation, face recognition, object detection, and classifier\nsignals. Code is available at\nhttps://github.com/arpitbansal297/Universal-Guided-Diffusion.",
+                    "authors": "Arpit Bansal, Hong-Min Chu, Avi Schwarzschild, Soumyadip Sengupta, Micah Goldblum, Jonas Geiping, Tom Goldstein",
+                    "published": "2023-02-14",
+                    "updated": "2023-02-14",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.LG"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2402.15194v2",
+                    "title": "Fine-Tuning of Continuous-Time Diffusion Models as Entropy-Regularized Control",
+                    "abstract": "Diffusion models excel at capturing complex data distributions, such as those\nof natural images and proteins. While diffusion models are trained to represent\nthe distribution in the training dataset, we often are more concerned with\nother properties, such as the aesthetic quality of the generated images or the\nfunctional properties of generated proteins. Diffusion models can be finetuned\nin a goal-directed way by maximizing the value of some reward function (e.g.,\nthe aesthetic quality of an image). However, these approaches may lead to\nreduced sample diversity, significant deviations from the training data\ndistribution, and even poor sample quality due to the exploitation of an\nimperfect reward function. The last issue often occurs when the reward function\nis a learned model meant to approximate a ground-truth \"genuine\" reward, as is\nthe case in many practical applications. These challenges, collectively termed\n\"reward collapse,\" pose a substantial obstacle. To address this reward\ncollapse, we frame the finetuning problem as entropy-regularized control\nagainst the pretrained diffusion model, i.e., directly optimizing\nentropy-enhanced rewards with neural SDEs. We present theoretical and empirical\nevidence that demonstrates our framework is capable of efficiently generating\ndiverse samples with high genuine rewards, mitigating the overoptimization of\nimperfect reward models.",
+                    "authors": "Masatoshi Uehara, Yulai Zhao, Kevin Black, Ehsan Hajiramezanali, Gabriele Scalia, Nathaniel Lee Diamant, Alex M Tseng, Tommaso Biancalani, Sergey Levine",
+                    "published": "2024-02-23",
+                    "updated": "2024-02-28",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI",
+                        "stat.ML"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2304.11449v1",
+                    "title": "Posterior Sampling from the Spiked Models via Diffusion Processes",
+                    "abstract": "Sampling from the posterior is a key technical problem in Bayesian\nstatistics. Rigorous guarantees are difficult to obtain for Markov Chain Monte\nCarlo algorithms of common use. In this paper, we study an alternative class of\nalgorithms based on diffusion processes. The diffusion is constructed in such a\nway that, at its final time, it approximates the target posterior distribution.\nThe stochastic differential equation that defines this process is discretized\n(using a Euler scheme) to provide an efficient sampling algorithm. Our\nconstruction of the diffusion is based on the notion of observation process and\nthe related idea of stochastic localization. Namely, the diffusion process\ndescribes a sample that is conditioned on increasing information. An\noverlapping family of processes was derived in the machine learning literature\nvia time-reversal.\n  We apply this method to posterior sampling in the high-dimensional symmetric\nspiked model. We observe a rank-one matrix ${\\boldsymbol \\theta}{\\boldsymbol\n\\theta}^{\\sf T}$ corrupted by Gaussian noise, and want to sample ${\\boldsymbol\n\\theta}$ from the posterior. Our sampling algorithm makes use of an oracle that\ncomputes the posterior expectation of ${\\boldsymbol \\theta}$ given the data and\nthe additional observation process. We provide an efficient implementation of\nthis oracle using approximate message passing. We thus develop the first\nsampling algorithm for this problem with approximation guarantees.",
+                    "authors": "Andrea Montanari, Yuchen Wu",
+                    "published": "2023-04-22",
+                    "updated": "2023-04-22",
+                    "primary_cat": "math.ST",
+                    "cats": [
+                        "math.ST",
+                        "stat.TH"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2105.05233v4",
+                    "title": "Diffusion Models Beat GANs on Image Synthesis",
+                    "abstract": "We show that diffusion models can achieve image sample quality superior to\nthe current state-of-the-art generative models. We achieve this on\nunconditional image synthesis by finding a better architecture through a series\nof ablations. For conditional image synthesis, we further improve sample\nquality with classifier guidance: a simple, compute-efficient method for\ntrading off diversity for fidelity using gradients from a classifier. We\nachieve an FID of 2.97 on ImageNet 128$\\times$128, 4.59 on ImageNet\n256$\\times$256, and 7.72 on ImageNet 512$\\times$512, and we match BigGAN-deep\neven with as few as 25 forward passes per sample, all while maintaining better\ncoverage of the distribution. Finally, we find that classifier guidance\ncombines well with upsampling diffusion models, further improving FID to 3.94\non ImageNet 256$\\times$256 and 3.85 on ImageNet 512$\\times$512. We release our\ncode at https://github.com/openai/guided-diffusion",
+                    "authors": "Prafulla Dhariwal, Alex Nichol",
+                    "published": "2021-05-11",
+                    "updated": "2021-06-01",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI",
+                        "cs.CV",
+                        "stat.ML"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2102.09672v1",
+                    "title": "Improved Denoising Diffusion Probabilistic Models",
+                    "abstract": "Denoising diffusion probabilistic models (DDPM) are a class of generative\nmodels which have recently been shown to produce excellent samples. We show\nthat with a few simple modifications, DDPMs can also achieve competitive\nlog-likelihoods while maintaining high sample quality. Additionally, we find\nthat learning variances of the reverse diffusion process allows sampling with\nan order of magnitude fewer forward passes with a negligible difference in\nsample quality, which is important for the practical deployment of these\nmodels. We additionally use precision and recall to compare how well DDPMs and\nGANs cover the target distribution. Finally, we show that the sample quality\nand likelihood of these models scale smoothly with model capacity and training\ncompute, making them easily scalable. We release our code at\nhttps://github.com/openai/improved-diffusion",
+                    "authors": "Alex Nichol, Prafulla Dhariwal",
+                    "published": "2021-02-18",
+                    "updated": "2021-02-18",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI",
+                        "stat.ML"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2309.17400v1",
+                    "title": "Directly Fine-Tuning Diffusion Models on Differentiable Rewards",
+                    "abstract": "We present Direct Reward Fine-Tuning (DRaFT), a simple and effective method\nfor fine-tuning diffusion models to maximize differentiable reward functions,\nsuch as scores from human preference models. We first show that it is possible\nto backpropagate the reward function gradient through the full sampling\nprocedure, and that doing so achieves strong performance on a variety of\nrewards, outperforming reinforcement learning-based approaches. We then propose\nmore efficient variants of DRaFT: DRaFT-K, which truncates backpropagation to\nonly the last K steps of sampling, and DRaFT-LV, which obtains lower-variance\ngradient estimates for the case when K=1. We show that our methods work well\nfor a variety of reward functions and can be used to substantially improve the\naesthetic quality of images generated by Stable Diffusion 1.4. Finally, we draw\nconnections between our approach and prior work, providing a unifying\nperspective on the design space of gradient-based fine-tuning algorithms.",
+                    "authors": "Kevin Clark, Paul Vicol, Kevin Swersky, David J Fleet",
+                    "published": "2023-09-29",
+                    "updated": "2023-09-29",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.LG"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2303.01861v1",
+                    "title": "Diffusion Models are Minimax Optimal Distribution Estimators",
+                    "abstract": "While efficient distribution learning is no doubt behind the groundbreaking\nsuccess of diffusion modeling, its theoretical guarantees are quite limited. In\nthis paper, we provide the first rigorous analysis on approximation and\ngeneralization abilities of diffusion modeling for well-known function spaces.\nThe highlight of this paper is that when the true density function belongs to\nthe Besov space and the empirical score matching loss is properly minimized,\nthe generated data distribution achieves the nearly minimax optimal estimation\nrates in the total variation distance and in the Wasserstein distance of order\none. Furthermore, we extend our theory to demonstrate how diffusion models\nadapt to low-dimensional data distributions. We expect these results advance\ntheoretical understandings of diffusion modeling and its ability to generate\nverisimilar outputs.",
+                    "authors": "Kazusato Oko, Shunta Akiyama, Taiji Suzuki",
+                    "published": "2023-03-03",
+                    "updated": "2023-03-03",
+                    "primary_cat": "stat.ML",
+                    "cats": [
+                        "stat.ML",
+                        "cs.LG"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2402.15194v2",
+                    "title": "Fine-Tuning of Continuous-Time Diffusion Models as Entropy-Regularized Control",
+                    "abstract": "Diffusion models excel at capturing complex data distributions, such as those\nof natural images and proteins. While diffusion models are trained to represent\nthe distribution in the training dataset, we often are more concerned with\nother properties, such as the aesthetic quality of the generated images or the\nfunctional properties of generated proteins. Diffusion models can be finetuned\nin a goal-directed way by maximizing the value of some reward function (e.g.,\nthe aesthetic quality of an image). However, these approaches may lead to\nreduced sample diversity, significant deviations from the training data\ndistribution, and even poor sample quality due to the exploitation of an\nimperfect reward function. The last issue often occurs when the reward function\nis a learned model meant to approximate a ground-truth \"genuine\" reward, as is\nthe case in many practical applications. These challenges, collectively termed\n\"reward collapse,\" pose a substantial obstacle. To address this reward\ncollapse, we frame the finetuning problem as entropy-regularized control\nagainst the pretrained diffusion model, i.e., directly optimizing\nentropy-enhanced rewards with neural SDEs. We present theoretical and empirical\nevidence that demonstrates our framework is capable of efficiently generating\ndiverse samples with high genuine rewards, mitigating the overoptimization of\nimperfect reward models.",
+                    "authors": "Masatoshi Uehara, Yulai Zhao, Kevin Black, Ehsan Hajiramezanali, Gabriele Scalia, Nathaniel Lee Diamant, Alex M Tseng, Tommaso Biancalani, Sergey Levine",
+                    "published": "2024-02-23",
+                    "updated": "2024-02-28",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI",
+                        "stat.ML"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2207.12598v1",
+                    "title": "Classifier-Free Diffusion Guidance",
+                    "abstract": "Classifier guidance is a recently introduced method to trade off mode\ncoverage and sample fidelity in conditional diffusion models post training, in\nthe same spirit as low temperature sampling or truncation in other types of\ngenerative models. Classifier guidance combines the score estimate of a\ndiffusion model with the gradient of an image classifier and thereby requires\ntraining an image classifier separate from the diffusion model. It also raises\nthe question of whether guidance can be performed without a classifier. We show\nthat guidance can be indeed performed by a pure generative model without such a\nclassifier: in what we call classifier-free guidance, we jointly train a\nconditional and an unconditional diffusion model, and we combine the resulting\nconditional and unconditional score estimates to attain a trade-off between\nsample quality and diversity similar to that obtained using classifier\nguidance.",
+                    "authors": "Jonathan Ho, Tim Salimans",
+                    "published": "2022-07-26",
+                    "updated": "2022-07-26",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2402.05468v1",
+                    "title": "Implicit Diffusion: Efficient Optimization through Stochastic Sampling",
+                    "abstract": "We present a new algorithm to optimize distributions defined implicitly by\nparameterized stochastic diffusions. Doing so allows us to modify the outcome\ndistribution of sampling processes by optimizing over their parameters. We\nintroduce a general framework for first-order optimization of these processes,\nthat performs jointly, in a single loop, optimization and sampling steps. This\napproach is inspired by recent advances in bilevel optimization and automatic\nimplicit differentiation, leveraging the point of view of sampling as\noptimization over the space of probability distributions. We provide\ntheoretical guarantees on the performance of our method, as well as\nexperimental results demonstrating its effectiveness in real-world settings.",
+                    "authors": "Pierre Marion, Anna Korba, Peter Bartlett, Mathieu Blondel, Valentin De Bortoli, Arnaud Doucet, Felipe Llinares-L\u00f3pez, Courtney Paquette, Quentin Berthet",
+                    "published": "2024-02-08",
+                    "updated": "2024-02-08",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2305.10028v1",
+                    "title": "Pyramid Diffusion Models For Low-light Image Enhancement",
+                    "abstract": "Recovering noise-covered details from low-light images is challenging, and\nthe results given by previous methods leave room for improvement. Recent\ndiffusion models show realistic and detailed image generation through a\nsequence of denoising refinements and motivate us to introduce them to\nlow-light image enhancement for recovering realistic details. However, we found\ntwo problems when doing this, i.e., 1) diffusion models keep constant\nresolution in one reverse process, which limits the speed; 2) diffusion models\nsometimes result in global degradation (e.g., RGB shift). To address the above\nproblems, this paper proposes a Pyramid Diffusion model (PyDiff) for low-light\nimage enhancement. PyDiff uses a novel pyramid diffusion method to perform\nsampling in a pyramid resolution style (i.e., progressively increasing\nresolution in one reverse process). Pyramid diffusion makes PyDiff much faster\nthan vanilla diffusion models and introduces no performance degradation.\nFurthermore, PyDiff uses a global corrector to alleviate the global degradation\nthat may occur in the reverse process, significantly improving the performance\nand making the training of diffusion models easier with little additional\ncomputational consumption. Extensive experiments on popular benchmarks show\nthat PyDiff achieves superior performance and efficiency. Moreover, PyDiff can\ngeneralize well to unseen noise and illumination distributions.",
+                    "authors": "Dewei Zhou, Zongxin Yang, Yi Yang",
+                    "published": "2023-05-17",
+                    "updated": "2023-05-17",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1304.0925v1",
+                    "title": "A new approach to multi-modal diffusions with applications to protein folding",
+                    "abstract": "This article demonstrates that flexible and statistically tractable\nmulti-modal diffusion models can be attained by transformation of simple\nwell-known diffusion models such as the Ornstein-Uhlenbeck model, or more\ngenerally a Pearson diffusion. The transformed diffusion inherits many\nproperties of the underlying simple diffusion including its mixing rates and\ndistributions of first passage times. Likelihood inference and martingale\nestimating functions are considered in the case of a discretely observed\nbimodal diffusion. It is further demonstrated that model parameters can be\nidentified and estimated when the diffusion is observed with additional\nmeasurement error. The new approach is applied to molecular dynamics data in\nform of a reaction coordinate of the small Trp-zipper protein, for which the\nfolding and unfolding rates are estimated. The new models provide a better fit\nto this type of protein folding data than previous models because the diffusion\ncoefficient is state-dependent.",
+                    "authors": "Julie Forman, Michael S\u00f8rensen",
+                    "published": "2013-04-03",
+                    "updated": "2013-04-03",
+                    "primary_cat": "stat.ME",
+                    "cats": [
+                        "stat.ME"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1709.05336v1",
+                    "title": "Cs diffusion in SiC high-energy grain boundaries",
+                    "abstract": "Cesium (Cs) is a radioactive fission product whose release is of concern for\nTristructural-Isotropic (TRISO) fuel particles. In this work, Cs diffusion\nthrough high energy grain boundaries (HEGBs) of cubic-SiC is studied using an\nab-initio based kinetic Monte Carlo (kMC) model. The HEGB environment was\nmodeled as an amorphous SiC (a-SiC), and Cs defect energies were calculated\nusing density functional theory (DFT). From defect energies, it was suggested\nthat the fastest diffusion mechanism as Cs interstitial in an amorphous SiC.\nThe diffusion of Cs interstitial was simulated using a kMC, based on the site\nand transition state energies sampled from the DFT. The Cs HEGB diffusion\nexhibited an Arrhenius type diffusion in the range of 1200-1600{\\deg}C. The\ncomparison between HEGB results and the other studies suggests not only that\nthe GB diffusion dominates the bulk diffusion, but also that the HEGB is one of\nthe fastest grain boundary paths for the Cs diffusion. The diffusion\ncoefficients in HEGB are clearly a few orders of magnitude lower than the\nreported diffusion coefficients from in- and out-of- pile samples, suggesting\nthat other contributions are responsible, such as a radiation enhanced\ndiffusion.",
+                    "authors": "Hyunseok Ko, Izabela Szlufarska, Dane Morgan",
+                    "published": "2017-09-11",
+                    "updated": "2017-09-11",
+                    "primary_cat": "cond-mat.mtrl-sci",
+                    "cats": [
+                        "cond-mat.mtrl-sci",
+                        "nucl-th"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2308.06342v2",
+                    "title": "Mirror Diffusion Models",
+                    "abstract": "Diffusion models have successfully been applied to generative tasks in\nvarious continuous domains. However, applying diffusion to discrete categorical\ndata remains a non-trivial task. Moreover, generation in continuous domains\noften requires clipping in practice, which motivates the need for a theoretical\nframework for adapting diffusion to constrained domains. Inspired by the mirror\nLangevin algorithm for the constrained sampling problem, in this theoretical\nreport we propose Mirror Diffusion Models (MDMs). We demonstrate MDMs in the\ncontext of simplex diffusion and propose natural extensions to popular domains\nsuch as image and text generation.",
+                    "authors": "Jaesung Tae",
+                    "published": "2023-08-11",
+                    "updated": "2023-08-18",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2302.07261v2",
+                    "title": "Where to Diffuse, How to Diffuse, and How to Get Back: Automated Learning for Multivariate Diffusions",
+                    "abstract": "Diffusion-based generative models (DBGMs) perturb data to a target noise\ndistribution and reverse this process to generate samples. The choice of\nnoising process, or inference diffusion process, affects both likelihoods and\nsample quality. For example, extending the inference process with auxiliary\nvariables leads to improved sample quality. While there are many such\nmultivariate diffusions to explore, each new one requires significant\nmodel-specific analysis, hindering rapid prototyping and evaluation. In this\nwork, we study Multivariate Diffusion Models (MDMs). For any number of\nauxiliary variables, we provide a recipe for maximizing a lower-bound on the\nMDMs likelihood without requiring any model-specific analysis. We then\ndemonstrate how to parameterize the diffusion for a specified target noise\ndistribution; these two points together enable optimizing the inference\ndiffusion process. Optimizing the diffusion expands easy experimentation from\njust a few well-known processes to an automatic search over all linear\ndiffusions. To demonstrate these ideas, we introduce two new specific\ndiffusions as well as learn a diffusion process on the MNIST, CIFAR10, and\nImageNet32 datasets. We show learned MDMs match or surpass bits-per-dims (BPDs)\nrelative to fixed choices of diffusions for a given dataset and model\narchitecture.",
+                    "authors": "Raghav Singhal, Mark Goldstein, Rajesh Ranganath",
+                    "published": "2023-02-14",
+                    "updated": "2023-03-03",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "stat.ML"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2305.14671v2",
+                    "title": "A Survey of Diffusion Models in Natural Language Processing",
+                    "abstract": "This survey paper provides a comprehensive review of the use of diffusion\nmodels in natural language processing (NLP). Diffusion models are a class of\nmathematical models that aim to capture the diffusion of information or signals\nacross a network or manifold. In NLP, diffusion models have been used in a\nvariety of applications, such as natural language generation, sentiment\nanalysis, topic modeling, and machine translation. This paper discusses the\ndifferent formulations of diffusion models used in NLP, their strengths and\nlimitations, and their applications. We also perform a thorough comparison\nbetween diffusion models and alternative generative models, specifically\nhighlighting the autoregressive (AR) models, while also examining how diverse\narchitectures incorporate the Transformer in conjunction with diffusion models.\nCompared to AR models, diffusion models have significant advantages for\nparallel generation, text interpolation, token-level controls such as syntactic\nstructures and semantic contents, and robustness. Exploring further\npermutations of integrating Transformers into diffusion models would be a\nvaluable pursuit. Also, the development of multimodal diffusion models and\nlarge-scale diffusion language models with notable capabilities for few-shot\nlearning would be important directions for the future advance of diffusion\nmodels in NLP.",
+                    "authors": "Hao Zou, Zae Myung Kim, Dongyeop Kang",
+                    "published": "2023-05-24",
+                    "updated": "2023-06-14",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2106.04745v2",
+                    "title": "Evaluation of diffuse mismatch model for phonon scattering at disordered interfaces",
+                    "abstract": "Diffuse phonon scattering strongly affects the phonon transport through a\ndisordered interface. The often-used diffuse mismatch model assumes that\nphonons lose memory of their origin after being scattered by the interface.\nUsing mode-resolved atomic Green's function simulation, we demonstrate that\ndiffuse phonon scattering by a single disordered interface cannot make a phonon\nlose its memory and thus the applicability of diffusive mismatch model is\nlimited. An analytical expression for diffuse scattering probability based on\nthe continuum approximation is also derived and shown to work reasonably well\nat low frequencies.",
+                    "authors": "Qichen Song, Gang Chen",
+                    "published": "2021-06-09",
+                    "updated": "2021-08-04",
+                    "primary_cat": "cond-mat.mes-hall",
+                    "cats": [
+                        "cond-mat.mes-hall"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2202.05830v1",
+                    "title": "Learning Fast Samplers for Diffusion Models by Differentiating Through Sample Quality",
+                    "abstract": "Diffusion models have emerged as an expressive family of generative models\nrivaling GANs in sample quality and autoregressive models in likelihood scores.\nStandard diffusion models typically require hundreds of forward passes through\nthe model to generate a single high-fidelity sample. We introduce\nDifferentiable Diffusion Sampler Search (DDSS): a method that optimizes fast\nsamplers for any pre-trained diffusion model by differentiating through sample\nquality scores. We also present Generalized Gaussian Diffusion Models (GGDM), a\nfamily of flexible non-Markovian samplers for diffusion models. We show that\noptimizing the degrees of freedom of GGDM samplers by maximizing sample quality\nscores via gradient descent leads to improved sample quality. Our optimization\nprocedure backpropagates through the sampling process using the\nreparametrization trick and gradient rematerialization. DDSS achieves strong\nresults on unconditional image generation across various datasets (e.g., FID\nscores on LSUN church 128x128 of 11.6 with only 10 inference steps, and 4.82\nwith 20 steps, compared to 51.1 and 14.9 with strongest DDPM/DDIM baselines).\nOur method is compatible with any pre-trained diffusion model without\nfine-tuning or re-training required.",
+                    "authors": "Daniel Watson, William Chan, Jonathan Ho, Mohammad Norouzi",
+                    "published": "2022-02-11",
+                    "updated": "2022-02-11",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1708.06890v1",
+                    "title": "Collaborative Inference of Coexisting Information Diffusions",
+                    "abstract": "Recently, \\textit{diffusion history inference} has become an emerging\nresearch topic due to its great benefits for various applications, whose\npurpose is to reconstruct the missing histories of information diffusion traces\naccording to incomplete observations. The existing methods, however, often\nfocus only on single information diffusion trace, while in a real-world social\nnetwork, there often coexist multiple information diffusions over the same\nnetwork. In this paper, we propose a novel approach called Collaborative\nInference Model (CIM) for the problem of the inference of coexisting\ninformation diffusions. By exploiting the synergism between the coexisting\ninformation diffusions, CIM holistically models multiple information diffusions\nas a sparse 4th-order tensor called Coexisting Diffusions Tensor (CDT) without\nany prior assumption of diffusion models, and collaboratively infers the\nhistories of the coexisting information diffusions via a low-rank approximation\nof CDT with a fusion of heterogeneous constraints generated from additional\ndata sources. To improve the efficiency, we further propose an optimal\nalgorithm called Time Window based Parallel Decomposition Algorithm (TWPDA),\nwhich can speed up the inference without compromise on the accuracy by\nutilizing the temporal locality of information diffusions. The extensive\nexperiments conducted on real world datasets and synthetic datasets verify the\neffectiveness and efficiency of CIM and TWPDA.",
+                    "authors": "Yanchao Sun, Cong Qian, Ning Yang, Philip S. Yu",
+                    "published": "2017-08-23",
+                    "updated": "2017-08-23",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1905.04004v2",
+                    "title": "Well-posedness of a cross-diffusion population model with nonlocal diffusion",
+                    "abstract": "We prove the existence and uniqueness of solution of a nonlocal\ncross-diffusion competitive population model for two species. The model may be\nconsidered as a version, or even an approximation, of the paradigmatic\nShigesada-Kawasaki-Teramoto cross-diffusion model, in which the usual diffusion\ndifferential operator is replaced by an integral diffusion operator. The proof\nof existence of solutions is based on a compactness argument, while the\nuniqueness of solution is achieved through a duality technique.",
+                    "authors": "Gonzalo Galiano, Juli\u00e1n Velasco",
+                    "published": "2019-05-10",
+                    "updated": "2024-01-24",
+                    "primary_cat": "math.AP",
+                    "cats": [
+                        "math.AP"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2307.06272v1",
+                    "title": "Exposing the Fake: Effective Diffusion-Generated Images Detection",
+                    "abstract": "Image synthesis has seen significant advancements with the advent of\ndiffusion-based generative models like Denoising Diffusion Probabilistic Models\n(DDPM) and text-to-image diffusion models. Despite their efficacy, there is a\ndearth of research dedicated to detecting diffusion-generated images, which\ncould pose potential security and privacy risks. This paper addresses this gap\nby proposing a novel detection method called Stepwise Error for\nDiffusion-generated Image Detection (SeDID). Comprising statistical-based\n$\\text{SeDID}_{\\text{Stat}}$ and neural network-based\n$\\text{SeDID}_{\\text{NNs}}$, SeDID exploits the unique attributes of diffusion\nmodels, namely deterministic reverse and deterministic denoising computation\nerrors. Our evaluations demonstrate SeDID's superior performance over existing\nmethods when applied to diffusion models. Thus, our work makes a pivotal\ncontribution to distinguishing diffusion model-generated images, marking a\nsignificant step in the domain of artificial intelligence security.",
+                    "authors": "Ruipeng Ma, Jinhao Duan, Fei Kong, Xiaoshuang Shi, Kaidi Xu",
+                    "published": "2023-07-12",
+                    "updated": "2023-07-12",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.CR",
+                        "cs.LG"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2002.02101v1",
+                    "title": "Trace of anomalous diffusion in a biased quenched trap model",
+                    "abstract": "Diffusion on a quenched heterogeneous environment in the presence of bias is\nconsidered analytically. The first-passage-time statistics can be applied to\nobtain the drift and the diffusion coefficient in periodic quenched\nenvironments. We show several transition points at which sample-to-sample\nfluctuations of the drift or the diffusion coefficient remain large even when\nthe system size becomes large, i.e., non-self-averaging. Moreover, we find that\nthe disorder average of the diffusion coefficient diverges or becomes zero when\nthe corresponding annealed model generates superdiffusion or subdiffusion,\nrespectively. This result implies that anomalous diffusion in an annealed model\nis traced by anomaly of the diffusion coefficients in the corresponding\nquenched model.",
+                    "authors": "Takuma Akimoto, Keiji Saito",
+                    "published": "2020-02-06",
+                    "updated": "2020-02-06",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1609.09697v1",
+                    "title": "Anomalous diffusion in time-fluctuating non-stationary diffusivity landscapes",
+                    "abstract": "We investigate the ensemble and time averaged mean squared displacements for\nparticle diffusion in a simple model for disordered media by assuming that the\nlocal diffusivity is both fluctuating in time and has a deterministic average\ngrowth or decay in time. In this study we compare computer simulations of the\nstochastic Langevin equation for this random diffusion process with analytical\nresults. We explore the regimes of normal Brownian motion as well as anomalous\ndiffusion in the sub- and superdiffusive regimes. We also consider effects of\nthe inertial term on the particle motion. The investigation of the resulting\ndiffusion is performed for unconfined and confined motion.",
+                    "authors": "A. G. Cherstvy, R. Metzler",
+                    "published": "2016-09-30",
+                    "updated": "2016-09-30",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2402.01965v2",
+                    "title": "Analyzing Neural Network-Based Generative Diffusion Models through Convex Optimization",
+                    "abstract": "Diffusion models are becoming widely used in state-of-the-art image, video\nand audio generation. Score-based diffusion models stand out among these\nmethods, necessitating the estimation of score function of the input data\ndistribution. In this study, we present a theoretical framework to analyze\ntwo-layer neural network-based diffusion models by reframing score matching and\ndenoising score matching as convex optimization. Though existing diffusion\ntheory is mainly asymptotic, we characterize the exact predicted score function\nand establish the convergence result for neural network-based diffusion models\nwith finite data. This work contributes to understanding what neural\nnetwork-based diffusion model learns in non-asymptotic settings.",
+                    "authors": "Fangzhao Zhang, Mert Pilanci",
+                    "published": "2024-02-03",
+                    "updated": "2024-02-06",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "math.OC"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/0912.3770v1",
+                    "title": "SLE(6) and the geometry of diffusion fronts",
+                    "abstract": "We study the diffusion front for a natural two-dimensional model where many\nparticles starting at the origin diffuse independently. It turns out that this\nmodel can be described using properties of near-critical percolation, and\nprovides a natural example where critical fractal geometries spontaneously\narise.",
+                    "authors": "Pierre Nolin",
+                    "published": "2009-12-18",
+                    "updated": "2009-12-18",
+                    "primary_cat": "math.PR",
+                    "cats": [
+                        "math.PR"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2303.06574v2",
+                    "title": "Diffusion Models for Non-autoregressive Text Generation: A Survey",
+                    "abstract": "Non-autoregressive (NAR) text generation has attracted much attention in the\nfield of natural language processing, which greatly reduces the inference\nlatency but has to sacrifice the generation accuracy. Recently, diffusion\nmodels, a class of latent variable generative models, have been introduced into\nNAR text generation, showing an improved text generation quality. In this\nsurvey, we review the recent progress in diffusion models for NAR text\ngeneration. As the background, we first present the general definition of\ndiffusion models and the text diffusion models, and then discuss their merits\nfor NAR generation. As the core content, we further introduce two mainstream\ndiffusion models in existing work of text diffusion, and review the key designs\nof the diffusion process. Moreover, we discuss the utilization of pre-trained\nlanguage models (PLMs) for text diffusion models and introduce optimization\ntechniques for text data. Finally, we discuss several promising directions and\nconclude this paper. Our survey aims to provide researchers with a systematic\nreference of related research on text diffusion models for NAR generation. We\npresent our collection of text diffusion models at\nhttps://github.com/RUCAIBox/Awesome-Text-Diffusion-Models.",
+                    "authors": "Yifan Li, Kun Zhou, Wayne Xin Zhao, Ji-Rong Wen",
+                    "published": "2023-03-12",
+                    "updated": "2023-05-13",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/nlin/0212039v2",
+                    "title": "Front dynamics in reaction-diffusion systems with Levy flights: a fractional diffusion approach",
+                    "abstract": "The use of reaction-diffusion models rests on the key assumption that the\nunderlying diffusive process is Gaussian. However, a growing number of studies\nhave pointed out the prevalence of anomalous diffusion, and there is a need to\nunderstand the dynamics of reactive systems in the presence of this type of\nnon-Gaussian diffusion. Here we present a study of front dynamics in\nreaction-diffusion systems where anomalous diffusion is due to the presence of\nasymmetric Levy flights. Our approach consists of replacing the Laplacian\ndiffusion operator by a fractional diffusion operator, whose fundamental\nsolutions are Levy $\\alpha$-stable distributions. Numerical simulation of the\nfractional Fisher-Kolmogorov equation, and analytical arguments show that\nanomalous diffusion leads to the exponential acceleration of fronts and a\nuniversal power law decay, $x^{-\\alpha}$, of the tail, where $\\alpha$, the\nindex of the Levy distribution, is the order of the fractional derivative.",
+                    "authors": "D. del-Castillo-Negrete, B. A. Carreras, V. E. Lynch",
+                    "published": "2002-12-17",
+                    "updated": "2003-06-30",
+                    "primary_cat": "nlin.PS",
+                    "cats": [
+                        "nlin.PS",
+                        "nlin.CD"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2210.07677v1",
+                    "title": "TransFusion: Transcribing Speech with Multinomial Diffusion",
+                    "abstract": "Diffusion models have shown exceptional scaling properties in the image\nsynthesis domain, and initial attempts have shown similar benefits for applying\ndiffusion to unconditional text synthesis. Denoising diffusion models attempt\nto iteratively refine a sampled noise signal until it resembles a coherent\nsignal (such as an image or written sentence). In this work we aim to see\nwhether the benefits of diffusion models can also be realized for speech\nrecognition. To this end, we propose a new way to perform speech recognition\nusing a diffusion model conditioned on pretrained speech features.\nSpecifically, we propose TransFusion: a transcribing diffusion model which\niteratively denoises a random character sequence into coherent text\ncorresponding to the transcript of a conditioning utterance. We demonstrate\ncomparable performance to existing high-performing contrastive models on the\nLibriSpeech speech recognition benchmark. To the best of our knowledge, we are\nthe first to apply denoising diffusion to speech recognition. We also propose\nnew techniques for effectively sampling and decoding multinomial diffusion\nmodels. These are required because traditional methods of sampling from\nacoustic models are not possible with our new discrete diffusion approach. Code\nand trained models are available: https://github.com/RF5/transfusion-asr",
+                    "authors": "Matthew Baas, Kevin Eloff, Herman Kamper",
+                    "published": "2022-10-14",
+                    "updated": "2022-10-14",
+                    "primary_cat": "eess.AS",
+                    "cats": [
+                        "eess.AS",
+                        "cs.AI",
+                        "cs.SD"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2012.06816v1",
+                    "title": "Evaluation and Comparison of Diffusion Models with Motif Features",
+                    "abstract": "Diffusion models simulate the propagation of influence in networks. The\ndesign and evaluation of diffusion models has been subjective and empirical.\nWhen being applied to a network represented by a graph, the diffusion model\ngenerates a sequence of edges on which the influence flows, such sequence forms\na temporal network. In most scenarios, the statistical properties or the\ncharacteristics of a network are inferred by analyzing the temporal networks\ngenerated by diffusion models. To analyze real temporal networks, the motif has\nbeen proposed as a reliable feature. However, it is unclear how the network\ntopology and the diffusion model affect the motif feature of a generated\ntemporal network. In this paper, we adopt the motif feature to evaluate the\ntemporal graph generated by a diffusion model, thence the diffusion model\nitself. Two benchmarks for quantitively evaluating diffusion models with motif,\nstability and separability, are proposed and measured on numerous diffusion\nmodels. One motif-based metric is proposed to measure the similarity between\ndiffusion models. The experiments suggest that the motif of a generated\ntemporal network is dominated by the diffusion model, while the network\ntopology is almost ignored. This result indicates that more practical and\nreliable diffusion models have to be designed with delicacy in order to capture\nthe propagation patterns of real temporal networks.",
+                    "authors": "Fangqi Li",
+                    "published": "2020-12-12",
+                    "updated": "2020-12-12",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "cs.NI"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2304.05060v2",
+                    "title": "SPIRiT-Diffusion: Self-Consistency Driven Diffusion Model for Accelerated MRI",
+                    "abstract": "Diffusion models have emerged as a leading methodology for image generation\nand have proven successful in the realm of magnetic resonance imaging (MRI)\nreconstruction. However, existing reconstruction methods based on diffusion\nmodels are primarily formulated in the image domain, making the reconstruction\nquality susceptible to inaccuracies in coil sensitivity maps (CSMs). k-space\ninterpolation methods can effectively address this issue but conventional\ndiffusion models are not readily applicable in k-space interpolation. To\novercome this challenge, we introduce a novel approach called SPIRiT-Diffusion,\nwhich is a diffusion model for k-space interpolation inspired by the iterative\nself-consistent SPIRiT method. Specifically, we utilize the iterative solver of\nthe self-consistent term (i.e., k-space physical prior) in SPIRiT to formulate\na novel stochastic differential equation (SDE) governing the diffusion process.\nSubsequently, k-space data can be interpolated by executing the diffusion\nprocess. This innovative approach highlights the optimization model's role in\ndesigning the SDE in diffusion models, enabling the diffusion process to align\nclosely with the physics inherent in the optimization model, a concept referred\nto as model-driven diffusion. We evaluated the proposed SPIRiT-Diffusion method\nusing a 3D joint intracranial and carotid vessel wall imaging dataset. The\nresults convincingly demonstrate its superiority over image-domain\nreconstruction methods, achieving high reconstruction quality even at a\nsubstantial acceleration rate of 10.",
+                    "authors": "Zhuo-Xu Cui, Chentao Cao, Yue Wang, Sen Jia, Jing Cheng, Xin Liu, Hairong Zheng, Dong Liang, Yanjie Zhu",
+                    "published": "2023-04-11",
+                    "updated": "2024-04-20",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2209.05557v3",
+                    "title": "Blurring Diffusion Models",
+                    "abstract": "Recently, Rissanen et al., (2022) have presented a new type of diffusion\nprocess for generative modeling based on heat dissipation, or blurring, as an\nalternative to isotropic Gaussian diffusion. Here, we show that blurring can\nequivalently be defined through a Gaussian diffusion process with non-isotropic\nnoise. In making this connection, we bridge the gap between inverse heat\ndissipation and denoising diffusion, and we shed light on the inductive bias\nthat results from this modeling choice. Finally, we propose a generalized class\nof diffusion models that offers the best of both standard Gaussian denoising\ndiffusion and inverse heat dissipation, which we call Blurring Diffusion\nModels.",
+                    "authors": "Emiel Hoogeboom, Tim Salimans",
+                    "published": "2022-09-12",
+                    "updated": "2024-05-01",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.CV",
+                        "stat.ML"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1404.3573v1",
+                    "title": "\"Diffusing diffusivity\": A model for anomalous and \"anomalous yet Brownian\" diffusion",
+                    "abstract": "Wang et al. [PNAS 106 (2009) 15160] have found that in several systems the\nlinear time dependence of the mean-square displacement (MSD) of diffusing\ncolloidal particles, typical of normal diffusion, is accompanied by a\nnon-Gaussian displacement distribution (DisD), with roughly exponential tails\nat short times, a situation they termed \"anomalous yet Brownian\" diffusion. The\ndiversity of systems in which this is observed calls for a generic model. We\npresent such a model where there is \"diffusivity memory\" but no \"direction\nmemory\" in the particle trajectory, and we show that it leads to both a linear\nMSD and a non-Gaussian DisD at short times. In our model, the diffusivity is\nundergoing a (perhaps biased) random walk, hence the expression \"diffusing\ndiffusivity\". The DisD is predicted to be exactly exponential at short times if\nthe distribution of diffusivities is itself exponential, but an exponential\nremains a good fit to the DisD for a variety of diffusivity distributions.\nMoreover, our generic model can be modified to produce subdiffusion.",
+                    "authors": "Mykyta V. Chubynsky, Gary W. Slater",
+                    "published": "2014-04-14",
+                    "updated": "2014-04-14",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech",
+                        "cond-mat.soft"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2305.09605v1",
+                    "title": "Expressiveness Remarks for Denoising Diffusion Models and Samplers",
+                    "abstract": "Denoising diffusion models are a class of generative models which have\nrecently achieved state-of-the-art results across many domains. Gradual noise\nis added to the data using a diffusion process, which transforms the data\ndistribution into a Gaussian. Samples from the generative model are then\nobtained by simulating an approximation of the time reversal of this diffusion\ninitialized by Gaussian samples. Recent research has explored adapting\ndiffusion models for sampling and inference tasks. In this paper, we leverage\nknown connections to stochastic control akin to the F\\\"ollmer drift to extend\nestablished neural network approximation results for the F\\\"ollmer drift to\ndenoising diffusion models and samplers.",
+                    "authors": "Francisco Vargas, Teodora Reu, Anna Kerekes",
+                    "published": "2023-05-16",
+                    "updated": "2023-05-16",
+                    "primary_cat": "stat.ML",
+                    "cats": [
+                        "stat.ML",
+                        "cs.LG"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2301.00527v1",
+                    "title": "Diffusion Probabilistic Models for Scene-Scale 3D Categorical Data",
+                    "abstract": "In this paper, we learn a diffusion model to generate 3D data on a\nscene-scale. Specifically, our model crafts a 3D scene consisting of multiple\nobjects, while recent diffusion research has focused on a single object. To\nrealize our goal, we represent a scene with discrete class labels, i.e.,\ncategorical distribution, to assign multiple objects into semantic categories.\nThus, we extend discrete diffusion models to learn scene-scale categorical\ndistributions. In addition, we validate that a latent diffusion model can\nreduce computation costs for training and deploying. To the best of our\nknowledge, our work is the first to apply discrete and latent diffusion for 3D\ncategorical data on a scene-scale. We further propose to perform semantic scene\ncompletion (SSC) by learning a conditional distribution using our diffusion\nmodel, where the condition is a partial observation in a sparse point cloud. In\nexperiments, we empirically show that our diffusion models not only generate\nreasonable scenes, but also perform the scene completion task better than a\ndiscriminative model. Our code and models are available at\nhttps://github.com/zoomin-lee/scene-scale-diffusion",
+                    "authors": "Jumin Lee, Woobin Im, Sebin Lee, Sung-Eui Yoon",
+                    "published": "2023-01-02",
+                    "updated": "2023-01-02",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2306.07491v2",
+                    "title": "Exact sharp-fronted solutions for nonlinear diffusion on evolving domains",
+                    "abstract": "Models of diffusive processes that occur on evolving domains are frequently\nemployed to describe biological and physical phenomena, such as diffusion\nwithin expanding tissues or substrates. Previous investigations into these\nmodels either report numerical solutions or require an assumption of linear\ndiffusion to determine exact solutions. Unfortunately, numerical solutions do\nnot reveal the relationship between the model parameters and the solution\nfeatures. Additionally, experimental observations typically report the presence\nof sharp fronts, which are not captured by linear diffusion. Here we address\nboth limitations by presenting exact sharp-fronted solutions to a model of\ndegenerate nonlinear diffusion on a growing domain. We obtain the solution by\nidentifying a series of transformations that converts the model of a nonlinear\ndiffusive process on an evolving domain to a nonlinear diffusion equation on a\nfixed domain, which admits known exact solutions for certain choices of\ndiffusivity functions. We determine expressions for critical time scales and\ndomain growth rates such that the diffusive population never reaches the domain\nboundaries and hence the solution remains valid.",
+                    "authors": "Stuart T. Johnston, Matthew J. Simpson",
+                    "published": "2023-06-13",
+                    "updated": "2023-10-06",
+                    "primary_cat": "q-bio.PE",
+                    "cats": [
+                        "q-bio.PE"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2403.05794v2",
+                    "title": "Privacy-Preserving Diffusion Model Using Homomorphic Encryption",
+                    "abstract": "In this paper, we introduce a privacy-preserving stable diffusion framework\nleveraging homomorphic encryption, called HE-Diffusion, which primarily focuses\non protecting the denoising phase of the diffusion process. HE-Diffusion is a\ntailored encryption framework specifically designed to align with the unique\narchitecture of stable diffusion, ensuring both privacy and functionality. To\naddress the inherent computational challenges, we propose a novel\nmin-distortion method that enables efficient partial image encryption,\nsignificantly reducing the overhead without compromising the model's output\nquality. Furthermore, we adopt a sparse tensor representation to expedite\ncomputational operations, enhancing the overall efficiency of the\nprivacy-preserving diffusion process. We successfully implement HE-based\nprivacy-preserving stable diffusion inference. The experimental results show\nthat HE-Diffusion achieves 500 times speedup compared with the baseline method,\nand reduces time cost of the homomorphically encrypted inference to the minute\nlevel. Both the performance and accuracy of the HE-Diffusion are on par with\nthe plaintext counterpart. Our approach marks a significant step towards\nintegrating advanced cryptographic techniques with state-of-the-art generative\nmodels, paving the way for privacy-preserving and efficient image generation in\ncritical applications.",
+                    "authors": "Yaojian Chen, Qiben Yan",
+                    "published": "2024-03-09",
+                    "updated": "2024-05-02",
+                    "primary_cat": "cs.CR",
+                    "cats": [
+                        "cs.CR",
+                        "cs.AI"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1906.02405v1",
+                    "title": "Indirect interactions influence contact network structure and diffusion dynamics",
+                    "abstract": "Interaction patterns at the individual level influence the behaviour of\ndiffusion over contact networks. Most of the current diffusion models only\nconsider direct interactions among individuals to build underlying infectious\nitems transmission networks. However, delayed indirect interactions, where a\nsusceptible individual interacts with infectious items after the infected\nindividual has left the interaction space, can also cause transmission events.\nWe define a diffusion model called the same place different time transmission\n(SPDT) based diffusion that considers transmission links for these indirect\ninteractions. Our SPDT model changes the network dynamics where the\nconnectivity among individuals varies with the decay rates of link infectivity.\nWe investigate SPDT diffusion behaviours by simulating airborne disease\nspreading on data-driven contact networks. The SPDT model significantly\nincreases diffusion dynamics (particularly for networks with low link densities\nwhere indirect interactions create new infection pathways) and is capable of\nproducing realistic disease reproduction number. Our results show that the SPDT\nmodel is significantly more likely to lead to outbreaks compared to current\ndiffusion models with direct interactions. We find that the diffusion dynamics\nwith including indirect links are not reproducible by the current models,\nhighlighting the importance of the indirect links for predicting outbreaks.",
+                    "authors": "Md Shahzamal, Raja Jurdak, Bernard Mans, Frank de Hoog",
+                    "published": "2019-06-06",
+                    "updated": "2019-06-06",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "physics.soc-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2303.16203v3",
+                    "title": "Your Diffusion Model is Secretly a Zero-Shot Classifier",
+                    "abstract": "The recent wave of large-scale text-to-image diffusion models has\ndramatically increased our text-based image generation abilities. These models\ncan generate realistic images for a staggering variety of prompts and exhibit\nimpressive compositional generalization abilities. Almost all use cases thus\nfar have solely focused on sampling; however, diffusion models can also provide\nconditional density estimates, which are useful for tasks beyond image\ngeneration. In this paper, we show that the density estimates from large-scale\ntext-to-image diffusion models like Stable Diffusion can be leveraged to\nperform zero-shot classification without any additional training. Our\ngenerative approach to classification, which we call Diffusion Classifier,\nattains strong results on a variety of benchmarks and outperforms alternative\nmethods of extracting knowledge from diffusion models. Although a gap remains\nbetween generative and discriminative approaches on zero-shot recognition\ntasks, our diffusion-based approach has significantly stronger multimodal\ncompositional reasoning ability than competing discriminative approaches.\nFinally, we use Diffusion Classifier to extract standard classifiers from\nclass-conditional diffusion models trained on ImageNet. Our models achieve\nstrong classification performance using only weak augmentations and exhibit\nqualitatively better \"effective robustness\" to distribution shift. Overall, our\nresults are a step toward using generative over discriminative models for\ndownstream tasks. Results and visualizations at\nhttps://diffusion-classifier.github.io/",
+                    "authors": "Alexander C. Li, Mihir Prabhudesai, Shivam Duggal, Ellis Brown, Deepak Pathak",
+                    "published": "2023-03-28",
+                    "updated": "2023-09-13",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI",
+                        "cs.CV",
+                        "cs.NE",
+                        "cs.RO"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2305.01115v2",
+                    "title": "In-Context Learning Unlocked for Diffusion Models",
+                    "abstract": "We present Prompt Diffusion, a framework for enabling in-context learning in\ndiffusion-based generative models. Given a pair of task-specific example\nimages, such as depth from/to image and scribble from/to image, and a text\nguidance, our model automatically understands the underlying task and performs\nthe same task on a new query image following the text guidance. To achieve\nthis, we propose a vision-language prompt that can model a wide range of\nvision-language tasks and a diffusion model that takes it as input. The\ndiffusion model is trained jointly over six different tasks using these\nprompts. The resulting Prompt Diffusion model is the first diffusion-based\nvision-language foundation model capable of in-context learning. It\ndemonstrates high-quality in-context generation on the trained tasks and\ngeneralizes effectively to new, unseen vision tasks with their respective\nprompts. Our model also shows compelling text-guided image editing results. Our\nframework aims to facilitate research into in-context learning for computer\nvision. We share our code and pre-trained models at\nhttps://github.com/Zhendong-Wang/Prompt-Diffusion.",
+                    "authors": "Zhendong Wang, Yifan Jiang, Yadong Lu, Yelong Shen, Pengcheng He, Weizhu Chen, Zhangyang Wang, Mingyuan Zhou",
+                    "published": "2023-05-01",
+                    "updated": "2023-10-18",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1409.3132v1",
+                    "title": "Front propagation in reaction-diffusion systems with anomalous diffusion",
+                    "abstract": "A numerical study of the role of anomalous diffusion in front propagation in\nreaction-diffusion systems is presented. Three models of anomalous diffusion\nare considered: fractional diffusion, tempered fractional diffusion, and a\nmodel that combines fractional diffusion and regular diffusion. The reaction\nkinetics corresponds to a Fisher-Kolmogorov nonlinearity. The numerical method\nis based on a finite-difference operator splitting algorithm with an explicit\nEuler step for the time advance of the reaction kinetics, and a Crank-Nicholson\nsemi-implicit time step for the transport operator. The anomalous diffusion\noperators are discretized using an upwind, flux-conserving, Grunwald-Letnikov\nfinite-difference scheme applied to the regularized fractional derivatives.\nWith fractional diffusion of order $\\alpha$, fronts exhibit exponential\nacceleration, $a_L(t) \\sim e^{\\gamma t/\\alpha}$, and develop algebraic decaying\ntails, $\\phi \\sim 1/x^{\\alpha}$. In the case of tempered fractional diffusion,\nthis phenomenology prevails in the intermediate asymptotic regime\n  $\\left(\\chi t \\right)^{1/\\alpha} \\ll x \\ll 1/\\lambda$, where $1/\\lambda$ is\nthe scale of the tempering. Outside this regime, i.e. for $x > 1/\\lambda$, the\ntail exhibits the tempered decay $\\phi \\sim e^{-\\lambda x}/x^{\\alpha+1}$, and\nthe front velocity approaches the terminal speed $v_*=\n\\left(\\gamma-\\lambda^\\alpha \\chi\\right)/ \\lambda$. Of particular interest is\nthe study of the interplay of regular and fractional diffusion. It is shown\nthat the main role of regular diffusion is to delay the onset of front\nacceleration. In particular, the crossover time, $t_c$, to transition to the\naccelerated fractional regime exhibits a logarithmic scaling of the form $t_c\n\\sim \\log \\left(\\chi_d/\\chi_f\\right)$ where $\\chi_d$ and $\\chi_f$ are the\nregular and fractional diffusivities.",
+                    "authors": "D. del-Castillo-Negrete",
+                    "published": "2014-09-10",
+                    "updated": "2014-09-10",
+                    "primary_cat": "nlin.PS",
+                    "cats": [
+                        "nlin.PS",
+                        "cond-mat.stat-mech"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2401.17181v1",
+                    "title": "Transfer Learning for Text Diffusion Models",
+                    "abstract": "In this report, we explore the potential for text diffusion to replace\nautoregressive (AR) decoding for the training and deployment of large language\nmodels (LLMs). We are particularly interested to see whether pretrained AR\nmodels can be transformed into text diffusion models through a lightweight\nadaptation procedure we call ``AR2Diff''. We begin by establishing a strong\nbaseline setup for training text diffusion models. Comparing across multiple\narchitectures and pretraining objectives, we find that training a decoder-only\nmodel with a prefix LM objective is best or near-best across several tasks.\nBuilding on this finding, we test various transfer learning setups for text\ndiffusion models. On machine translation, we find that text diffusion\nunderperforms the standard AR approach. However, on code synthesis and\nextractive QA, we find diffusion models trained from scratch outperform AR\nmodels in many cases. We also observe quality gains from AR2Diff -- adapting AR\nmodels to use diffusion decoding. These results are promising given that text\ndiffusion is relatively underexplored and can be significantly faster than AR\ndecoding for long text generation.",
+                    "authors": "Kehang Han, Kathleen Kenealy, Aditya Barua, Noah Fiedel, Noah Constant",
+                    "published": "2024-01-30",
+                    "updated": "2024-01-30",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1506.05574v1",
+                    "title": "Information Diffusion issues",
+                    "abstract": "In this report there will be a discussion for Information Diffusion. There\nwill be discussions on what information diffusion is, its key characteristics\nand on several other aspects of these kinds of networks. This report will focus\non peer to peer models in information diffusion. There will be discussions on\nepidemic model, OSN and other details related to information diffusion.",
+                    "authors": "Jonathan Helmigh",
+                    "published": "2015-06-18",
+                    "updated": "2015-06-18",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2305.12377v1",
+                    "title": "The vanishing diffusion limit for an Oldroyd-B model in $\\mathbb{R}^2_+$",
+                    "abstract": "We consider the initial-boundary value problem for an incompressible\nOldroyd-B model with stress diffusion in two-dimensional upper half plane which\ndescribes the motion of viscoelastic polymeric fluids. From the physical point\nof view, the diffusive coefficient is several orders of magnitude smaller than\nother parameters in the model, and is usually assumed to be zero. However, the\nlink between the diffusive model and the standard one (zero diffusion) via\nvanishing diffusion limit is still unknown from the mathematical point of view,\nin particular for the problem with boundary. Some numerical results [13]\nsuggest that this should be true. In this work, we provide a rigorous\njustification for the vanishing diffusion in $L^\\infty$-norm.",
+                    "authors": "Yinghui Wang, Huanyao Wen",
+                    "published": "2023-05-21",
+                    "updated": "2023-05-21",
+                    "primary_cat": "math.AP",
+                    "cats": [
+                        "math.AP",
+                        "35Q35, 76A10, 76D10"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2305.08379v2",
+                    "title": "TESS: Text-to-Text Self-Conditioned Simplex Diffusion",
+                    "abstract": "Diffusion models have emerged as a powerful paradigm for generation,\nobtaining strong performance in various continuous domains. However, applying\ncontinuous diffusion models to natural language remains challenging due to its\ndiscrete nature and the need for a large number of diffusion steps to generate\ntext, making diffusion-based generation expensive. In this work, we propose\nText-to-text Self-conditioned Simplex Diffusion (TESS), a text diffusion model\nthat is fully non-autoregressive, employs a new form of self-conditioning, and\napplies the diffusion process on the logit simplex space rather than the\nlearned embedding space. Through extensive experiments on natural language\nunderstanding and generation tasks including summarization, text\nsimplification, paraphrase generation, and question generation, we demonstrate\nthat TESS outperforms state-of-the-art non-autoregressive models, requires\nfewer diffusion steps with minimal drop in performance, and is competitive with\npretrained autoregressive sequence-to-sequence models. We publicly release our\ncodebase at https://github.com/allenai/tess-diffusion.",
+                    "authors": "Rabeeh Karimi Mahabadi, Hamish Ivison, Jaesung Tae, James Henderson, Iz Beltagy, Matthew E. Peters, Arman Cohan",
+                    "published": "2023-05-15",
+                    "updated": "2024-02-21",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL",
+                        "cs.LG"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1308.3393v2",
+                    "title": "Cosmology with matter diffusion",
+                    "abstract": "We construct a viable cosmological model based on velocity diffusion of\nmatter particles. In order to ensure the conservation of the total\nenergy-momentum tensor in the presence of diffusion, we include a cosmological\nscalar field $\\phi$ which we identify with the dark energy component of the\nUniverse. The model is characterized by only one new degree of freedom, the\ndiffusion parameter $\\sigma$. The standard $\\Lambda$CDM model can be recovered\nby setting $\\sigma=0$. If diffusion takes place ($\\sigma >0$) the dynamics of\nthe matter and of the dark energy fields are coupled. We argue that the\nexistence of a diffusion mechanism in the Universe can serve as a theoretical\nmotivation for interacting models. We constrain the background dynamics of the\ndiffusion model with Supernovae, H(z) and BAO data. We also perform a\nperturbative analysis of this model in order to understand structure formation\nin the Universe. We calculate the impact of diffusion both on the CMB spectrum,\nwith particular attention to the integrated Sachs-Wolfe signal, and on the\nmatter power spectrum $P(k)$. The latter analysis places strong constraints on\nthe magnitude of the diffusion mechanism but does not rule out the model.",
+                    "authors": "Simone Calogero, Hermano Velten",
+                    "published": "2013-08-15",
+                    "updated": "2013-10-29",
+                    "primary_cat": "astro-ph.CO",
+                    "cats": [
+                        "astro-ph.CO"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2305.13122v1",
+                    "title": "Policy Representation via Diffusion Probability Model for Reinforcement Learning",
+                    "abstract": "Popular reinforcement learning (RL) algorithms tend to produce a unimodal\npolicy distribution, which weakens the expressiveness of complicated policy and\ndecays the ability of exploration. The diffusion probability model is powerful\nto learn complicated multimodal distributions, which has shown promising and\npotential applications to RL. In this paper, we formally build a theoretical\nfoundation of policy representation via the diffusion probability model and\nprovide practical implementations of diffusion policy for online model-free RL.\nConcretely, we character diffusion policy as a stochastic process, which is a\nnew approach to representing a policy. Then we present a convergence guarantee\nfor diffusion policy, which provides a theory to understand the multimodality\nof diffusion policy. Furthermore, we propose the DIPO which is an\nimplementation for model-free online RL with DIffusion POlicy. To the best of\nour knowledge, DIPO is the first algorithm to solve model-free online RL\nproblems with the diffusion model. Finally, extensive empirical results show\nthe effectiveness and superiority of DIPO on the standard continuous control\nMujoco benchmark.",
+                    "authors": "Long Yang, Zhixiong Huang, Fenghao Lei, Yucun Zhong, Yiming Yang, Cong Fang, Shiting Wen, Binbin Zhou, Zhouchen Lin",
+                    "published": "2023-05-22",
+                    "updated": "2023-05-22",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1212.2829v1",
+                    "title": "Spin diffusion in one-dimensional classical Heisenberg mode",
+                    "abstract": "The problem of spin diffusion is studied numerically in one-dimensional\nclassical Heisenberg model using a deterministic odd even spin precession\ndynamics. We demonstrate that spin diffusion in this model, like energy\ndiffusion, is normal and one obtains a long time diffusive tail in the decay of\nautocorrelation function (ACF). Some variations of the model with different\ncoupling schemes and with anisotropy are also studied and we find normal\ndiffusion in all of them. A systematic finite size analysis of the Heisenberg\nmodel also suggests diffusive spreading of fluctuation, contrary to previous\nclaims of anomalous diffusion.",
+                    "authors": "Debarshee Bagchi",
+                    "published": "2012-12-12",
+                    "updated": "2012-12-12",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2301.00059v2",
+                    "title": "Describing NMR chemical exchange by effective phase diffusion approach",
+                    "abstract": "This paper proposes an effective phase diffusion method to analyze chemical\nexchange in nuclear magnetic resonance (NMR). The chemical exchange involves\nspin jumps around different sites where the spin angular frequencies vary,\nwhich leads to a random phase walk viewed from the rotating frame reference.\nTherefore, the random walk in phase space can be treated by the effective phase\ndiffusion method. Both the coupled and uncoupled phase diffusions are\nconsidered; additionally, it includes normal diffusion as well as fractional\ndiffusion. Based on these phase diffusion equations, the line shape of NMR\nexchange spectrum can be analyzed. By comparing these theoretical results with\nthe conventional theory, this phase diffusion approach works for fast exchange,\nranging from slightly faster than intermediate exchange to very fast exchange.\nFor normal diffusion models, the theoretically predicted curves agree with\nthose predicted from traditional models in the literature, and the\ncharacteristic exchange time obtained from phase diffusion with a fixed jump\ntime is the same as that obtained from the conventional model. However, the\nphase diffusion with a monoexponential time distribution gives a characteristic\nexchange time constant which is half of that obtained from the traditional\nmodel. Additionally, the fractional diffusion obtains a significantly different\nline shape than that predicted based on normal diffusion.",
+                    "authors": "Guoxing Lin",
+                    "published": "2022-12-30",
+                    "updated": "2023-05-17",
+                    "primary_cat": "physics.chem-ph",
+                    "cats": [
+                        "physics.chem-ph",
+                        "cond-mat.stat-mech"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2207.09786v1",
+                    "title": "Non-Uniform Diffusion Models",
+                    "abstract": "Diffusion models have emerged as one of the most promising frameworks for\ndeep generative modeling. In this work, we explore the potential of non-uniform\ndiffusion models. We show that non-uniform diffusion leads to multi-scale\ndiffusion models which have similar structure to this of multi-scale\nnormalizing flows. We experimentally find that in the same or less training\ntime, the multi-scale diffusion model achieves better FID score than the\nstandard uniform diffusion model. More importantly, it generates samples $4.4$\ntimes faster in $128\\times 128$ resolution. The speed-up is expected to be\nhigher in higher resolutions where more scales are used. Moreover, we show that\nnon-uniform diffusion leads to a novel estimator for the conditional score\nfunction which achieves on par performance with the state-of-the-art\nconditional denoising estimator. Our theoretical and experimental findings are\naccompanied by an open source library MSDiff which can facilitate further\nresearch of non-uniform diffusion models.",
+                    "authors": "Georgios Batzolis, Jan Stanczuk, Carola-Bibiane Sch\u00f6nlieb, Christian Etmann",
+                    "published": "2022-07-20",
+                    "updated": "2022-07-20",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2211.08892v2",
+                    "title": "Fast Graph Generation via Spectral Diffusion",
+                    "abstract": "Generating graph-structured data is a challenging problem, which requires\nlearning the underlying distribution of graphs. Various models such as graph\nVAE, graph GANs, and graph diffusion models have been proposed to generate\nmeaningful and reliable graphs, among which the diffusion models have achieved\nstate-of-the-art performance. In this paper, we argue that running full-rank\ndiffusion SDEs on the whole graph adjacency matrix space hinders diffusion\nmodels from learning graph topology generation, and hence significantly\ndeteriorates the quality of generated graph data. To address this limitation,\nwe propose an efficient yet effective Graph Spectral Diffusion Model (GSDM),\nwhich is driven by low-rank diffusion SDEs on the graph spectrum space. Our\nspectral diffusion model is further proven to enjoy a substantially stronger\ntheoretical guarantee than standard diffusion models. Extensive experiments\nacross various datasets demonstrate that, our proposed GSDM turns out to be the\nSOTA model, by exhibiting both significantly higher generation quality and much\nless computational consumption than the baselines.",
+                    "authors": "Tianze Luo, Zhanfeng Mo, Sinno Jialin Pan",
+                    "published": "2022-11-16",
+                    "updated": "2022-11-19",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2402.13144v1",
+                    "title": "Neural Network Diffusion",
+                    "abstract": "Diffusion models have achieved remarkable success in image and video\ngeneration. In this work, we demonstrate that diffusion models can also\n\\textit{generate high-performing neural network parameters}. Our approach is\nsimple, utilizing an autoencoder and a standard latent diffusion model. The\nautoencoder extracts latent representations of a subset of the trained network\nparameters. A diffusion model is then trained to synthesize these latent\nparameter representations from random noise. It then generates new\nrepresentations that are passed through the autoencoder's decoder, whose\noutputs are ready to use as new subsets of network parameters. Across various\narchitectures and datasets, our diffusion process consistently generates models\nof comparable or improved performance over trained networks, with minimal\nadditional cost. Notably, we empirically find that the generated models perform\ndifferently with the trained networks. Our results encourage more exploration\non the versatile use of diffusion models.",
+                    "authors": "Kai Wang, Zhaopan Xu, Yukun Zhou, Zelin Zang, Trevor Darrell, Zhuang Liu, Yang You",
+                    "published": "2024-02-20",
+                    "updated": "2024-02-20",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.CV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2310.01221v2",
+                    "title": "Nonlocal diffusion model with maximum principle",
+                    "abstract": "In this paper, we propose nonlocal diffusion models with Dirichlet boundary.\nThese nonlocal diffusion models preserve the maximum principle and also have\ncorresponding variational form. With these good properties, It is relatively\neasy to prove the well-posedness and the vanishing nonlocality convergence.\nFurthermore, by specifically designed weight function, we can get a nonlocal\ndiffusion model with second order convergence which is optimal for nonlocal\ndiffusion models.",
+                    "authors": "Zuoqiang Shi",
+                    "published": "2023-10-02",
+                    "updated": "2023-10-12",
+                    "primary_cat": "math.AP",
+                    "cats": [
+                        "math.AP",
+                        "cs.NA",
+                        "math.NA"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/math/0204289v1",
+                    "title": "On diffusion approximation with discontinuous coefficients",
+                    "abstract": "Convergence of stochastic processes with jumps to diffusion processes is\ninvestigated in the case when the limit process has discontinuous coefficients.\n  An example is given in which the diffusion approximation of a queueing model\nyields a diffusion process with discontinuous diffusion and drift coefficients.",
+                    "authors": "N. V. Krylov, R. Liptser",
+                    "published": "2002-04-24",
+                    "updated": "2002-04-24",
+                    "primary_cat": "math.PR",
+                    "cats": [
+                        "math.PR",
+                        "math.SG",
+                        "60B10; 60K25}"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2212.10777v4",
+                    "title": "Hierarchically branched diffusion models leverage dataset structure for class-conditional generation",
+                    "abstract": "Class-labeled datasets, particularly those common in scientific domains, are\nrife with internal structure, yet current class-conditional diffusion models\nignore these relationships and implicitly diffuse on all classes in a flat\nfashion. To leverage this structure, we propose hierarchically branched\ndiffusion models as a novel framework for class-conditional generation.\nBranched diffusion models rely on the same diffusion process as traditional\nmodels, but learn reverse diffusion separately for each branch of a hierarchy.\nWe highlight several advantages of branched diffusion models over the current\nstate-of-the-art methods for class-conditional diffusion, including extension\nto novel classes in a continual-learning setting, a more sophisticated form of\nanalogy-based conditional generation (i.e. transmutation), and a novel\ninterpretability into the generation process. We extensively evaluate branched\ndiffusion models on several benchmark and large real-world scientific datasets\nspanning many data modalities.",
+                    "authors": "Alex M. Tseng, Max Shen, Tommaso Biancalani, Gabriele Scalia",
+                    "published": "2022-12-21",
+                    "updated": "2024-02-01",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2110.14851v1",
+                    "title": "Behavior of Spiral Wave Spectra with a Rank-Deficient Diffusion Matrix",
+                    "abstract": "Spiral waves emerge in numerous pattern forming systems and are commonly\nmodeled with reaction-diffusion systems. Some systems used to model biological\nprocesses, such as ion-channel models, fall under the reaction-diffusion\ncategory and often have one or more non-diffusing species which results in a\nrank-deficient diffusion matrix. Previous theoretical research focused on\nspiral spectra for strictly positive diffusion matrices. In this paper, we use\na general two-variable reaction-diffusion system to compare the essential and\nabsolute spectra of spiral waves for strictly positive and rank-deficient\ndiffusion matrices. We show that the essential spectrum is not continuous in\nthe limit of vanishing diffusion in one component. Moreover, we predict\nlocations for the absolute spectrum in the case of a non-diffusing slow\nvariable. Predictions are confirmed numerically for the Barkley and Karma\nmodels.",
+                    "authors": "Stephanie Dodson, Bjorn Sandstede",
+                    "published": "2021-10-28",
+                    "updated": "2021-10-28",
+                    "primary_cat": "math.DS",
+                    "cats": [
+                        "math.DS"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2010.02514v1",
+                    "title": "Diffusion model and analysis of diffusion process at lagrangian method",
+                    "abstract": "Based on Fick's 2nd law the development of moving particle semi-implicit\nmethod for predicting diffusion process is proposed in this study",
+                    "authors": "Ziqi Zhou",
+                    "published": "2020-10-06",
+                    "updated": "2020-10-06",
+                    "primary_cat": "physics.flu-dyn",
+                    "cats": [
+                        "physics.flu-dyn"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/0910.2253v1",
+                    "title": "Linearized Kompaneetz equation as a relativistic diffusion",
+                    "abstract": "We show that Kompaneetz equation describing photon diffusion in an\nenvironment of an electron gas, when linearized around its equilibrium\ndistribution, coincides with the relativistic diffusion discussed in recent\npublications. The model of the relativistic diffusion is related to soluble\nmodels of imaginary time quantum mechanics. We suggest some non-linear\ngeneralizations of the relativistic diffusion equation and their astrophysical\napplications (in particular to the Sunyaev-Zeldovich effect).",
+                    "authors": "Z. Haba",
+                    "published": "2009-10-12",
+                    "updated": "2009-10-12",
+                    "primary_cat": "astro-ph.CO",
+                    "cats": [
+                        "astro-ph.CO"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2312.14589v1",
+                    "title": "Non-Denoising Forward-Time Diffusions",
+                    "abstract": "The scope of this paper is generative modeling through diffusion processes.\nAn approach falling within this paradigm is the work of Song et al. (2021),\nwhich relies on a time-reversal argument to construct a diffusion process\ntargeting the desired data distribution. We show that the time-reversal\nargument, common to all denoising diffusion probabilistic modeling proposals,\nis not necessary. We obtain diffusion processes targeting the desired data\ndistribution by taking appropriate mixtures of diffusion bridges. The resulting\ntransport is exact by construction, allows for greater flexibility in choosing\nthe dynamics of the underlying diffusion, and can be approximated by means of a\nneural network via novel training objectives. We develop a unifying view of the\ndrift adjustments corresponding to our and to time-reversal approaches and make\nuse of this representation to inspect the inner workings of diffusion-based\ngenerative models. Finally, we leverage on scalable simulation and inference\ntechniques common in spatial statistics to move beyond fully factorial\ndistributions in the underlying diffusion dynamics. The methodological advances\ncontained in this work contribute toward establishing a general framework for\ngenerative modeling based on diffusion processes.",
+                    "authors": "Stefano Peluchetti",
+                    "published": "2023-12-22",
+                    "updated": "2023-12-22",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "stat.ML"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2111.03914v2",
+                    "title": "A systematic approach for modeling a nonlocal eddy diffusivity",
+                    "abstract": "This study considers advective and diffusive transport of passive scalar\nfields by spatially-varying incompressible flows. Prior studies have shown that\nthe eddy diffusivities governing the mean field transport in such systems can\ngenerally be nonlocal in space and time. While for many flows nonlocal eddy\ndiffusivities are more accurate than commonly-used Boussinesq eddy\ndiffusivities, nonlocal eddy diffusivities are often computationally\ncost-prohibitive to obtain and difficult to implement in practice. We develop a\nsystematic and more cost-effective approach for modeling nonlocal eddy\ndiffusivities using matched moment inverse (MMI) operators. These operators are\nconstructed using only a few leading-order moments of the exact nonlocal eddy\ndiffusivity kernel, which can be easily computed using the inverse macroscopic\nforcing method (IMFM) (Mani and Park (2021)). The resulting reduced-order\nmodels for the mean fields that incorporate the modeled eddy diffusivities\noften improve Boussinesq-limit models since they capture leading-order nonlocal\neffects. But more importantly, these models can be expressed as partial\ndifferential equations that are readily solvable using existing computational\nfluid dynamics capabilities rather than as integro-partial differential\nequations.",
+                    "authors": "Jessie Liu, Hannah Williams, Ali Mani",
+                    "published": "2021-11-06",
+                    "updated": "2023-06-28",
+                    "primary_cat": "physics.flu-dyn",
+                    "cats": [
+                        "physics.flu-dyn"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1906.02856v1",
+                    "title": "Diffusion on dynamic contact networks with indirect transmission links",
+                    "abstract": "Modelling diffusion processes on dynamic contact networks is an important\nresearch area for epidemiology, marketing, cybersecurity, and ecology. However,\ncurrent diffusion models cannot capture transmissions occurring for indirect\ninteractions. For example, an airborne infected individual releases infectious\nparticles at locations that can suspend in the air and infect susceptible\nindividuals arriving even after the infected individual left. Thus, current\ndiffusion models miss transmissions during indirect interactions. In this\nthesis, a novel diffusion model called the same place different time\ntransmission based diffusion (SPDT) is introduced to take into account the\ntransmissions through indirect interactions. The behaviour of SPDT diffusion is\nanalysed on real dynamic contact networks and a significant amplification in\ndiffusion dynamics is observed. The SPDT model also introduces some novel\nbehaviours different from current diffusion models. In this work, a new SPDT\ngraph model is also developed to generate synthetic traces to explore SPDT\ndiffusion in several scenarios. The analysis shows that the emergence of new\ndiffusion becomes common thanks to the inclusion of indirect transmissions\nwithin the SPDT model. This work finally investigates how diffusion can be\ncontrolled and develops new methods to hinder diffusion.",
+                    "authors": "Md Shahzamal",
+                    "published": "2019-06-07",
+                    "updated": "2019-06-07",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "physics.soc-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2307.13949v1",
+                    "title": "How Does Diffusion Influence Pretrained Language Models on Out-of-Distribution Data?",
+                    "abstract": "Transformer-based pretrained language models (PLMs) have achieved great\nsuccess in modern NLP. An important advantage of PLMs is good\nout-of-distribution (OOD) robustness. Recently, diffusion models have attracted\na lot of work to apply diffusion to PLMs. It remains under-explored how\ndiffusion influences PLMs on OOD data. The core of diffusion models is a\nforward diffusion process which gradually applies Gaussian noise to inputs, and\na reverse denoising process which removes noise. The noised input\nreconstruction is a fundamental ability of diffusion models. We directly\nanalyze OOD robustness by measuring the reconstruction loss, including testing\nthe abilities to reconstruct OOD data, and to detect OOD samples. Experiments\nare conducted by analyzing different training parameters and data statistical\nfeatures on eight datasets. It shows that finetuning PLMs with diffusion\ndegrades the reconstruction ability on OOD data. The comparison also shows that\ndiffusion models can effectively detect OOD samples, achieving state-of-the-art\nperformance in most of the datasets with an absolute accuracy improvement up to\n18%. These results indicate that diffusion reduces OOD robustness of PLMs.",
+                    "authors": "Huazheng Wang, Daixuan Cheng, Haifeng Sun, Jingyu Wang, Qi Qi, Jianxin Liao, Jing Wang, Cong Liu",
+                    "published": "2023-07-26",
+                    "updated": "2023-07-26",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL",
+                        "cs.AI"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1701.00257v2",
+                    "title": "Analyzing PFG anisotropic anomalous diffusions by instantaneous signal attenuation method",
+                    "abstract": "Anomalous diffusion has been investigated in many systems. Pulsed field\ngradient (PFG) anomalous diffusion is much more complicated than PFG normal\ndiffusion. There have been many theoretical and experimental studies for PFG\nisotropic anomalous diffusion, but there are very few theoretical treatments\nreported for anisotropic anomalous diffusion. Currently, there is not a general\nPFG signal attenuation expression, which includes the finite gradient pulse\neffect and can treat all three types of anisotropic fractional diffusions:\ngeneral fractional diffusion, time fractional diffusion, and space-fractional\ndiffusion. In this paper, the recently developed instantaneous signal\nattenuation (ISA) method was applied to obtain PFG signal attenuation\nexpression for free and restricted anisotropic anomalous diffusion with two\nmodels: fractal derivative and fractional derivative models. The obtained PFG\nsignal attenuation expression for anisotropic anomalous diffusion can reduce to\nthe reported result for PFG anisotropic normal diffusion. The results can also\nreduce to reported PFG isotropic anomalous diffusion results obtained by\neffective phase shift diffusion equation method and instantaneous signal\nattenuation method. For anisotropic space-fractional diffusion, the obtained\nresult agrees with that obtained by the modified Bloch equation method.\nAdditionally, The PFG signal attenuation expressions for free and restricted\nanisotropic curvilinear diffusions were derived by the traditional method, the\nresults of which agree with the PFG anisotropic fractional diffusion results\nbased on the fractional derivative model. The powder pattern of PFG anisotropic\ndiffusion was also discussed. The results here improve our understanding of PFG\nanomalous diffusion, and provide new formalisms for PFG anisotropic anomalous\ndiffusion in NMR and MRI.",
+                    "authors": "Guoxing Lin",
+                    "published": "2017-01-01",
+                    "updated": "2017-01-05",
+                    "primary_cat": "physics.chem-ph",
+                    "cats": [
+                        "physics.chem-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1603.05605v1",
+                    "title": "Multiscale modeling of diffusion in a crowded environment",
+                    "abstract": "We present a multiscale approach to model diffusion in a crowded environment\nand its effect on the reaction rates. Diffusion in biological systems is often\nmodeled by a discrete space jump process in order to capture the inherent noise\nof biological systems, which becomes important in the low copy number regime.\nTo model diffusion in the crowded cell environment efficiently, we compute the\njump rates in this mesoscopic model from local first exit times, which account\nfor the microscopic positions of the crowding molecules, while the diffusing\nmolecules jump on a coarser Cartesian grid. We then extract a macroscopic\ndescription from the resulting jump rates, where the excluded volume effect is\nmodeled by a diffusion equation with space dependent diffusion coefficient. The\ncrowding molecules can be of arbitrary shape and size and numerical experiments\ndemonstrate that those factors together with the size of the diffusing molecule\nplay a crucial role on the magnitude of the decrease in diffusive motion. When\ncorrecting the reaction rates for the altered diffusion we can show that\nmolecular crowding either enhances or inhibits chemical reactions depending on\nlocal fluctuations of the obstacle density.",
+                    "authors": "Lina Meinecke",
+                    "published": "2016-03-12",
+                    "updated": "2016-03-12",
+                    "primary_cat": "q-bio.SC",
+                    "cats": [
+                        "q-bio.SC",
+                        "math.NA",
+                        "92-08"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1009.5965v1",
+                    "title": "Sensitivity of a Babcock-Leighton Flux-Transport Dynamo to Magnetic Diffusivity Profiles",
+                    "abstract": "We study the influence of various magnetic diffusivity profiles on the\nevolution of the poloidal and toroidal magnetic fields in a kinematic flux\ntransport dynamo model for the Sun. The diffusivity is a poorly understood\ningredient in solar dynamo models. We mathematically construct various\ntheoretical profiles of the depth-dependent diffusivity, based on constraints\nfrom mixing length theory and turbulence, and on comparisons of poloidal field\nevolution on the Sun with that from the flux-transport dynamo model.\n  We then study the effect of each diffusivity profile in the cyclic evolution\nof the magnetic fields in the Sun, by solving the mean-field dynamo equations.\nWe investigate effects on the solar cycle periods, the maximum tachocline field\nstrengths, and the evolution of the toroidal and poloidal field structures\ninside the convection zone, due to different diffusivity profiles.\n  We conduct three experiments: (I) comparing very different magnetic\ndiffusivity profiles; (II) comparing different locations of diffusivity\ngradient near the tachocline for the optimal profile; and (III) comparing\ndifferent slopes of diffusivity gradient for an optimal profile.\n  Based on these simulations, we discuss which aspects of depth-dependent\ndiffusivity profiles may be most relevant for magnetic flux evolution in the\nSun, and how certain observations could help improve knowledge of this dynamo\ningredient.",
+                    "authors": "E. J. Zita",
+                    "published": "2010-09-29",
+                    "updated": "2010-09-29",
+                    "primary_cat": "astro-ph.SR",
+                    "cats": [
+                        "astro-ph.SR",
+                        "physics.flu-dyn"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1812.07249v1",
+                    "title": "A unifying approach to first-passage time distributions in diffusing diffusivity and switching diffusion models",
+                    "abstract": "We propose a unifying theoretical framework for the analysis of first-passage\ntime distributions in two important classes of stochastic processes in which\nthe diffusivity of a particle evolves randomly in time. In the first class of\n\"diffusing diffusivity\" models, the diffusivity changes continuously via a\nprescribed stochastic equation. In turn, the diffusivity switches randomly\nbetween discrete values in the second class of \"switching diffusion\" models.\nFor both cases, we quantify the impact of the diffusivity dynamics onto the\nfirst-passage time distribution of a particle via the moment-generating\nfunction of the integrated diffusivity. We provide general formulas and some\nexplicit solutions for some particular cases of practical interest.",
+                    "authors": "D. S. Grebenkov",
+                    "published": "2018-12-18",
+                    "updated": "2018-12-18",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech",
+                        "physics.bio-ph",
+                        "physics.chem-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1908.03076v3",
+                    "title": "The strategy of survival for a competition between normal and anomalous diffusion",
+                    "abstract": "In this paper, we study the competition of two diffusion processes for\nachieving the maximum possible diffusion in an area. This competition, however,\ndoes not occur in the same circumstance; one of these processes is a normal\ndiffusion with a higher growth rate, and another one is an anomalous diffusion\nwith a lower growth rate. The trivial solution of the proposed model suggests\nthat the winner is the one with the higher growth rate. But, the question is:\nwhat characteristics and strategies should the second diffusion include to\nprolong the survival in such a competition? The studied diffusion equations\ncorrespond to the SI model such that the anomalous diffusion has memory\ndescribed by a fractional order derivative. The strategy promise that anomalous\ndiffusion reaches maximum survival in case of forgetting some parts of the\nmemory. This model can represent some of real phenomena, such as the contest of\ntwo companies in a market share, the spreading of two epidemic diseases, the\ndiffusion of two species, or any reaction-diffusion related to real-world\ncompetition.",
+                    "authors": "Moein Khalighi, Jamshid Ardalankia, Abbas Karimi Rizi, Haleh Ebadi, Gholamreza Jafari",
+                    "published": "2019-08-07",
+                    "updated": "2020-10-18",
+                    "primary_cat": "physics.soc-ph",
+                    "cats": [
+                        "physics.soc-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2404.08926v2",
+                    "title": "Diffusion Models Meet Remote Sensing: Principles, Methods, and Perspectives",
+                    "abstract": "As a newly emerging advance in deep generative models, diffusion models have\nachieved state-of-the-art results in many fields, including computer vision,\nnatural language processing, and molecule design. The remote sensing community\nhas also noticed the powerful ability of diffusion models and quickly applied\nthem to a variety of tasks for image processing. Given the rapid increase in\nresearch on diffusion models in the field of remote sensing, it is necessary to\nconduct a comprehensive review of existing diffusion model-based remote sensing\npapers, to help researchers recognize the potential of diffusion models and\nprovide some directions for further exploration. Specifically, this paper first\nintroduces the theoretical background of diffusion models, and then\nsystematically reviews the applications of diffusion models in remote sensing,\nincluding image generation, enhancement, and interpretation. Finally, the\nlimitations of existing remote sensing diffusion models and worthy research\ndirections for further exploration are discussed and summarized.",
+                    "authors": "Yidan Liu, Jun Yue, Shaobo Xia, Pedram Ghamisi, Weiying Xie, Leyuan Fang",
+                    "published": "2024-04-13",
+                    "updated": "2024-04-17",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1503.03201v2",
+                    "title": "Fractional Diffusion Equations for Lattice and Continuum: Grunwald-Letnikov Differences and Derivatives Approach",
+                    "abstract": "Fractional diffusion equations for three-dimensional lattice models based on\nfractional-order differences of the Grunwald-Letnikov type are suggested. These\nlattice fractional diffusion equations contain difference operators that\ndescribe long-range jumps from one lattice site to other. In continuum limit,\nthe suggested lattice diffusion equations with non-integer order differences\ngive the diffusion equations with the Grunwald-Letnikov fractional derivatives\nfor continuum. We propose a consistent derivation of the fractional diffusion\nequation with the fractional derivatives of Grunwald-Letnikov type. The\nsuggested lattice diffusion equations can be considered as a new\nmicrostructural basis of space-fractional diffusion in nonlocal media.",
+                    "authors": "Vasily E. Tarasov",
+                    "published": "2015-03-11",
+                    "updated": "2015-03-12",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2305.16269v1",
+                    "title": "UDPM: Upsampling Diffusion Probabilistic Models",
+                    "abstract": "In recent years, Denoising Diffusion Probabilistic Models (DDPM) have caught\nsignificant attention. By composing a Markovian process that starts in the data\ndomain and then gradually adds noise until reaching pure white noise, they\nachieve superior performance in learning data distributions. Yet, these models\nrequire a large number of diffusion steps to produce aesthetically pleasing\nsamples, which is inefficient. In addition, unlike common generative\nadversarial networks, the latent space of diffusion models is not\ninterpretable. In this work, we propose to generalize the denoising diffusion\nprocess into an Upsampling Diffusion Probabilistic Model (UDPM), in which we\nreduce the latent variable dimension in addition to the traditional noise level\naddition. As a result, we are able to sample images of size $256\\times 256$\nwith only 7 diffusion steps, which is less than two orders of magnitude\ncompared to standard DDPMs. We formally develop the Markovian diffusion\nprocesses of the UDPM, and demonstrate its generation capabilities on the\npopular FFHQ, LSUN horses, ImageNet, and AFHQv2 datasets. Another favorable\nproperty of UDPM is that it is very easy to interpolate its latent space, which\nis not the case with standard diffusion models. Our code is available online\n\\url{https://github.com/shadyabh/UDPM}",
+                    "authors": "Shady Abu-Hussein, Raja Giryes",
+                    "published": "2023-05-25",
+                    "updated": "2023-05-25",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.LG",
+                        "eess.IV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1801.09352v1",
+                    "title": "Distributed order Hausdorff derivative diffusion model to characterize non-Fickian diffusion in porous media",
+                    "abstract": "Many theoretical and experimental results show that solute transport in\nheterogeneous porous media exhibits multi-scaling behaviors. To describe such\nnon-Fickian diffusions, this work provides a distributed order Hausdorff\ndiffusion model to describe the tracer transport in porous media. This model is\nproved to be equivalent with the diffusion equation model with a nonlinear time\ndependent diffusion coefficient. In conjunction with the structural derivative,\nits mean squared displacement (MSD) of the tracer particles is explicitly\nderived as a dilogarithm function when the weight function of the order\ndistribution is a linear function of the time derivative order. This model can\ncapture both accelerating and decelerating anomalous and ultraslow diffusions\nby varying the weight parameter c. In this study, the tracer transport in\nwater-filled pore spaces of two-dimensional Euclidean is demonstrated as a\ndecelerating sub-diffusion, and can well be described by the distributed order\nHausdorff diffusion model with c = 1.73. While the Hausdorff diffusion model\ncan accurately fit the sub-diffusion experimental data of the tracer transport\nin the pore-solid prefractal porous media.",
+                    "authors": "Yingjie Liang, Wen Chen, Wei Xu, HongGuang Sun",
+                    "published": "2018-01-29",
+                    "updated": "2018-01-29",
+                    "primary_cat": "physics.flu-dyn",
+                    "cats": [
+                        "physics.flu-dyn"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2104.13565v2",
+                    "title": "Generalisation of continuous time random walk to anomalous diffusion MRI models with an age-related evaluation of human corpus callosum",
+                    "abstract": "Diffusion MRI measures of the human brain provide key insight into\nmicrostructural variations across individuals and into the impact of central\nnervous system diseases and disorders. One approach to extract information from\ndiffusion signals has been to use biologically relevant analytical models to\nlink millimetre scale diffusion MRI measures with microscale influences. The\nother approach has been to represent diffusion as an anomalous transport\nprocess and infer microstructural information from the different anomalous\ndiffusion equation parameters. In this study, we investigated how parameters of\nvarious anomalous diffusion models vary with age in the human brain white\nmatter, particularly focusing on the corpus callosum. We first unified several\nestablished anomalous diffusion models (the super-diffusion, sub-diffusion,\nquasi-diffusion and fractional Bloch-Torrey models) under the continuous time\nrandom walk modelling framework. This unification allows a consistent parameter\nfitting strategy to be applied from which meaningful model parameter\ncomparisons can be made. We then provided a novel way to derive the diffusional\nkurtosis imaging (DKI) model, which is shown to be a degree two approximation\nof the sub-diffusion model. This link between the DKI and sub-diffusion models\nled to a new robust technique for generating maps of kurtosis and diffusivity\nusing the sub-diffusion parameters \\b{eta}_SUB and D_SUB. Superior tissue\ncontrast is achieved in kurtosis maps based on the sub-diffusion model. 7T\ndiffusion weighted MRI data for 65 healthy participants in the age range 19-78\nyears was used in this study. Results revealed that anomalous diffusion model\nparameters {\\alpha} and \\b{eta} have shown consistent positive correlation with\nage in the corpus callosum, indicating {\\alpha} and \\b{eta} are sensitive to\ntissue microstructural changes in aging.",
+                    "authors": "Qianqian Yang, David C. Reutens, Viktor Vegh",
+                    "published": "2021-04-28",
+                    "updated": "2022-01-17",
+                    "primary_cat": "physics.med-ph",
+                    "cats": [
+                        "physics.med-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1907.09989v1",
+                    "title": "Rogue Heat and Diffusion Waves",
+                    "abstract": "In this paper, we numerically show and discuss the existence and\ncharacteristics of rogue heat and diffusion waves. More specifically, we use\ntwo different nonlinear heat (diffusion) models and show that modulation\ninstability leads to the generation of unexpected and large fluctuations in the\nframe of these models. These fluctuations can be named as rogue heat\n(diffusion) waves. We discuss the properties and statistics of such rogue\nwaves. Our results can find many important applications in many branches such\nas the nonlinear heat transfer, turbulence, financial mathematics, chemical or\nbiological diffusion, nuclear reactions, subsurface water infiltration, and\npore water pressure diffusion modeled in the frame of nonlinear Terzaghi\nconsolidation models, just to name a few.",
+                    "authors": "Cihan Bayindir",
+                    "published": "2019-07-18",
+                    "updated": "2019-07-18",
+                    "primary_cat": "nlin.PS",
+                    "cats": [
+                        "nlin.PS",
+                        "physics.flu-dyn"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/0805.0647v1",
+                    "title": "Scaling of Rough Surfaces: Effects of Surface Diffusion on Growth and Roughness Exponents",
+                    "abstract": "Random deposition model with surface diffusion over several next nearest\nneighbours is studied. The results agree with the results obtained by Family\nfor the case of nearest neighbour diffusion [F. Family, J. Phys. A 19(8), L441,\n1986]. However for larger diffusion steps, the growth exponent and the\nroughness exponent show interesting dependence on diffusion length.",
+                    "authors": "Baisakhi Mal, Subhankar Ray, J. Shamanna",
+                    "published": "2008-05-06",
+                    "updated": "2008-05-06",
+                    "primary_cat": "cond-mat.soft",
+                    "cats": [
+                        "cond-mat.soft",
+                        "cond-mat.stat-mech"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2403.15766v1",
+                    "title": "BEND: Bagging Deep Learning Training Based on Efficient Neural Network Diffusion",
+                    "abstract": "Bagging has achieved great success in the field of machine learning by\nintegrating multiple base classifiers to build a single strong classifier to\nreduce model variance. The performance improvement of bagging mainly relies on\nthe number and diversity of base classifiers. However, traditional deep\nlearning model training methods are expensive to train individually and\ndifficult to train multiple models with low similarity in a restricted dataset.\nRecently, diffusion models, which have been tremendously successful in the\nfields of imaging and vision, have been found to be effective in generating\nneural network model weights and biases with diversity. We creatively propose a\nBagging deep learning training algorithm based on Efficient Neural network\nDiffusion (BEND). The originality of BEND comes from the first use of a neural\nnetwork diffusion model to efficiently build base classifiers for bagging. Our\napproach is simple but effective, first using multiple trained model weights\nand biases as inputs to train autoencoder and latent diffusion model to realize\na diffusion model from noise to valid neural network parameters. Subsequently,\nwe generate several base classifiers using the trained diffusion model.\nFinally, we integrate these ba se classifiers for various inference tasks using\nthe Bagging method. Resulting experiments on multiple models and datasets show\nthat our proposed BEND algorithm can consistently outperform the mean and\nmedian accuracies of both the original trained model and the diffused model. At\nthe same time, new models diffused using the diffusion model have higher\ndiversity and lower cost than multiple models trained using traditional\nmethods. The BEND approach successfully introduces diffusion models into the\nnew deep learning training domain and provides a new paradigm for future deep\nlearning training and inference.",
+                    "authors": "Jia Wei, Xingjun Zhang, Witold Pedrycz",
+                    "published": "2024-03-23",
+                    "updated": "2024-03-23",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/physics/0403039v1",
+                    "title": "Non-diffusive transport in plasma turbulence: a fractional diffusion approach",
+                    "abstract": "Numerical evidence of non-diffusive transport in three-dimensional, resistive\npressure-gradient-driven plasma turbulence is presented. It is shown that the\nprobability density function (pdf) of test particles' radial displacements is\nstrongly non-Gaussian and exhibits algebraic decaying tails. To model these\nresults we propose a macroscopic transport model for the pdf based on the use\nof fractional derivatives in space and time, that incorporate in a unified way\nspace-time non-locality (non-Fickian transport), non-Gaussianity, and\nnon-diffusive scaling. The fractional diffusion model reproduces the shape, and\nspace-time scaling of the non-Gaussian pdf of turbulent transport calculations.\nThe model also reproduces the observed super-diffusive scaling.",
+                    "authors": "D. del-Castillo-Negrete, B. A. Carreras, V. E. Lynch",
+                    "published": "2004-03-04",
+                    "updated": "2004-03-04",
+                    "primary_cat": "physics.plasm-ph",
+                    "cats": [
+                        "physics.plasm-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/0907.0417v1",
+                    "title": "Microscopic origin of the jump diffusion model",
+                    "abstract": "The present paper is aimed at studying the microscopic origin of the jump\ndiffusion. Starting from the $N$-body Liouville equation and making only the\nassumption that molecular reorientation is overdamped, we derive and solve the\nnew (hereafter generalized diffusion) equation. This is the most general\nequation which governs orientational relaxation of an equilibrium molecular\nensemble in the hindered rotation limit and in the long time limit. The\ngeneralized diffusion equation is an extension of the small-angle diffusion\nequation beyond the impact approximation. We establish the conditions under\nwhich the generalized diffusion equation can be identified with the jump\ndiffusion equation, and also discuss the similarities and differences between\nthe two approaches.",
+                    "authors": "M. F. Gelin, D. S. Kosov",
+                    "published": "2009-07-02",
+                    "updated": "2009-07-02",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2403.01742v2",
+                    "title": "Diffusion-TS: Interpretable Diffusion for General Time Series Generation",
+                    "abstract": "Denoising diffusion probabilistic models (DDPMs) are becoming the leading\nparadigm for generative models. It has recently shown breakthroughs in audio\nsynthesis, time series imputation and forecasting. In this paper, we propose\nDiffusion-TS, a novel diffusion-based framework that generates multivariate\ntime series samples of high quality by using an encoder-decoder transformer\nwith disentangled temporal representations, in which the decomposition\ntechnique guides Diffusion-TS to capture the semantic meaning of time series\nwhile transformers mine detailed sequential information from the noisy model\ninput. Different from existing diffusion-based approaches, we train the model\nto directly reconstruct the sample instead of the noise in each diffusion step,\ncombining a Fourier-based loss term. Diffusion-TS is expected to generate time\nseries satisfying both interpretablity and realness. In addition, it is shown\nthat the proposed Diffusion-TS can be easily extended to conditional generation\ntasks, such as forecasting and imputation, without any model changes. This also\nmotivates us to further explore the performance of Diffusion-TS under irregular\nsettings. Finally, through qualitative and quantitative experiments, results\nshow that Diffusion-TS achieves the state-of-the-art results on various\nrealistic analyses of time series.",
+                    "authors": "Xinyu Yuan, Yan Qiao",
+                    "published": "2024-03-04",
+                    "updated": "2024-03-14",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1705.01542v2",
+                    "title": "A Spatial Structural Derivative Model for Ultraslow Diffusion",
+                    "abstract": "This study investigates the ultraslow diffusion by a spatial structural\nderivative, in which the exponential function exp(x)is selected as the\nstructural function to construct the local structural derivative diffusion\nequation model. The analytical solution of the diffusion equation is a form of\nBiexponential distribution. Its corresponding mean squared displacement is\nnumerically calculated, and increases more slowly than the logarithmic function\nof time. The local structural derivative diffusion equation with the structural\nfunction exp(x)in space is an alternative physical and mathematical modeling\nmodel to characterize a kind of ultraslow diffusion.",
+                    "authors": "Wei Xu, Wen Chen, Yingjie Liang, Jose Weberszpil",
+                    "published": "2017-05-03",
+                    "updated": "2017-06-13",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1807.03744v2",
+                    "title": "Enhanced Diffusivity in Perturbed Senile Reinforced Random Walk Models",
+                    "abstract": "We consider diffusivity of random walks with transition probabilities\ndepending on the number of consecutive traversals of the last traversed edge,\nthe so called senile reinforced random walk (SeRW). In one dimension, the walk\nis known to be sub-diffusive with identity reinforcement function. We perturb\nthe model by introducing a small probability $\\delta$ of escaping the last\ntraversed edge at each step. The perturbed SeRW model is diffusive for any\n$\\delta >0 $, with enhanced diffusivity ($\\gg O(\\delta^2)$) in the small\n$\\delta$ regime. We further study stochastically perturbed SeRW models by\nhaving the last edge escape probability of the form $\\delta\\, \\xi_n$ with\n$\\xi_n$'s being independent random variables. Enhanced diffusivity in such\nmodels are logarithmically close to the so called residual diffusivity\n(positive in the zero $\\delta$ limit), with diffusivity between\n$O\\left(\\frac{1}{|\\log\\delta |}\\right)$ and\n$O\\left(\\frac{1}{\\log|\\log\\delta|}\\right)$. Finally, we generalize our results\nto higher dimensions where the unperturbed model is already diffusive. The\nenhanced diffusivity can be as much as $O(\\log^{-2}\\delta)$.",
+                    "authors": "Thu Dinh, Jack Xin",
+                    "published": "2018-07-10",
+                    "updated": "2020-03-16",
+                    "primary_cat": "math.PR",
+                    "cats": [
+                        "math.PR",
+                        "60G50, 60H30, 58J37"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/cond-mat/0210703v1",
+                    "title": "Membrane bound protein diffusion viewed by fluorescence recovery after bleaching experiments : models analysis",
+                    "abstract": "Diffusion processes in biological membranes are of interest to understand the\nmacromolecular organisation and function of several molecules. Fluorescence\nRecovery After Photobleaching (FRAP) has been widely used as a method to\nanalyse this processes using classical Brownian diffusion model. In the first\npart of this work, the analytical expression of the fluorescence recovery as a\nfunction of time has been established for anomalous diffusion due to long\nwaiting times. Then, experimental fluorescence recoveries recorded in living\ncells on a membrane-bound protein have been analysed using three different\nmodels : normal Brownian diffusion, Brownian diffusion with an immobile\nfraction and anomalous diffusion due to long waiting times.",
+                    "authors": "C. Favard, N. Olivi-Tran, J. -L. Meunier",
+                    "published": "2002-10-31",
+                    "updated": "2002-10-31",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech",
+                        "physics.bio-ph",
+                        "q-bio.BM"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1911.11645v1",
+                    "title": "Effects of different discretisations of the Laplacian upon stochastic simulations of reaction-diffusion systems on both static and growing domains",
+                    "abstract": "By discretising space into compartments and letting system dynamics be\ngoverned by the reaction-diffusion master equation, it is possible to derive\nand simulate a stochastic model of reaction and diffusion on an arbitrary\ndomain. However, there are many implementation choices involved in this\nprocess, such as the choice of discretisation and method of derivation of the\ndiffusive jump rates, and it is not clear a priori how these affect model\npredictions. To shed light on this issue, in this work we explore how a variety\nof discretisations and method for derivation of the diffusive jump rates affect\nthe outputs of stochastic simulations of reaction-diffusion models, in\nparticular using Turing's model of pattern formation as a key example. We\nconsider both static and uniformly growing domains and demonstrate that, while\nonly minor differences are observed for simple reaction-diffusion systems,\nthere can be vast differences in model predictions for systems that include\ncomplicated reaction kinetics, such as Turing's model of pattern formation. Our\nwork highlights that care must be taken in using the reaction-diffusion master\nequation to make predictions as to the dynamics of stochastic\nreaction-diffusion systems.",
+                    "authors": "Bartosz J. Bartmanski, Ruth E. Baker",
+                    "published": "2019-11-26",
+                    "updated": "2019-11-26",
+                    "primary_cat": "physics.comp-ph",
+                    "cats": [
+                        "physics.comp-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2303.09295v1",
+                    "title": "DIRE for Diffusion-Generated Image Detection",
+                    "abstract": "Diffusion models have shown remarkable success in visual synthesis, but have\nalso raised concerns about potential abuse for malicious purposes. In this\npaper, we seek to build a detector for telling apart real images from\ndiffusion-generated images. We find that existing detectors struggle to detect\nimages generated by diffusion models, even if we include generated images from\na specific diffusion model in their training data. To address this issue, we\npropose a novel image representation called DIffusion Reconstruction Error\n(DIRE), which measures the error between an input image and its reconstruction\ncounterpart by a pre-trained diffusion model. We observe that\ndiffusion-generated images can be approximately reconstructed by a diffusion\nmodel while real images cannot. It provides a hint that DIRE can serve as a\nbridge to distinguish generated and real images. DIRE provides an effective way\nto detect images generated by most diffusion models, and it is general for\ndetecting generated images from unseen diffusion models and robust to various\nperturbations. Furthermore, we establish a comprehensive diffusion-generated\nbenchmark including images generated by eight diffusion models to evaluate the\nperformance of diffusion-generated image detectors. Extensive experiments on\nour collected benchmark demonstrate that DIRE exhibits superiority over\nprevious generated-image detectors. The code and dataset are available at\nhttps://github.com/ZhendongWang6/DIRE.",
+                    "authors": "Zhendong Wang, Jianmin Bao, Wengang Zhou, Weilun Wang, Hezhen Hu, Hong Chen, Houqiang Li",
+                    "published": "2023-03-16",
+                    "updated": "2023-03-16",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Diffusion AND Model"
+                }
+            ],
+            [
+                {
+                    "url": "http://arxiv.org/abs/2404.07990v1",
+                    "title": "OpenBias: Open-set Bias Detection in Text-to-Image Generative Models",
+                    "abstract": "Text-to-image generative models are becoming increasingly popular and\naccessible to the general public. As these models see large-scale deployments,\nit is necessary to deeply investigate their safety and fairness to not\ndisseminate and perpetuate any kind of biases. However, existing works focus on\ndetecting closed sets of biases defined a priori, limiting the studies to\nwell-known concepts. In this paper, we tackle the challenge of open-set bias\ndetection in text-to-image generative models presenting OpenBias, a new\npipeline that identifies and quantifies the severity of biases agnostically,\nwithout access to any precompiled set. OpenBias has three stages. In the first\nphase, we leverage a Large Language Model (LLM) to propose biases given a set\nof captions. Secondly, the target generative model produces images using the\nsame set of captions. Lastly, a Vision Question Answering model recognizes the\npresence and extent of the previously proposed biases. We study the behavior of\nStable Diffusion 1.5, 2, and XL emphasizing new biases, never investigated\nbefore. Via quantitative experiments, we demonstrate that OpenBias agrees with\ncurrent closed-set bias detection methods and human judgement.",
+                    "authors": "Moreno D'Inc\u00e0, Elia Peruzzo, Massimiliano Mancini, Dejia Xu, Vidit Goel, Xingqian Xu, Zhangyang Wang, Humphrey Shi, Nicu Sebe",
+                    "published": "2024-04-11",
+                    "updated": "2024-04-11",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.AI"
+                    ],
+                    "label": "Original Paper",
+                    "paper_cat": "Diffusion AND Model",
+                    "gt": "Pipeline with Foundation Models. We broadly refer to foundation models [5] as large-scale deep learning models trained on extensive data corpora, usually with a selfsupervised objective [5]. This approach has been used across different modalities, such as text [9, 63], vision [10, 15, 49] and multi-modal models [42, 51, 76]. These models can be fine-tuned on downstream tasks or applied in a zero-shot manner, generalizing to unseen tasks [9, 60, 68]. Lately, several works combined different foundation models to solve complex tasks. [22, 61] use an LLM to generate Python code that invokes vision-language models to produce results. TIFA [27] assesses the faithfulness of a generated image to a given text prompt, by querying a VQA model with questions produced by an LLM from the original caption. Similarly, [11, 76] enhance image/video captioning by iteratively querying an LLM to ask questions to a VQA model. Differently, [35] identify spurious correlations in synthetic images via captioning and language interpretation, but without categorizing or quantifying bias. We share a similar motivation, i.e., we leverage powerful foundation models to build an automatic pipeline, tailored to the novel task of open-set bias discovery. OpenBias builds a knowledge base of biases leveraging the domainspecific knowledge from real captions and LLMs. Bias Mitigation in Generative Models. Bias mitigation is a long-studied topic in generative models. A substantial line of work focused on GAN-based methods. Some works improve fairness at inference time by altering the latent space semantic distribution [62] or by gradient clipping to control the gradient ensuring fairer representations for sensitive groups [33]. The advent of T2I generative models has directed research efforts towards fairness within this domain. FairDiffusion [17] guides Stable Diffusion [53] toward fairer generation in job-related contexts. It enhances classifier-free guidance [25] by adding a fair guidance term based on user-provided fair instructions. Similarly, [7] demonstrates that (negative) prompt and semantic guidance [6] mitigate inappropriateness generation in several T2I models. Given handwritten text as input, ITIGEN [72] enhances the fairness of T2I generative models through prompt learning. To improve fairness, [59] guide generation using the data manifold of the training set, estimated via unsupervised learning. While yielding notable result, these bias mitigation methods rely on predefined lists of biases. Here, we argue that there may exist other biases not considered by these methods. Therefore, our proposed pipeline is orthogonal, providing a valuable tool to enhance their utility.",
+                    "pre_questions": [],
+                    "main_content": "Introduction Text-to-Image (T2I) generation has become increasingly popular, thanks to its intuitive conditioning and the high quality and fidelity of the generated content [48, 50, 52, 53, 55]. Several works extended the base T2I model, unlocking additional use cases, including personalization [18, 54], image editing [8, 16, 21, 24], and various forms of conditioning [2, 28, 73]. This rapid progress urges to investigate other key aspects beyond image quality improvements, such as their fairness and potential bias perpetration [13, 17, 72]. It is widely acknowledged that deep learning models learn the underlying biases present in their training sets [4, 23, 74], and generative models are no exception [13, 17, 45, 72]. \u2020Corresponding authors. OpenBias (ours) Closed-set \"A person using a laptop\" Pre-defined biases Bias proposals \"A person using a laptop\" Bias assessment Male ... Apple Open-set biases Gender ... Laptop brand Bias specific Classifier\u00a0 Male Figure 1. OpenBias discovers biases in T2I models within an open-set scenario. In contrast to previous works [17, 33, 72], our pipeline does not require a predefined list of biases but proposes a set of novel domain-specific biases. Ethical topics such as fairness and biases have seen many definitions and frameworks [64]; defining them comprehensively poses a challenge, as interpretations vary and are subjective to the individual user. Following previous works [17, 70], a model is considered unbiased regarding a specific concept if, given a context t that is agnostic to class distinctions, the possible classes c \u2208C exhibit a uniform distribution. In practice, for a T2I model, this reflects to the tendency of the generator to produce content of a certain class c (e.g. \u201cman\u201d), given a textual prompt t that does not specify the intended class (e.g. \u201cA picture of a doctor\u201d). Several works studied bias mitigation in pre-trained models, by introducing training-related methods [29, 46, 56, 67] or using data augmentation techniques [1, 14]. Nevertheless, a notable limitation of these approaches is their dependence on a predefined set of biases, such as gender, age, and race [13, 17], as well as specific face attributes [72]. While these represent perhaps the most sensitive biases, we argue that there could be biases that remain undiscovered and unstudied. Considering the example in 1 arXiv:2404.07990v1  [cs.CV]  11 Apr 2024 Fig.1, the prompt \u201cA person using a laptop\u201d does not specify the person\u2019s appearance and neither the specific laptop nor the scenario. While closed-set pipelines can detect wellknown biases (e.g. gender, race), the T2I model may exhibit biases also for other elements (e.g. laptop brand, office). Thus, an open research question is: Can we identify arbitrary biases present in T2I models given only prompts and no pre-specified classes? This is challenging as collecting annotated data for all potential biases is prohibitive. Toward this goal, we propose OpenBias, the first pipeline that operates in an open-set scenario, enabling to identify, recognize, and quantify biases in a specific T2I model without constraints (or data collection) for a specific predefined set. Specifically, we exploit the multi-modal nature of T2I models and create a knowledge base of possible biases given a collection of target textual captions, by querying a Large Language Model (LLM). In this way, we discover specific biases for the given captions. Next, we need to recognize whether these biases are actually present in the images. For this step, we leverage available Visual Question Answering (VQA) models, directly using them to assess the bias presence. By doing this, we overcome the limitation of using attributes-specific classifiers as done in previous works [17, 59, 72], which is not efficient nor feasible in an open-set scenario. Our pipeline is modular and flexible, allowing for the seamless replacement of each component with newer or domain-specific versions as they become available. Moreover, we treat the generative model as a black box, querying it with specific prompts to mimic end-user interactions (i.e. without control over training data and algorithm). We test OpenBias on variants of Stable Diffusion [50, 53] showing human-agreement, model-level comparisons, and the discovery of novel biases. Contributions. To summarize, our key contributions are: \u2022 To the best of our knowledge, we are the first to study the problem of open-set bias detection at large scale without relying on a predefined list of biases. Our method discovers novel biases that have never been studied before. \u2022 We propose OpenBias, a modular pipeline, that, given a ers novel biases that have never been studied before. \u2022 We propose OpenBias, a modular pipeline, that, given a list of prompts, leverages a Large Language Model to extract a knowledge base of possible biases, and a Vision Question Answer model to recognize and quantify them. \u2022 We test our pipeline on multiple text-to-image generative Question Answer model to recognize and quantify them. \u2022 We test our pipeline on multiple text-to-image generative models: Stable Diffusion XL, 1.5, 2 [50, 53]. We assess our pipeline showing its agreement with closed-set classifier-based methods and with human judgement. This section presents OpenBias, our pipeline for proposing, assessing, and quantifying biases in T2I generative models. The overview of the proposed framework is outlined in Fig. 2. Starting from a dataset of real textual captions, we leverage a Large Language Model (LLM) to build a knowledge base of possible biases that may occur during image generation. This process enables the identification of domain-specific biases unexplored up to now. In the sec2 Bias Proposals Person gender Train color Vehicle Type ... Person Race Classes  Captions Questions Person Race What is the race of the person? ... What is the race of the person throwing a Frisbee? Target Generative Model G Synthetic Images VQA Class 1 Class 2 ... Class  Bias  A chef in a kitchen standing next to jars ... \u00a0 \u00a0 A kid on a beach throwing a Frisbee \u00a0  \u00a0\u00a0 Bias Assessment Ranking ... LLM Caucasian African American ... Hispanic Bias Quantification \u00a0  \u00a0\u00a0 A chef in a kitchen standing next to jars A person that is posing by a plane A large round cake rests on a glass plate ... A baby eating in a baby seat A boy with a book sitting on a toilet A man is playing tennis on a tennis court \u00a0 \u00a0\u00a0 \u00a0 \u00a0\u00a0 \u00a0  \u00a0\u00a0 ... Figure 2. OpenBias pipeline. Starting with a dataset of real textual captions (T ) we leverage a Large Language Model (LLM) to build a knowledge base B of possible biases that may occur during the image generation process. In the second stage, synthesized images are generated using the target generative model conditioned on captions where a potential bias has been identified. Finally, the biases are assessed and quantified by querying a VQA model with caption-specific questions extracted during the bias proposal phase. ond stage, we synthesize images using the target generative model, conditioned on captions where a potential bias has been identified. Lastly, we assess the biases with a VQA model, querying it with caption-specific questions generated during the bias proposal phase. 3.1. Bias Proposals Given a dataset of real captions T , we construct a knowledge base B of possible biases. For each caption in the dataset, we task a LLM with providing three outputs: the potential bias name, a set of classes associated with the bias, and a question to identify the bias. Formally, given a caption t \u2208T , let us denote the LLM\u2019s output as a set of triplets Lt = {(bt i, Ct i, qt i)}nt i=1 where the cardinality of the set nt is caption dependent, and each triplet (b, C, q) has a proposed bias b, a set of associated classes C, and the question q assigned to the specific caption t. To obtain this set, we propose to use in-context learning [9, 58], providing task description and demonstrations directly in the textual prompt.1 We build the knowledge base B by aggregating the per-caption information on the whole dataset. Specifically, we can define the set of captionspecific biases Bt as the union of its potential biases, i.e. Bt = Snt i=1 bi. The dataset-level set of biases is then the union of the caption-level ones, i.e. B = S t\u2208T Bt. Next, we aggregate the bias-specific information across the whole dataset. We define the database of captions and questions as   \\ math ca l  { D } _ b =  \\ { ( t,q )  \\mid \\forall t \\in \\mathcal {T}, (x,\\mathcal {C},q)\\in \\mathtt {L}_t, x=b\\}.  (1) Db collects captions and questions specific to the bias b. Moreover, we define Tb = {t | (t, q) \u2208Db} as the set of captions, and Cb is the union of the set of classes associated 1We refer the reader to the Supp. Mat. for system prompt details. to the bias b in T . Nevertheless, Db does not account for the potential specification of the classes of b in the caption. For instance, if we aim to generate \u201cAn image of a large dog\u201d, the dog\u2019s size should not be included among the biases. To address this, we implement a two-stage filtering procedure of Db. First, given a pair (t, q) \u2208Db we ask the LLM to output whether the answer to the question q is explicitly present in the caption t. Secondly, we leverage ConceptNet [57] to identify synonyms for the classes Cb related to the specific bias b, and filter out the captions in containing either a class Cb or its synonyms. We empirically observe that combining these two stages produces more robust results. By executing the aforementioned steps, we generate bias proposals in an open-set manner tailored to the given dataset. In the following sections, we elaborate on the process of bias quantification in a target generative model. 3.2. Bias Assessment and Quantification Let G be the target T2I generative model. Our objective is to evaluate if G generates images with the identified biases. Given a bias b \u2208B and a caption t \u2208Tb, we generate the set of N images It b as    \\ m athca l {I} ^ t_b = \\{\\generator (t,s) | \\forall s\\in {S}\\}  (2) where S is the set of sampled random noise, of cardinality |S| = N. Sampling multiple noise vectors allows us to obtain a distribution of the G output on the same prompt t. To assess the bias within It b, we propose to leverage a state-of-the-art Vision Question Answering (VQA) model VQA mapping images and questions to answers in natural language. The VQA processes the images It b, and their associated question q in the pair (t, q) \u2208Db, choosing an answer from the possible classes Cb. Formally, given an image 3 I \u2208It b we denote the predicted class as    \\ label {e q:vqa} \\hat {c} = \\mathtt {VQA}(I, q, \\mathcal {C}_b).  (3) With this score, we gather statistics on the distribution of the classes on a set of images, and use them to quantify the severity of the bias. In the following, we investigate two distinct scenarios, namely context-aware, where we analyze the bias on caption-specific images It b, and contextfree, where we consider the whole set of images Ib associated to one bias b \u2208B. 3.2.1 Context-Aware Bias As discussed in Section 1, our focus lies in examining bias exclusively when the classes are not explicitly mentioned in the caption. The bias proposals pipeline described in Sec. 3.1 filters out such cases; nevertheless, there could be additional aspects within the caption that impact the outcome. For example, the two captions \u201cA military is running\u201d and \u201cA person is running\u201d are both agnostic to the bias \u201cperson gender\u201d, but the direction and magnitude of the bias may be very different in the two cases. To consider the role of the context in the bias assessment, we collect statistics at the caption level, analyzing the set of images It b produced from a specific caption t \u2208T . Given a bias b we compute the probability for a class c \u2208Cb as:   \\lab el {eq : c ont ex t _awa r e }   p ( c  | t,\\mathcal {C}_b, \\mathcal {D}_b) = \\dfrac {1}{|\\mathcal {I}_b^t|} \\sum _{I\\in \\mathcal {I}_b^t}\\indicatorfunction \\bigl (\\hat {c}=c\\bigr )  (4) with \u02c6 c = VQA(I, q, Cb) the prediction of the VQA as defined in Eq. (3), and 1(\u00b7) the indicator function. 3.2.2 Context-Free Bias Differently from the context-aware scenario, our interest lies in characterizing the overall behavior of the model G. This is crucial as it offers valuable insights into aspects such as the majority class (i.e. the direction toward which the bias tends) and the overall intensity of the bias. To effectively exclude the role of the context in the captions, we propose to average the VQA scores for c \u2208Cb over all captions t related to that bias b \u2208B:   \\labe l { e q :con t ext_free } p(c | \\ mathcal {C}_b, \\mathcal {D}_b) =\\dfrac {1}{|\\mathcal {D}_b|}\\sum _{(t,q)\\in \\mathcal {D}_b} p(c | t, \\mathcal {C}_b, \\mathcal {D}_b)  (5) Note that the context-aware bias is a special case of this scenario, where Db has a single instance, i.e. Db = {(t, q)}. 3.2.3 Bias Quantification and Ranking After collecting the scores for each individual attribute class c \u2208Cb, we can aggregate them to rank the severity of biases within the generative model. As mentioned in Sec. 1, we follow existing work [17, 70] and consider the model G as unbiased with respect to a concept b when the distribution of the possible classes c \u2208Cb is uniform. To quantitatively assess the severity of the bias, we compute the entropy of the probability distribution of the classes obtained using either Eq. (4) or Eq. (5). To compare biases with different numbers of classes, we normalize the entropy by the maximum possible entropy [69]. Additionally, we adjust the score for enhanced human readability. In practice, our bias severity score is defined as follows:    \\ l a b e l {e q:e ntropy_ sco re} \\bar {\\mathcal {H}}_b = 1 + \\dfrac {\\sum _{c\\in \\mathcal {C}_b}\\log p(c | \\mathcal {C}_b, \\mathcal {D}_b) }{\\log (|\\mathcal {C}_b|)}  (6) The resulting score is always bounded \u00af Hb \u2208[0, 1], where 0 indicates an unbiased concept while 1 a biased one. We note that, while we focused our pipeline on conditional generative models, our model can be easily extended for studying biases in both real-world multimodal datasets (e.g. by assuming images It b are provided rather than generated), and to unconditional generative models (i.e. by using a captioning system on their outputs as set T ). We refer the reader to the Supp. Mat. for details where we will also show an analysis between the unconditional GAN StyleGAN3 [32] and its training set FFHQ [31]. 4. Experiments In this section, we conduct a series of experiments to assess the proposed framework quantitatively. In Sec. 4.1, we provide implementation details and the preprocessing steps applied to the datasets. In Sec. 4.2, we quantitative evaluate OpenBias on two directions, (i) comparing it with a state-of-the-art classifier-based method on a closed set of well-known social biases, (ii) testing the agreement between OpenBias and human judgment via a user study. 4.1. Pipeline Implementation Datasets. We study the bias in two multimodal datasets Flickr 30k [71] and COCO [40]. Flickr30k [71] comprises 30K images with 5 caption per image, depicting images in the wild. Similarly, COCO [40] is a large-scale dataset containing a diverse range of images that capture everyday scenes and objects in complex contexts. We filter this dataset, creating a subset of images whose caption contains a single person. This procedure results in roughly 123K captions. Our choice is motivated by building a large subset of captions specifically tied to people. This focus on the person-domain is crucial as it represents one of the most sensitive scenarios for exploring bias-related settings. Nevertheless, it is worth noting that the biases we discover within this context extend beyond person-related biases to include objects, animals, and actions associated with people. Further details are highlighted in Sec. 5. 4 child gender cat color train color baby gender cake type surfboard type snow condition phone type horse age snowboarder age water condition dog color pizza size person activity person age skateboarder age motorcycle type cat age person emotion skateboard type skiing location child race person attire person gender person race skiing ability person occupation dog age horse breed dog breed player age player gender skiing ability kite size laptop brand wave size vehicle type wave type ski type tennis player level skiing level aircraft size snowboard type horse breed skiing location bed type slope difficulty cat breed 0.0 0.2 0.4 0.6 0.8 1.0 Bias Intensity SD-XL SD-2 SD-1.5 Figure 3. Comparison of context-aware discovered biases on Stable Diffusion XL, 2 and 1.5 [50, 53] with captions from COCO [40]. child gender performer age dog color artist age soccer position person gender performer race skateboard type worker race person activity water type person age child race person race person hair color person attire dog activity person emotion vehicle type dog breed skiing ability worker age horse breed person occupation motorcycle type dog age player age person height bicycle type wave size beach location dog coat player gender crowd size boat type 0.0 0.2 0.4 0.6 0.8 1.0 Bias Intensity SD-XL SD-2 SD-1.5 Figure 4. Comparison of context-aware found biases on Stable Diffusion XL, 2 and 1.5 [50, 53] on captions from Flick30k [71]. Implementation Details. Our pipeline is designed to be flexible and modular, enabling us to replace individual components as needed. In this study, we leverage LLama2-7B [63] as our foundation LLM. This model is exploited to build the knowledge base of possible biases, as described in Sec. 3.1. We refer the reader to the Supp. Mat. for details regarding the prompts and examples we use to instruct LLama to perform the desired tasks. To assess the presence of the bias, we rely on state-of-the-art Visual Question Answering (VQA) models. From our evaluation outlined in Sec. 4.2, Llava1.5-13B [41, 42] emerges as the top-performing, thus we adopt it as our default VQA model. Finally, we conduct our study by randomly selecting 100 captions associated with each bias and generating N = 10 images for each caption using a different random seed. In this way, we obtain a set of 1000 images, that we use to study the contextfree and context-aware bias of the target generative model. 4.2. Quantitative Results Our open-set setting harnesses the zero-shot performance of each component. As in [17], we evaluate OpenBias using FairFace [30], a well-established classifier fairly trained, as the ground truth on gender, age, and race. While FairFace treats socially sensitive attributes as closed-set, we uphold our commitment to inclusivity by also evaluating OpenBias with self-identified ones, reported in the Supp. Mat.. Model Gender Age Race Acc. F1 Acc. F1 Acc. F1 CLIP-L [51] 91.43 75.46 58.96 45.77 36.02 33.60 OFA-Large [66] 93.03 83.07 53.79 41.72 24.61 21.22 mPLUG-Large [37] 93.03 82.81 61.37 52.74 21.46 23.26 BLIP-Large [38] 92.23 82.18 48.61 31.29 36.22 35.52 Llava1.5-7B [41, 42] 92.03 82.33 66.54 62.16 55.71 42.80 Llava1.5-13B [41, 42] 92.83 83.21 72.27 70.00 55.91 44.33 Table 1. VQA evaluation on the generated images using COCO captions. We highlight in gray the chosen default VQA model. Model Flickr 30k [71] COCO [40] gender age race gender age race Real 0 0.032 0.030 0 0.041 0.028 SD-1.5 [53] 0.072 0.032 0.052 0.075 0.028 0.092 SD-2 [53] 0.036 0.069 0.047 0.060 0.045 0.105 SD-XL [50] 0.006 0.028 0.180 0.002 0.027 0.184 Table 2. KL divergence (\u2193) computed over the predictions of Llava1.5-13B and FairFace on generated and real images. Agreement with FairFace. We compare the predictions of multiple SoTA Visual Question Answering models with FairFace. Firstly, we assess the zero-shot performance of the VQA models on synthetic images, performing our comparisons using images generated by SD XL. The evaluation involves assessing accuracy and F1 scores, which are computed against FairFace predictions treated as the ground truth. The results are reported in Tab. 1. Llava1.5-13B 5 emerges as the top-performing model across different tasks, consequently, we employ it as our default VQA model. Next, we evaluate the agreement between Llava and FairFace [30] on different scenarios. Specifically, we run the two models on real and synthetic images generated with Stable Diffusion 1.5, 2, and XL. We measure the agreement between the two as the KL Divergence between the probability distributions obtained using the predictions of the respective model. We report the results in Tab. 2. We can observe that the models are highly aligned, obtaining low KL scores, proving the VQA model\u2019s robustness in both generative and real settings. Supp. Mat. provides a more comprehensive evaluation of the VQA. User Study. We conduct a human evaluation of the proposed pipeline at the context-aware level, to assess its alignment with human judgment. The study presents 10 images generated from the same caption for each bias. We use public crowdsourcing platforms, without geographical restrictions, and randomizing the questions\u2019 order. Each participant is asked to identify the direction (majority class) of each bias and its intensity in a range from 0 to 10. The option \u201cNo bias\u201d is provided to capture the instances where no bias is perceived, corresponding to a bias intensity of 0. We conduct the user study on a subsection of the biases, resulting in 15 diverse object-related and person-related biases and 390 diverse images. We collect answers from 55 unique users, for a total of 2200 valid responses. The user study results are shown in Fig. 5, where we compare the bias intensity as collected from the human participants with the severity score computed with OpenBias. We can observe that there is a high alignment on various biases such as \u201cPerson age\u201d, \u201cPerson gender\u201d, \u201cVehicle type\u201d, \u201cPerson emotion\u201d and \u201cTrain color\u201d. We compute the Absolute Mean Error (AME) between the bias intensity produced by the model and the average user score, resulting in an AME = 0.15. Furthermore, we compute the agreement on the majority class, i.e. the direction of the bias. In this case, OpenBias matches the collected human choices 67% of the cases. We remark that concepts of bias and fairness are highly subjective, and this can introduce further errors in the evaluation process. Nevertheless, our results show a correlation between the scores, validating our pipeline. 5. Findings In this section, we present our findings from the examination of three extensively utilized text-to-image generative models, specifically Stable Diffusion XL, 2, and 1.5 [50, 53]. We use captions from Flickr and COCO, as detailed in Sec. 4.1. We structure our findings by examining the biases of different models and delineating the distinctions between context-free and context-aware bias. Rankings. We present here the biases identified by our pipeline on Stable Diffusion XL, 2, and 1.5 [50, 53], in Cake type Train color Person occupation Pizza size Wave size Person emotion Person race Aircraft size Snow condition Person activity Person attire Person age Bed type Vehicle type Person gender 0.0 0.2 0.4 0.6 0.8 1.0 Bias Intensity Human OpenBias (ours) Figure 5. Human evaluation results. Fig. 3 and 4. Importantly, OpenBias identifies both wellknown (e.g. \u201cperson gender\u201d, \u201cperson race\u201d) and novel biases (e.g. \u201ccake type\u201d, \u201cbed type\u201d and \u201claptop brand\u201d). From the comparison of different models, we observe a correlation between the intensities of the biases across different Stable Diffusion versions. We note, however, a subtle predominance of SD XL in the amplification of bias compared to earlier versions of the model. Moreover, the set of proposed biases varies depending on the initial set of captions used for the extraction. Generally, biases extracted from Flickr are more object-centric compared to those from COCO, aligning with the filtering operation applied to the latter. This difference highlights the potential of OpenBias to propose a tailored set of biases according to the captions it is applied to, making the bias proposals domain-specific. Context-Free vs Context-Aware. Next, we study the different behavior of a given model, when compared in a context-free vs context-aware scenario (see Sec. 3 for formal definition). This analysis assesses the influence of other elements within the captions on the perpetuation of a particular bias. In Fig. 9 we report the results obtained on SD XL. It is noteworthy to observe that, in this case, the correlation between the scores is not consistently present. For example, the intensity score for \u201cmotorcycle type\u201d is significantly higher when computed within the context, compared to the same evaluation free of context. This discrepancy suggests that there is no majority class (i.e. the general direction of the bias), but rather the model generates motorcycles of one specific type in a given context. Vice versa, for \u201cbed type\u201d we observe a high score in both settings, suggesting that the model always generates the same type of bed. Qualitative Results. We show examples of biases discovered by OpenBias on Stable Diffusion XL. We present the results in a context-aware fashion and visualize images generated from the same caption where our pipeline identifies a bias. We organize the results in three sets and present unexplored biases on objects and animals, novel biases as6 Train color \u201cA train zips down the railway in the sun\u201d Laptop brand \u201cA photo of a person on a laptop in a coffee shop\u201d Horse breed \u201cA cop riding a horse through a city neighborhood\u201d Figure 6. Novel biases discovered on Stable Diffusion XL [50] by OpenBias. Child gender \u201cToddler in a baseball cap on a wooden bench\u201d Child race \u201cSmall child hurrying toward a bus on a dirt road\u201d Person attire \u201cThe lady is sitting on the bench holding her handbag\u201d Figure 7. Novel person-related biases identified on Stable Diffusion XL [50] by OpenBias. Person gender \u201cA traffic officer leaning on a no turn sign\u201d Person race \u201cA man riding an elephant into some water of a creek\u201d Person age \u201cA woman riding a horse in front of a car next to a fence\u201d Figure 8. Person-related biases found on Stable Diffusion XL [50] by OpenBias. 7 child gender person age motorcycle type person emotion child race person attire person gender person race laptop brand bed type 0.0 0.2 0.4 0.6 0.8 1.0 Bias Intensity Context Aware Context Free Figure 9. Highlighting the importance of the context aware approach on Stable Diffusion XL [50] on the captions from COCO. sociated with persons, and well-known social biases. We highlight biases discovered on objects and animals in Fig. 6. For example, the model tends to generate \u201cyellow\u201d trains or \u201cquarter horses\u201d even if not specified in the caption. Furthermore, the model generates laptops featuring a distinct \u201cApple\u201d logo, showing a bias toward the brand. Next, we display novel biases related to persons discovered by OpenBias. For instance, we unveil unexplored biases such as the \u201cperson attire\u201d, with the model often generating people in a formal outfit rather than more casual ones. Furthermore, we specifically study \u201cchild gender\u201d and \u201cchild race\u201d diverging from the typical examination centered on adults. For example, in Fig. 7 second column, we observe that the generative model links a black child with an economically disadvantaged environment described in the caption as \u201ca dirt road\u201d. The association between racial identity and socioeconomic status perpetuates harmful stereotypes and proves the need to consider novel biases within bias mitigation frameworks. Lastly, we show qualitative results on the well-studied and sensitive biases of \u201cperson gender\u201d, \u201crace\u201d, and \u201cage\u201d. In the first column of Fig. 8, Stable Diffusion XL exclusively generates \u201cmale\u201d officers, despite the presence of a gender-neutral job title. Moreover, it explicitly depicts a \u201cwoman\u201d labeled as \u201cmiddle-aged\u201d when engaged in horseback riding. Finally, we observe a \u201crace\u201d bias, with depictions of solely black individuals for \u201ca man riding an elephant\u201d. This context-aware approach ensures a thorough comprehension of emerging biases in both novel and socially significant contexts. These results emphasize the necessity for more inclusive open-set bias detection frameworks. We provide additional qualitatives and comparisons in the Supp. Mat.. 6. Limitations OpenBias is based on two foundation models to propose and quantify biases of a generative model, namely LLama [63] and LLava [42]. We rely on the prediction of these models, without considering their intrinsic limitations. Existing research [19, 47] highlights the presence of biases in these models which may be propagated in our pipeline. Nevertheless, the modular nature of our pipeline provides flexibility, allowing us to seamlessly incorporate improved models should they become available in the future. Finally, in this work, we delve into the distinction between contextfree and context-aware biases, revealing different behaviors exhibited by models in these two scenarios. However, our evaluation of the role of the context is only qualitative. We identify the possibility of systematically studying the context\u2019s role as a promising future direction. 7. Conclusions AI-generated content has seen rapid growth in the last few years, with the potential to become even more ubiquitous in society. While the usage of such models increases, characterizing the stereotypes perpetrated by the model becomes of significant importance. In this work, we propose to study the bias in generative models in a novel open-set scenario, paving the way to the discovery of biases previously unexplored. We propose OpenBias, an automatic bias detection pipeline, capable of discovering and quantifying traditional and novel biases without the need to pre-define them. The proposed method builds a domain-specific knowledge base of biases which are then assessed and quantified via Vision Question Answering. We validate OpenBias showing its agreement with classifier-based methods on a closed set of concepts and with human judgement through a user study. Our method can be plugged into existing bias mitigation works, extending their capabilities to novel biases. OpenBias can foster further research in open-set scenarios, moving beyond classical pre-defined biases and assessing generative models more comprehensively. Ethical statement and broader impact. This work contributes to fairer and more inclusive AI, by detecting biases in T2I generative models. We conduct our research responsibly, transparently, and with a strong commitment to ethical principles. Despite this, due to technical constraints, socially sensitive attributes, such as gender, are treated as closed sets for research purposes only. Moreover, OpenBias entails the biases of the LLM and VQA models, thus it may not discover all possible biases. We do not intend to discriminate against any social group but raise awareness on the challenges of detecting biases beyond closed sets. Acknowledgments: This work was supported by the MUR PNRR project FAIR (PE00000013) funded by the NextGenerationEU and by the EU Horizon projects ELIAS (No. 101120237) and AI4Media (No. 951911), NSF CAREER Award #2239840, and the National AI Institute for Exceptional Education (Award #2229873) by National Science Foundation and the Institute of Education Sciences, U.S. Department of Education, and Picsart AI Research (PAIR). 8"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2207.10653v1",
+                    "title": "RepFair-GAN: Mitigating Representation Bias in GANs Using Gradient Clipping",
+                    "abstract": "Fairness has become an essential problem in many domains of Machine Learning\n(ML), such as classification, natural language processing, and Generative\nAdversarial Networks (GANs). In this research effort, we study the unfairness\nof GANs. We formally define a new fairness notion for generative models in\nterms of the distribution of generated samples sharing the same protected\nattributes (gender, race, etc.). The defined fairness notion (representational\nfairness) requires the distribution of the sensitive attributes at the test\ntime to be uniform, and, in particular for GAN model, we show that this\nfairness notion is violated even when the dataset contains equally represented\ngroups, i.e., the generator favors generating one group of samples over the\nothers at the test time. In this work, we shed light on the source of this\nrepresentation bias in GANs along with a straightforward method to overcome\nthis problem. We first show on two widely used datasets (MNIST, SVHN) that when\nthe norm of the gradient of one group is more important than the other during\nthe discriminator's training, the generator favours sampling data from one\ngroup more than the other at test time. We then show that controlling the\ngroups' gradient norm by performing group-wise gradient norm clipping in the\ndiscriminator during the training leads to a more fair data generation in terms\nof representational fairness compared to existing models while preserving the\nquality of generated samples.",
+                    "authors": "Patrik Joslin Kenfack, Kamil Sabbagh, Ad\u00edn Ram\u00edrez Rivera, Adil Khan",
+                    "published": "2022-07-13",
+                    "updated": "2022-07-13",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2302.13971v1",
+                    "title": "LLaMA: Open and Efficient Foundation Language Models",
+                    "abstract": "We introduce LLaMA, a collection of foundation language models ranging from\n7B to 65B parameters. We train our models on trillions of tokens, and show that\nit is possible to train state-of-the-art models using publicly available\ndatasets exclusively, without resorting to proprietary and inaccessible\ndatasets. In particular, LLaMA-13B outperforms GPT-3 (175B) on most benchmarks,\nand LLaMA-65B is competitive with the best models, Chinchilla-70B and\nPaLM-540B. We release all our models to the research community.",
+                    "authors": "Hugo Touvron, Thibaut Lavril, Gautier Izacard, Xavier Martinet, Marie-Anne Lachaux, Timoth\u00e9e Lacroix, Baptiste Rozi\u00e8re, Naman Goyal, Eric Hambro, Faisal Azhar, Aurelien Rodriguez, Armand Joulin, Edouard Grave, Guillaume Lample",
+                    "published": "2023-02-27",
+                    "updated": "2023-02-27",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2204.05991v2",
+                    "title": "ReCLIP: A Strong Zero-Shot Baseline for Referring Expression Comprehension",
+                    "abstract": "Training a referring expression comprehension (ReC) model for a new visual\ndomain requires collecting referring expressions, and potentially corresponding\nbounding boxes, for images in the domain. While large-scale pre-trained models\nare useful for image classification across domains, it remains unclear if they\ncan be applied in a zero-shot manner to more complex tasks like ReC. We present\nReCLIP, a simple but strong zero-shot baseline that repurposes CLIP, a\nstate-of-the-art large-scale model, for ReC. Motivated by the close connection\nbetween ReC and CLIP's contrastive pre-training objective, the first component\nof ReCLIP is a region-scoring method that isolates object proposals via\ncropping and blurring, and passes them to CLIP. However, through controlled\nexperiments on a synthetic dataset, we find that CLIP is largely incapable of\nperforming spatial reasoning off-the-shelf. Thus, the second component of\nReCLIP is a spatial relation resolver that handles several types of spatial\nrelations. We reduce the gap between zero-shot baselines from prior work and\nsupervised models by as much as 29% on RefCOCOg, and on RefGTA (video game\nimagery), ReCLIP's relative improvement over supervised ReC models trained on\nreal images is 8%.",
+                    "authors": "Sanjay Subramanian, William Merrill, Trevor Darrell, Matt Gardner, Sameer Singh, Anna Rohrbach",
+                    "published": "2022-04-12",
+                    "updated": "2022-05-02",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.CL"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2108.07258v3",
+                    "title": "On the Opportunities and Risks of Foundation Models",
+                    "abstract": "AI is undergoing a paradigm shift with the rise of models (e.g., BERT,\nDALL-E, GPT-3) that are trained on broad data at scale and are adaptable to a\nwide range of downstream tasks. We call these models foundation models to\nunderscore their critically central yet incomplete character. This report\nprovides a thorough account of the opportunities and risks of foundation\nmodels, ranging from their capabilities (e.g., language, vision, robotics,\nreasoning, human interaction) and technical principles(e.g., model\narchitectures, training procedures, data, systems, security, evaluation,\ntheory) to their applications (e.g., law, healthcare, education) and societal\nimpact (e.g., inequity, misuse, economic and environmental impact, legal and\nethical considerations). Though foundation models are based on standard deep\nlearning and transfer learning, their scale results in new emergent\ncapabilities,and their effectiveness across so many tasks incentivizes\nhomogenization. Homogenization provides powerful leverage but demands caution,\nas the defects of the foundation model are inherited by all the adapted models\ndownstream. Despite the impending widespread deployment of foundation models,\nwe currently lack a clear understanding of how they work, when they fail, and\nwhat they are even capable of due to their emergent properties. To tackle these\nquestions, we believe much of the critical research on foundation models will\nrequire deep interdisciplinary collaboration commensurate with their\nfundamentally sociotechnical nature.",
+                    "authors": "Rishi Bommasani, Drew A. Hudson, Ehsan Adeli, Russ Altman, Simran Arora, Sydney von Arx, Michael S. Bernstein, Jeannette Bohg, Antoine Bosselut, Emma Brunskill, Erik Brynjolfsson, Shyamal Buch, Dallas Card, Rodrigo Castellon, Niladri Chatterji, Annie Chen, Kathleen Creel, Jared Quincy Davis, Dora Demszky, Chris Donahue, Moussa Doumbouya, Esin Durmus, Stefano Ermon, John Etchemendy, Kawin Ethayarajh, Li Fei-Fei, Chelsea Finn, Trevor Gale, Lauren Gillespie, Karan Goel, Noah Goodman, Shelby Grossman, Neel Guha, Tatsunori Hashimoto, Peter Henderson, John Hewitt, Daniel E. Ho, Jenny Hong, Kyle Hsu, Jing Huang, Thomas Icard, Saahil Jain, Dan Jurafsky, Pratyusha Kalluri, Siddharth Karamcheti, Geoff Keeling, Fereshte Khani, Omar Khattab, Pang Wei Koh, Mark Krass, Ranjay Krishna, Rohith Kuditipudi, Ananya Kumar, Faisal Ladhak, Mina Lee, Tony Lee, Jure Leskovec, Isabelle Levent, Xiang Lisa Li, Xuechen Li, Tengyu Ma, Ali Malik, Christopher D. Manning, Suvir Mirchandani, Eric Mitchell, Zanele Munyikwa, Suraj Nair, Avanika Narayan, Deepak Narayanan, Ben Newman, Allen Nie, Juan Carlos Niebles, Hamed Nilforoshan, Julian Nyarko, Giray Ogut, Laurel Orr, Isabel Papadimitriou, Joon Sung Park, Chris Piech, Eva Portelance, Christopher Potts, Aditi Raghunathan, Rob Reich, Hongyu Ren, Frieda Rong, Yusuf Roohani, Camilo Ruiz, Jack Ryan, Christopher R\u00e9, Dorsa Sadigh, Shiori Sagawa, Keshav Santhanam, Andy Shih, Krishnan Srinivasan, Alex Tamkin, Rohan Taori, Armin W. Thomas, Florian Tram\u00e8r, Rose E. Wang, William Wang, Bohan Wu, Jiajun Wu, Yuhuai Wu, Sang Michael Xie, Michihiro Yasunaga, Jiaxuan You, Matei Zaharia, Michael Zhang, Tianyi Zhang, Xikun Zhang, Yuhui Zhang, Lucia Zheng, Kaitlyn Zhou, Percy Liang",
+                    "published": "2021-08-16",
+                    "updated": "2022-07-12",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI",
+                        "cs.CY"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2211.11559v1",
+                    "title": "Visual Programming: Compositional visual reasoning without training",
+                    "abstract": "We present VISPROG, a neuro-symbolic approach to solving complex and\ncompositional visual tasks given natural language instructions. VISPROG avoids\nthe need for any task-specific training. Instead, it uses the in-context\nlearning ability of large language models to generate python-like modular\nprograms, which are then executed to get both the solution and a comprehensive\nand interpretable rationale. Each line of the generated program may invoke one\nof several off-the-shelf computer vision models, image processing routines, or\npython functions to produce intermediate outputs that may be consumed by\nsubsequent parts of the program. We demonstrate the flexibility of VISPROG on 4\ndiverse tasks - compositional visual question answering, zero-shot reasoning on\nimage pairs, factual knowledge object tagging, and language-guided image\nediting. We believe neuro-symbolic approaches like VISPROG are an exciting\navenue to easily and effectively expand the scope of AI systems to serve the\nlong tail of complex tasks that people may wish to perform.",
+                    "authors": "Tanmay Gupta, Aniruddha Kembhavi",
+                    "published": "2022-11-18",
+                    "updated": "2022-11-18",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.AI",
+                        "cs.CL"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2303.08128v1",
+                    "title": "ViperGPT: Visual Inference via Python Execution for Reasoning",
+                    "abstract": "Answering visual queries is a complex task that requires both visual\nprocessing and reasoning. End-to-end models, the dominant approach for this\ntask, do not explicitly differentiate between the two, limiting\ninterpretability and generalization. Learning modular programs presents a\npromising alternative, but has proven challenging due to the difficulty of\nlearning both the programs and modules simultaneously. We introduce ViperGPT, a\nframework that leverages code-generation models to compose vision-and-language\nmodels into subroutines to produce a result for any query. ViperGPT utilizes a\nprovided API to access the available modules, and composes them by generating\nPython code that is later executed. This simple approach requires no further\ntraining, and achieves state-of-the-art results across various complex visual\ntasks.",
+                    "authors": "D\u00eddac Sur\u00eds, Sachit Menon, Carl Vondrick",
+                    "published": "2023-03-14",
+                    "updated": "2023-03-14",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2103.00020v1",
+                    "title": "Learning Transferable Visual Models From Natural Language Supervision",
+                    "abstract": "State-of-the-art computer vision systems are trained to predict a fixed set\nof predetermined object categories. This restricted form of supervision limits\ntheir generality and usability since additional labeled data is needed to\nspecify any other visual concept. Learning directly from raw text about images\nis a promising alternative which leverages a much broader source of\nsupervision. We demonstrate that the simple pre-training task of predicting\nwhich caption goes with which image is an efficient and scalable way to learn\nSOTA image representations from scratch on a dataset of 400 million (image,\ntext) pairs collected from the internet. After pre-training, natural language\nis used to reference learned visual concepts (or describe new ones) enabling\nzero-shot transfer of the model to downstream tasks. We study the performance\nof this approach by benchmarking on over 30 different existing computer vision\ndatasets, spanning tasks such as OCR, action recognition in videos,\ngeo-localization, and many types of fine-grained object classification. The\nmodel transfers non-trivially to most tasks and is often competitive with a\nfully supervised baseline without the need for any dataset specific training.\nFor instance, we match the accuracy of the original ResNet-50 on ImageNet\nzero-shot without needing to use any of the 1.28 million training examples it\nwas trained on. We release our code and pre-trained model weights at\nhttps://github.com/OpenAI/CLIP.",
+                    "authors": "Alec Radford, Jong Wook Kim, Chris Hallacy, Aditya Ramesh, Gabriel Goh, Sandhini Agarwal, Girish Sastry, Amanda Askell, Pamela Mishkin, Jack Clark, Gretchen Krueger, Ilya Sutskever",
+                    "published": "2021-02-26",
+                    "updated": "2021-02-26",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.LG"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2301.12247v2",
+                    "title": "SEGA: Instructing Text-to-Image Models using Semantic Guidance",
+                    "abstract": "Text-to-image diffusion models have recently received a lot of interest for\ntheir astonishing ability to produce high-fidelity images from text only.\nHowever, achieving one-shot generation that aligns with the user's intent is\nnearly impossible, yet small changes to the input prompt often result in very\ndifferent images. This leaves the user with little semantic control. To put the\nuser in control, we show how to interact with the diffusion process to flexibly\nsteer it along semantic directions. This semantic guidance (SEGA) generalizes\nto any generative architecture using classifier-free guidance. More\nimportantly, it allows for subtle and extensive edits, changes in composition\nand style, as well as optimizing the overall artistic conception. We\ndemonstrate SEGA's effectiveness on both latent and pixel-based diffusion\nmodels such as Stable Diffusion, Paella, and DeepFloyd-IF using a variety of\ntasks, thus providing strong evidence for its versatility, flexibility, and\nimprovements over existing methods.",
+                    "authors": "Manuel Brack, Felix Friedrich, Dominik Hintersdorf, Lukas Struppek, Patrick Schramowski, Kristian Kersting",
+                    "published": "2023-01-28",
+                    "updated": "2023-11-02",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.AI",
+                        "cs.LG"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2201.11903v6",
+                    "title": "Chain-of-Thought Prompting Elicits Reasoning in Large Language Models",
+                    "abstract": "We explore how generating a chain of thought -- a series of intermediate\nreasoning steps -- significantly improves the ability of large language models\nto perform complex reasoning. In particular, we show how such reasoning\nabilities emerge naturally in sufficiently large language models via a simple\nmethod called chain of thought prompting, where a few chain of thought\ndemonstrations are provided as exemplars in prompting. Experiments on three\nlarge language models show that chain of thought prompting improves performance\non a range of arithmetic, commonsense, and symbolic reasoning tasks. The\nempirical gains can be striking. For instance, prompting a 540B-parameter\nlanguage model with just eight chain of thought exemplars achieves state of the\nart accuracy on the GSM8K benchmark of math word problems, surpassing even\nfinetuned GPT-3 with a verifier.",
+                    "authors": "Jason Wei, Xuezhi Wang, Dale Schuurmans, Maarten Bosma, Brian Ichter, Fei Xia, Ed Chi, Quoc Le, Denny Zhou",
+                    "published": "2022-01-28",
+                    "updated": "2023-01-10",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL",
+                        "cs.AI"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2304.04227v3",
+                    "title": "Video ChatCaptioner: Towards Enriched Spatiotemporal Descriptions",
+                    "abstract": "Video captioning aims to convey dynamic scenes from videos using natural\nlanguage, facilitating the understanding of spatiotemporal information within\nour environment. Although there have been recent advances, generating detailed\nand enriched video descriptions continues to be a substantial challenge. In\nthis work, we introduce Video ChatCaptioner, an innovative approach for\ncreating more comprehensive spatiotemporal video descriptions. Our method\nemploys a ChatGPT model as a controller, specifically designed to select frames\nfor posing video content-driven questions. Subsequently, a robust algorithm is\nutilized to answer these visual queries. This question-answer framework\neffectively uncovers intricate video details and shows promise as a method for\nenhancing video content. Following multiple conversational rounds, ChatGPT can\nsummarize enriched video content based on previous conversations. We\nqualitatively demonstrate that our Video ChatCaptioner can generate captions\ncontaining more visual details about the videos. The code is publicly available\nat https://github.com/Vision-CAIR/ChatCaptioner",
+                    "authors": "Jun Chen, Deyao Zhu, Kilichbek Haydarov, Xiang Li, Mohamed Elhoseiny",
+                    "published": "2023-04-09",
+                    "updated": "2023-05-24",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.AI"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2104.14294v2",
+                    "title": "Emerging Properties in Self-Supervised Vision Transformers",
+                    "abstract": "In this paper, we question if self-supervised learning provides new\nproperties to Vision Transformer (ViT) that stand out compared to convolutional\nnetworks (convnets). Beyond the fact that adapting self-supervised methods to\nthis architecture works particularly well, we make the following observations:\nfirst, self-supervised ViT features contain explicit information about the\nsemantic segmentation of an image, which does not emerge as clearly with\nsupervised ViTs, nor with convnets. Second, these features are also excellent\nk-NN classifiers, reaching 78.3% top-1 on ImageNet with a small ViT. Our study\nalso underlines the importance of momentum encoder, multi-crop training, and\nthe use of small patches with ViTs. We implement our findings into a simple\nself-supervised method, called DINO, which we interpret as a form of\nself-distillation with no labels. We show the synergy between DINO and ViTs by\nachieving 80.1% top-1 on ImageNet in linear evaluation with ViT-Base.",
+                    "authors": "Mathilde Caron, Hugo Touvron, Ishan Misra, Herv\u00e9 J\u00e9gou, Julien Mairal, Piotr Bojanowski, Armand Joulin",
+                    "published": "2021-04-29",
+                    "updated": "2021-05-24",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2303.11897v3",
+                    "title": "TIFA: Accurate and Interpretable Text-to-Image Faithfulness Evaluation with Question Answering",
+                    "abstract": "Despite thousands of researchers, engineers, and artists actively working on\nimproving text-to-image generation models, systems often fail to produce images\nthat accurately align with the text inputs. We introduce TIFA (Text-to-Image\nFaithfulness evaluation with question Answering), an automatic evaluation\nmetric that measures the faithfulness of a generated image to its text input\nvia visual question answering (VQA). Specifically, given a text input, we\nautomatically generate several question-answer pairs using a language model. We\ncalculate image faithfulness by checking whether existing VQA models can answer\nthese questions using the generated image. TIFA is a reference-free metric that\nallows for fine-grained and interpretable evaluations of generated images. TIFA\nalso has better correlations with human judgments than existing metrics. Based\non this approach, we introduce TIFA v1.0, a benchmark consisting of 4K diverse\ntext inputs and 25K questions across 12 categories (object, counting, etc.). We\npresent a comprehensive evaluation of existing text-to-image models using TIFA\nv1.0 and highlight the limitations and challenges of current models. For\ninstance, we find that current text-to-image models, despite doing well on\ncolor and material, still struggle in counting, spatial relations, and\ncomposing multiple objects. We hope our benchmark will help carefully measure\nthe research progress in text-to-image synthesis and provide valuable insights\nfor further research.",
+                    "authors": "Yushi Hu, Benlin Liu, Jungo Kasai, Yizhong Wang, Mari Ostendorf, Ranjay Krishna, Noah A Smith",
+                    "published": "2023-03-21",
+                    "updated": "2023-08-17",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2207.12598v1",
+                    "title": "Classifier-Free Diffusion Guidance",
+                    "abstract": "Classifier guidance is a recently introduced method to trade off mode\ncoverage and sample fidelity in conditional diffusion models post training, in\nthe same spirit as low temperature sampling or truncation in other types of\ngenerative models. Classifier guidance combines the score estimate of a\ndiffusion model with the gradient of an image classifier and thereby requires\ntraining an image classifier separate from the diffusion model. It also raises\nthe question of whether guidance can be performed without a classifier. We show\nthat guidance can be indeed performed by a pure generative model without such a\nclassifier: in what we call classifier-free guidance, we jointly train a\nconditional and an unconditional diffusion model, and we combine the resulting\nconditional and unconditional score estimates to attain a trade-off between\nsample quality and diversity similar to that obtained using classifier\nguidance.",
+                    "authors": "Jonathan Ho, Tim Salimans",
+                    "published": "2022-07-26",
+                    "updated": "2022-07-26",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2012.04842v2",
+                    "title": "Improving the Fairness of Deep Generative Models without Retraining",
+                    "abstract": "Generative Adversarial Networks (GANs) advance face synthesis through\nlearning the underlying distribution of observed data. Despite the high-quality\ngenerated faces, some minority groups can be rarely generated from the trained\nmodels due to a biased image generation process. To study the issue, we first\nconduct an empirical study on a pre-trained face synthesis model. We observe\nthat after training the GAN model not only carries the biases in the training\ndata but also amplifies them to some degree in the image generation process. To\nfurther improve the fairness of image generation, we propose an interpretable\nbaseline method to balance the output facial attributes without retraining. The\nproposed method shifts the interpretable semantic distribution in the latent\nspace for a more balanced image generation while preserving the sample\ndiversity. Besides producing more balanced data regarding a particular\nattribute (e.g., race, gender, etc.), our method is generalizable to handle\nmore than one attribute at a time and synthesize samples of fine-grained\nsubgroups. We further show the positive applicability of the balanced data\nsampled from GANs to quantify the biases in other face recognition systems,\nlike commercial face attribute classifiers and face super-resolution\nalgorithms.",
+                    "authors": "Shuhan Tan, Yujun Shen, Bolei Zhou",
+                    "published": "2020-12-09",
+                    "updated": "2021-03-29",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.AI"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2303.06594v1",
+                    "title": "ChatGPT Asks, BLIP-2 Answers: Automatic Questioning Towards Enriched Visual Descriptions",
+                    "abstract": "Asking insightful questions is crucial for acquiring knowledge and expanding\nour understanding of the world. However, the importance of questioning has been\nlargely overlooked in AI research, where models have been primarily developed\nto answer questions. With the recent advancements of large language models\n(LLMs) like ChatGPT, we discover their capability to ask high-quality questions\nwhen provided with a suitable prompt. This discovery presents a new opportunity\nto develop an automatic questioning system. In this paper, we introduce\nChatCaptioner, a novel automatic-questioning method deployed in image\ncaptioning. Here, ChatGPT is prompted to ask a series of informative questions\nabout images to BLIP-2, a strong vision question-answering model. By keeping\nacquiring new visual information from BLIP-2's answers, ChatCaptioner is able\nto generate more enriched image descriptions. We conduct human-subject\nevaluations on common image caption datasets such as COCO, Conceptual Caption,\nand WikiArt, and compare ChatCaptioner with BLIP-2 as well as ground truth. Our\nresults demonstrate that ChatCaptioner's captions are significantly more\ninformative, receiving three times as many votes from human evaluators for\nproviding the most image information. Besides, ChatCaptioner identifies 53%\nmore objects within the image than BLIP-2 alone measured by WordNet synset\nmatching. Code is available at https://github.com/Vision-CAIR/ChatCaptioner",
+                    "authors": "Deyao Zhu, Jun Chen, Kilichbek Haydarov, Xiaoqian Shen, Wenxuan Zhang, Mohamed Elhoseiny",
+                    "published": "2023-03-12",
+                    "updated": "2023-03-12",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.AI",
+                        "cs.LG"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2309.05569v1",
+                    "title": "ITI-GEN: Inclusive Text-to-Image Generation",
+                    "abstract": "Text-to-image generative models often reflect the biases of the training\ndata, leading to unequal representations of underrepresented groups. This study\ninvestigates inclusive text-to-image generative models that generate images\nbased on human-written prompts and ensure the resulting images are uniformly\ndistributed across attributes of interest. Unfortunately, directly expressing\nthe desired attributes in the prompt often leads to sub-optimal results due to\nlinguistic ambiguity or model misrepresentation. Hence, this paper proposes a\ndrastically different approach that adheres to the maxim that \"a picture is\nworth a thousand words\". We show that, for some attributes, images can\nrepresent concepts more expressively than text. For instance, categories of\nskin tones are typically hard to specify by text but can be easily represented\nby example images. Building upon these insights, we propose a novel approach,\nITI-GEN, that leverages readily available reference images for Inclusive\nText-to-Image GENeration. The key idea is learning a set of prompt embeddings\nto generate images that can effectively represent all desired attribute\ncategories. More importantly, ITI-GEN requires no model fine-tuning, making it\ncomputationally efficient to augment existing text-to-image models. Extensive\nexperiments demonstrate that ITI-GEN largely improves over state-of-the-art\nmodels to generate inclusive images from a prompt. Project page:\nhttps://czhang0528.github.io/iti-gen.",
+                    "authors": "Cheng Zhang, Xuanbai Chen, Siqi Chai, Chen Henry Wu, Dmitry Lagun, Thabo Beeler, Fernando De la Torre",
+                    "published": "2023-09-11",
+                    "updated": "2023-09-11",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.AI",
+                        "cs.CL",
+                        "cs.LG"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2302.10893v3",
+                    "title": "Fair Diffusion: Instructing Text-to-Image Generation Models on Fairness",
+                    "abstract": "Generative AI models have recently achieved astonishing results in quality\nand are consequently employed in a fast-growing number of applications.\nHowever, since they are highly data-driven, relying on billion-sized datasets\nrandomly scraped from the internet, they also suffer from degenerated and\nbiased human behavior, as we demonstrate. In fact, they may even reinforce such\nbiases. To not only uncover but also combat these undesired effects, we present\na novel strategy, called Fair Diffusion, to attenuate biases after the\ndeployment of generative text-to-image models. Specifically, we demonstrate\nshifting a bias, based on human instructions, in any direction yielding\narbitrarily new proportions for, e.g., identity groups. As our empirical\nevaluation demonstrates, this introduced control enables instructing generative\nimage models on fairness, with no data filtering and additional training\nrequired.",
+                    "authors": "Felix Friedrich, Manuel Brack, Lukas Struppek, Dominik Hintersdorf, Patrick Schramowski, Sasha Luccioni, Kristian Kersting",
+                    "published": "2023-02-07",
+                    "updated": "2023-07-17",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI",
+                        "cs.CV",
+                        "cs.CY",
+                        "cs.HC"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2010.11929v2",
+                    "title": "An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale",
+                    "abstract": "While the Transformer architecture has become the de-facto standard for\nnatural language processing tasks, its applications to computer vision remain\nlimited. In vision, attention is either applied in conjunction with\nconvolutional networks, or used to replace certain components of convolutional\nnetworks while keeping their overall structure in place. We show that this\nreliance on CNNs is not necessary and a pure transformer applied directly to\nsequences of image patches can perform very well on image classification tasks.\nWhen pre-trained on large amounts of data and transferred to multiple mid-sized\nor small image recognition benchmarks (ImageNet, CIFAR-100, VTAB, etc.), Vision\nTransformer (ViT) attains excellent results compared to state-of-the-art\nconvolutional networks while requiring substantially fewer computational\nresources to train.",
+                    "authors": "Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner, Mostafa Dehghani, Matthias Minderer, Georg Heigold, Sylvain Gelly, Jakob Uszkoreit, Neil Houlsby",
+                    "published": "2020-10-22",
+                    "updated": "2021-06-03",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.AI",
+                        "cs.LG"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2112.10752v2",
+                    "title": "High-Resolution Image Synthesis with Latent Diffusion Models",
+                    "abstract": "By decomposing the image formation process into a sequential application of\ndenoising autoencoders, diffusion models (DMs) achieve state-of-the-art\nsynthesis results on image data and beyond. Additionally, their formulation\nallows for a guiding mechanism to control the image generation process without\nretraining. However, since these models typically operate directly in pixel\nspace, optimization of powerful DMs often consumes hundreds of GPU days and\ninference is expensive due to sequential evaluations. To enable DM training on\nlimited computational resources while retaining their quality and flexibility,\nwe apply them in the latent space of powerful pretrained autoencoders. In\ncontrast to previous work, training diffusion models on such a representation\nallows for the first time to reach a near-optimal point between complexity\nreduction and detail preservation, greatly boosting visual fidelity. By\nintroducing cross-attention layers into the model architecture, we turn\ndiffusion models into powerful and flexible generators for general conditioning\ninputs such as text or bounding boxes and high-resolution synthesis becomes\npossible in a convolutional manner. Our latent diffusion models (LDMs) achieve\na new state of the art for image inpainting and highly competitive performance\non various tasks, including unconditional image generation, semantic scene\nsynthesis, and super-resolution, while significantly reducing computational\nrequirements compared to pixel-based DMs. Code is available at\nhttps://github.com/CompVis/latent-diffusion .",
+                    "authors": "Robin Rombach, Andreas Blattmann, Dominik Lorenz, Patrick Esser, Bj\u00f6rn Ommer",
+                    "published": "2021-12-20",
+                    "updated": "2022-04-13",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2304.08485v2",
+                    "title": "Visual Instruction Tuning",
+                    "abstract": "Instruction tuning large language models (LLMs) using machine-generated\ninstruction-following data has improved zero-shot capabilities on new tasks,\nbut the idea is less explored in the multimodal field. In this paper, we\npresent the first attempt to use language-only GPT-4 to generate multimodal\nlanguage-image instruction-following data. By instruction tuning on such\ngenerated data, we introduce LLaVA: Large Language and Vision Assistant, an\nend-to-end trained large multimodal model that connects a vision encoder and\nLLM for general-purpose visual and language understanding.Our early experiments\nshow that LLaVA demonstrates impressive multimodel chat abilities, sometimes\nexhibiting the behaviors of multimodal GPT-4 on unseen images/instructions, and\nyields a 85.1% relative score compared with GPT-4 on a synthetic multimodal\ninstruction-following dataset. When fine-tuned on Science QA, the synergy of\nLLaVA and GPT-4 achieves a new state-of-the-art accuracy of 92.53%. We make\nGPT-4 generated visual instruction tuning data, our model and code base\npublicly available.",
+                    "authors": "Haotian Liu, Chunyuan Li, Qingyang Wu, Yong Jae Lee",
+                    "published": "2023-04-17",
+                    "updated": "2023-12-11",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.AI",
+                        "cs.CL",
+                        "cs.LG"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2304.07193v2",
+                    "title": "DINOv2: Learning Robust Visual Features without Supervision",
+                    "abstract": "The recent breakthroughs in natural language processing for model pretraining\non large quantities of data have opened the way for similar foundation models\nin computer vision. These models could greatly simplify the use of images in\nany system by producing all-purpose visual features, i.e., features that work\nacross image distributions and tasks without finetuning. This work shows that\nexisting pretraining methods, especially self-supervised methods, can produce\nsuch features if trained on enough curated data from diverse sources. We\nrevisit existing approaches and combine different techniques to scale our\npretraining in terms of data and model size. Most of the technical\ncontributions aim at accelerating and stabilizing the training at scale. In\nterms of data, we propose an automatic pipeline to build a dedicated, diverse,\nand curated image dataset instead of uncurated data, as typically done in the\nself-supervised literature. In terms of models, we train a ViT model\n(Dosovitskiy et al., 2020) with 1B parameters and distill it into a series of\nsmaller models that surpass the best available all-purpose features, OpenCLIP\n(Ilharco et al., 2021) on most of the benchmarks at image and pixel levels.",
+                    "authors": "Maxime Oquab, Timoth\u00e9e Darcet, Th\u00e9o Moutakanni, Huy Vo, Marc Szafraniec, Vasil Khalidov, Pierre Fernandez, Daniel Haziza, Francisco Massa, Alaaeldin El-Nouby, Mahmoud Assran, Nicolas Ballas, Wojciech Galuba, Russell Howes, Po-Yao Huang, Shang-Wen Li, Ishan Misra, Michael Rabbat, Vasu Sharma, Gabriel Synnaeve, Hu Xu, Herv\u00e9 Jegou, Julien Mairal, Patrick Labatut, Armand Joulin, Piotr Bojanowski",
+                    "published": "2023-04-14",
+                    "updated": "2024-02-02",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1705.01542v2",
+                    "title": "A Spatial Structural Derivative Model for Ultraslow Diffusion",
+                    "abstract": "This study investigates the ultraslow diffusion by a spatial structural\nderivative, in which the exponential function exp(x)is selected as the\nstructural function to construct the local structural derivative diffusion\nequation model. The analytical solution of the diffusion equation is a form of\nBiexponential distribution. Its corresponding mean squared displacement is\nnumerically calculated, and increases more slowly than the logarithmic function\nof time. The local structural derivative diffusion equation with the structural\nfunction exp(x)in space is an alternative physical and mathematical modeling\nmodel to characterize a kind of ultraslow diffusion.",
+                    "authors": "Wei Xu, Wen Chen, Yingjie Liang, Jose Weberszpil",
+                    "published": "2017-05-03",
+                    "updated": "2017-06-13",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2403.01742v2",
+                    "title": "Diffusion-TS: Interpretable Diffusion for General Time Series Generation",
+                    "abstract": "Denoising diffusion probabilistic models (DDPMs) are becoming the leading\nparadigm for generative models. It has recently shown breakthroughs in audio\nsynthesis, time series imputation and forecasting. In this paper, we propose\nDiffusion-TS, a novel diffusion-based framework that generates multivariate\ntime series samples of high quality by using an encoder-decoder transformer\nwith disentangled temporal representations, in which the decomposition\ntechnique guides Diffusion-TS to capture the semantic meaning of time series\nwhile transformers mine detailed sequential information from the noisy model\ninput. Different from existing diffusion-based approaches, we train the model\nto directly reconstruct the sample instead of the noise in each diffusion step,\ncombining a Fourier-based loss term. Diffusion-TS is expected to generate time\nseries satisfying both interpretablity and realness. In addition, it is shown\nthat the proposed Diffusion-TS can be easily extended to conditional generation\ntasks, such as forecasting and imputation, without any model changes. This also\nmotivates us to further explore the performance of Diffusion-TS under irregular\nsettings. Finally, through qualitative and quantitative experiments, results\nshow that Diffusion-TS achieves the state-of-the-art results on various\nrealistic analyses of time series.",
+                    "authors": "Xinyu Yuan, Yan Qiao",
+                    "published": "2024-03-04",
+                    "updated": "2024-03-14",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2305.09605v1",
+                    "title": "Expressiveness Remarks for Denoising Diffusion Models and Samplers",
+                    "abstract": "Denoising diffusion models are a class of generative models which have\nrecently achieved state-of-the-art results across many domains. Gradual noise\nis added to the data using a diffusion process, which transforms the data\ndistribution into a Gaussian. Samples from the generative model are then\nobtained by simulating an approximation of the time reversal of this diffusion\ninitialized by Gaussian samples. Recent research has explored adapting\ndiffusion models for sampling and inference tasks. In this paper, we leverage\nknown connections to stochastic control akin to the F\\\"ollmer drift to extend\nestablished neural network approximation results for the F\\\"ollmer drift to\ndenoising diffusion models and samplers.",
+                    "authors": "Francisco Vargas, Teodora Reu, Anna Kerekes",
+                    "published": "2023-05-16",
+                    "updated": "2023-05-16",
+                    "primary_cat": "stat.ML",
+                    "cats": [
+                        "stat.ML",
+                        "cs.LG"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1603.05605v1",
+                    "title": "Multiscale modeling of diffusion in a crowded environment",
+                    "abstract": "We present a multiscale approach to model diffusion in a crowded environment\nand its effect on the reaction rates. Diffusion in biological systems is often\nmodeled by a discrete space jump process in order to capture the inherent noise\nof biological systems, which becomes important in the low copy number regime.\nTo model diffusion in the crowded cell environment efficiently, we compute the\njump rates in this mesoscopic model from local first exit times, which account\nfor the microscopic positions of the crowding molecules, while the diffusing\nmolecules jump on a coarser Cartesian grid. We then extract a macroscopic\ndescription from the resulting jump rates, where the excluded volume effect is\nmodeled by a diffusion equation with space dependent diffusion coefficient. The\ncrowding molecules can be of arbitrary shape and size and numerical experiments\ndemonstrate that those factors together with the size of the diffusing molecule\nplay a crucial role on the magnitude of the decrease in diffusive motion. When\ncorrecting the reaction rates for the altered diffusion we can show that\nmolecular crowding either enhances or inhibits chemical reactions depending on\nlocal fluctuations of the obstacle density.",
+                    "authors": "Lina Meinecke",
+                    "published": "2016-03-12",
+                    "updated": "2016-03-12",
+                    "primary_cat": "q-bio.SC",
+                    "cats": [
+                        "q-bio.SC",
+                        "math.NA",
+                        "92-08"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1801.09352v1",
+                    "title": "Distributed order Hausdorff derivative diffusion model to characterize non-Fickian diffusion in porous media",
+                    "abstract": "Many theoretical and experimental results show that solute transport in\nheterogeneous porous media exhibits multi-scaling behaviors. To describe such\nnon-Fickian diffusions, this work provides a distributed order Hausdorff\ndiffusion model to describe the tracer transport in porous media. This model is\nproved to be equivalent with the diffusion equation model with a nonlinear time\ndependent diffusion coefficient. In conjunction with the structural derivative,\nits mean squared displacement (MSD) of the tracer particles is explicitly\nderived as a dilogarithm function when the weight function of the order\ndistribution is a linear function of the time derivative order. This model can\ncapture both accelerating and decelerating anomalous and ultraslow diffusions\nby varying the weight parameter c. In this study, the tracer transport in\nwater-filled pore spaces of two-dimensional Euclidean is demonstrated as a\ndecelerating sub-diffusion, and can well be described by the distributed order\nHausdorff diffusion model with c = 1.73. While the Hausdorff diffusion model\ncan accurately fit the sub-diffusion experimental data of the tracer transport\nin the pore-solid prefractal porous media.",
+                    "authors": "Yingjie Liang, Wen Chen, Wei Xu, HongGuang Sun",
+                    "published": "2018-01-29",
+                    "updated": "2018-01-29",
+                    "primary_cat": "physics.flu-dyn",
+                    "cats": [
+                        "physics.flu-dyn"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1709.05336v1",
+                    "title": "Cs diffusion in SiC high-energy grain boundaries",
+                    "abstract": "Cesium (Cs) is a radioactive fission product whose release is of concern for\nTristructural-Isotropic (TRISO) fuel particles. In this work, Cs diffusion\nthrough high energy grain boundaries (HEGBs) of cubic-SiC is studied using an\nab-initio based kinetic Monte Carlo (kMC) model. The HEGB environment was\nmodeled as an amorphous SiC (a-SiC), and Cs defect energies were calculated\nusing density functional theory (DFT). From defect energies, it was suggested\nthat the fastest diffusion mechanism as Cs interstitial in an amorphous SiC.\nThe diffusion of Cs interstitial was simulated using a kMC, based on the site\nand transition state energies sampled from the DFT. The Cs HEGB diffusion\nexhibited an Arrhenius type diffusion in the range of 1200-1600{\\deg}C. The\ncomparison between HEGB results and the other studies suggests not only that\nthe GB diffusion dominates the bulk diffusion, but also that the HEGB is one of\nthe fastest grain boundary paths for the Cs diffusion. The diffusion\ncoefficients in HEGB are clearly a few orders of magnitude lower than the\nreported diffusion coefficients from in- and out-of- pile samples, suggesting\nthat other contributions are responsible, such as a radiation enhanced\ndiffusion.",
+                    "authors": "Hyunseok Ko, Izabela Szlufarska, Dane Morgan",
+                    "published": "2017-09-11",
+                    "updated": "2017-09-11",
+                    "primary_cat": "cond-mat.mtrl-sci",
+                    "cats": [
+                        "cond-mat.mtrl-sci",
+                        "nucl-th"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2305.14671v2",
+                    "title": "A Survey of Diffusion Models in Natural Language Processing",
+                    "abstract": "This survey paper provides a comprehensive review of the use of diffusion\nmodels in natural language processing (NLP). Diffusion models are a class of\nmathematical models that aim to capture the diffusion of information or signals\nacross a network or manifold. In NLP, diffusion models have been used in a\nvariety of applications, such as natural language generation, sentiment\nanalysis, topic modeling, and machine translation. This paper discusses the\ndifferent formulations of diffusion models used in NLP, their strengths and\nlimitations, and their applications. We also perform a thorough comparison\nbetween diffusion models and alternative generative models, specifically\nhighlighting the autoregressive (AR) models, while also examining how diverse\narchitectures incorporate the Transformer in conjunction with diffusion models.\nCompared to AR models, diffusion models have significant advantages for\nparallel generation, text interpolation, token-level controls such as syntactic\nstructures and semantic contents, and robustness. Exploring further\npermutations of integrating Transformers into diffusion models would be a\nvaluable pursuit. Also, the development of multimodal diffusion models and\nlarge-scale diffusion language models with notable capabilities for few-shot\nlearning would be important directions for the future advance of diffusion\nmodels in NLP.",
+                    "authors": "Hao Zou, Zae Myung Kim, Dongyeop Kang",
+                    "published": "2023-05-24",
+                    "updated": "2023-06-14",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1701.00257v2",
+                    "title": "Analyzing PFG anisotropic anomalous diffusions by instantaneous signal attenuation method",
+                    "abstract": "Anomalous diffusion has been investigated in many systems. Pulsed field\ngradient (PFG) anomalous diffusion is much more complicated than PFG normal\ndiffusion. There have been many theoretical and experimental studies for PFG\nisotropic anomalous diffusion, but there are very few theoretical treatments\nreported for anisotropic anomalous diffusion. Currently, there is not a general\nPFG signal attenuation expression, which includes the finite gradient pulse\neffect and can treat all three types of anisotropic fractional diffusions:\ngeneral fractional diffusion, time fractional diffusion, and space-fractional\ndiffusion. In this paper, the recently developed instantaneous signal\nattenuation (ISA) method was applied to obtain PFG signal attenuation\nexpression for free and restricted anisotropic anomalous diffusion with two\nmodels: fractal derivative and fractional derivative models. The obtained PFG\nsignal attenuation expression for anisotropic anomalous diffusion can reduce to\nthe reported result for PFG anisotropic normal diffusion. The results can also\nreduce to reported PFG isotropic anomalous diffusion results obtained by\neffective phase shift diffusion equation method and instantaneous signal\nattenuation method. For anisotropic space-fractional diffusion, the obtained\nresult agrees with that obtained by the modified Bloch equation method.\nAdditionally, The PFG signal attenuation expressions for free and restricted\nanisotropic curvilinear diffusions were derived by the traditional method, the\nresults of which agree with the PFG anisotropic fractional diffusion results\nbased on the fractional derivative model. The powder pattern of PFG anisotropic\ndiffusion was also discussed. The results here improve our understanding of PFG\nanomalous diffusion, and provide new formalisms for PFG anisotropic anomalous\ndiffusion in NMR and MRI.",
+                    "authors": "Guoxing Lin",
+                    "published": "2017-01-01",
+                    "updated": "2017-01-05",
+                    "primary_cat": "physics.chem-ph",
+                    "cats": [
+                        "physics.chem-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1503.03201v2",
+                    "title": "Fractional Diffusion Equations for Lattice and Continuum: Grunwald-Letnikov Differences and Derivatives Approach",
+                    "abstract": "Fractional diffusion equations for three-dimensional lattice models based on\nfractional-order differences of the Grunwald-Letnikov type are suggested. These\nlattice fractional diffusion equations contain difference operators that\ndescribe long-range jumps from one lattice site to other. In continuum limit,\nthe suggested lattice diffusion equations with non-integer order differences\ngive the diffusion equations with the Grunwald-Letnikov fractional derivatives\nfor continuum. We propose a consistent derivation of the fractional diffusion\nequation with the fractional derivatives of Grunwald-Letnikov type. The\nsuggested lattice diffusion equations can be considered as a new\nmicrostructural basis of space-fractional diffusion in nonlocal media.",
+                    "authors": "Vasily E. Tarasov",
+                    "published": "2015-03-11",
+                    "updated": "2015-03-12",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1908.03076v3",
+                    "title": "The strategy of survival for a competition between normal and anomalous diffusion",
+                    "abstract": "In this paper, we study the competition of two diffusion processes for\nachieving the maximum possible diffusion in an area. This competition, however,\ndoes not occur in the same circumstance; one of these processes is a normal\ndiffusion with a higher growth rate, and another one is an anomalous diffusion\nwith a lower growth rate. The trivial solution of the proposed model suggests\nthat the winner is the one with the higher growth rate. But, the question is:\nwhat characteristics and strategies should the second diffusion include to\nprolong the survival in such a competition? The studied diffusion equations\ncorrespond to the SI model such that the anomalous diffusion has memory\ndescribed by a fractional order derivative. The strategy promise that anomalous\ndiffusion reaches maximum survival in case of forgetting some parts of the\nmemory. This model can represent some of real phenomena, such as the contest of\ntwo companies in a market share, the spreading of two epidemic diseases, the\ndiffusion of two species, or any reaction-diffusion related to real-world\ncompetition.",
+                    "authors": "Moein Khalighi, Jamshid Ardalankia, Abbas Karimi Rizi, Haleh Ebadi, Gholamreza Jafari",
+                    "published": "2019-08-07",
+                    "updated": "2020-10-18",
+                    "primary_cat": "physics.soc-ph",
+                    "cats": [
+                        "physics.soc-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2012.06816v1",
+                    "title": "Evaluation and Comparison of Diffusion Models with Motif Features",
+                    "abstract": "Diffusion models simulate the propagation of influence in networks. The\ndesign and evaluation of diffusion models has been subjective and empirical.\nWhen being applied to a network represented by a graph, the diffusion model\ngenerates a sequence of edges on which the influence flows, such sequence forms\na temporal network. In most scenarios, the statistical properties or the\ncharacteristics of a network are inferred by analyzing the temporal networks\ngenerated by diffusion models. To analyze real temporal networks, the motif has\nbeen proposed as a reliable feature. However, it is unclear how the network\ntopology and the diffusion model affect the motif feature of a generated\ntemporal network. In this paper, we adopt the motif feature to evaluate the\ntemporal graph generated by a diffusion model, thence the diffusion model\nitself. Two benchmarks for quantitively evaluating diffusion models with motif,\nstability and separability, are proposed and measured on numerous diffusion\nmodels. One motif-based metric is proposed to measure the similarity between\ndiffusion models. The experiments suggest that the motif of a generated\ntemporal network is dominated by the diffusion model, while the network\ntopology is almost ignored. This result indicates that more practical and\nreliable diffusion models have to be designed with delicacy in order to capture\nthe propagation patterns of real temporal networks.",
+                    "authors": "Fangqi Li",
+                    "published": "2020-12-12",
+                    "updated": "2020-12-12",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "cs.NI"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2306.03436v2",
+                    "title": "Intellectual Property Protection of Diffusion Models via the Watermark Diffusion Process",
+                    "abstract": "Diffusion models have rapidly become a vital part of deep generative\narchitectures, given today's increasing demands. Obtaining large,\nhigh-performance diffusion models demands significant resources, highlighting\ntheir importance as intellectual property worth protecting. However, existing\nwatermarking techniques for ownership verification are insufficient when\napplied to diffusion models. Very recent research in watermarking diffusion\nmodels either exposes watermarks during task generation, which harms the\nimperceptibility, or is developed for conditional diffusion models that require\nprompts to trigger the watermark. This paper introduces WDM, a novel\nwatermarking solution for diffusion models without imprinting the watermark\nduring task generation. It involves training a model to concurrently learn a\nWatermark Diffusion Process (WDP) for embedding watermarks alongside the\nstandard diffusion process for task generation. We provide a detailed\ntheoretical analysis of WDP training and sampling, relating it to a shifted\nGaussian diffusion process via the same reverse noise. Extensive experiments\nare conducted to validate the effectiveness and robustness of our approach in\nvarious trigger and watermark data configurations.",
+                    "authors": "Sen Peng, Yufei Chen, Cong Wang, Xiaohua Jia",
+                    "published": "2023-06-06",
+                    "updated": "2023-11-29",
+                    "primary_cat": "cs.CR",
+                    "cats": [
+                        "cs.CR",
+                        "cs.LG"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/cond-mat/0210703v1",
+                    "title": "Membrane bound protein diffusion viewed by fluorescence recovery after bleaching experiments : models analysis",
+                    "abstract": "Diffusion processes in biological membranes are of interest to understand the\nmacromolecular organisation and function of several molecules. Fluorescence\nRecovery After Photobleaching (FRAP) has been widely used as a method to\nanalyse this processes using classical Brownian diffusion model. In the first\npart of this work, the analytical expression of the fluorescence recovery as a\nfunction of time has been established for anomalous diffusion due to long\nwaiting times. Then, experimental fluorescence recoveries recorded in living\ncells on a membrane-bound protein have been analysed using three different\nmodels : normal Brownian diffusion, Brownian diffusion with an immobile\nfraction and anomalous diffusion due to long waiting times.",
+                    "authors": "C. Favard, N. Olivi-Tran, J. -L. Meunier",
+                    "published": "2002-10-31",
+                    "updated": "2002-10-31",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech",
+                        "physics.bio-ph",
+                        "q-bio.BM"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2305.13122v1",
+                    "title": "Policy Representation via Diffusion Probability Model for Reinforcement Learning",
+                    "abstract": "Popular reinforcement learning (RL) algorithms tend to produce a unimodal\npolicy distribution, which weakens the expressiveness of complicated policy and\ndecays the ability of exploration. The diffusion probability model is powerful\nto learn complicated multimodal distributions, which has shown promising and\npotential applications to RL. In this paper, we formally build a theoretical\nfoundation of policy representation via the diffusion probability model and\nprovide practical implementations of diffusion policy for online model-free RL.\nConcretely, we character diffusion policy as a stochastic process, which is a\nnew approach to representing a policy. Then we present a convergence guarantee\nfor diffusion policy, which provides a theory to understand the multimodality\nof diffusion policy. Furthermore, we propose the DIPO which is an\nimplementation for model-free online RL with DIffusion POlicy. To the best of\nour knowledge, DIPO is the first algorithm to solve model-free online RL\nproblems with the diffusion model. Finally, extensive empirical results show\nthe effectiveness and superiority of DIPO on the standard continuous control\nMujoco benchmark.",
+                    "authors": "Long Yang, Zhixiong Huang, Fenghao Lei, Yucun Zhong, Yiming Yang, Cong Fang, Shiting Wen, Binbin Zhou, Zhouchen Lin",
+                    "published": "2023-05-22",
+                    "updated": "2023-05-22",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2110.14851v1",
+                    "title": "Behavior of Spiral Wave Spectra with a Rank-Deficient Diffusion Matrix",
+                    "abstract": "Spiral waves emerge in numerous pattern forming systems and are commonly\nmodeled with reaction-diffusion systems. Some systems used to model biological\nprocesses, such as ion-channel models, fall under the reaction-diffusion\ncategory and often have one or more non-diffusing species which results in a\nrank-deficient diffusion matrix. Previous theoretical research focused on\nspiral spectra for strictly positive diffusion matrices. In this paper, we use\na general two-variable reaction-diffusion system to compare the essential and\nabsolute spectra of spiral waves for strictly positive and rank-deficient\ndiffusion matrices. We show that the essential spectrum is not continuous in\nthe limit of vanishing diffusion in one component. Moreover, we predict\nlocations for the absolute spectrum in the case of a non-diffusing slow\nvariable. Predictions are confirmed numerically for the Barkley and Karma\nmodels.",
+                    "authors": "Stephanie Dodson, Bjorn Sandstede",
+                    "published": "2021-10-28",
+                    "updated": "2021-10-28",
+                    "primary_cat": "math.DS",
+                    "cats": [
+                        "math.DS"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2211.07804v3",
+                    "title": "Diffusion Models for Medical Image Analysis: A Comprehensive Survey",
+                    "abstract": "Denoising diffusion models, a class of generative models, have garnered\nimmense interest lately in various deep-learning problems. A diffusion\nprobabilistic model defines a forward diffusion stage where the input data is\ngradually perturbed over several steps by adding Gaussian noise and then learns\nto reverse the diffusion process to retrieve the desired noise-free data from\nnoisy data samples. Diffusion models are widely appreciated for their strong\nmode coverage and quality of the generated samples despite their known\ncomputational burdens. Capitalizing on the advances in computer vision, the\nfield of medical imaging has also observed a growing interest in diffusion\nmodels. To help the researcher navigate this profusion, this survey intends to\nprovide a comprehensive overview of diffusion models in the discipline of\nmedical image analysis. Specifically, we introduce the solid theoretical\nfoundation and fundamental concepts behind diffusion models and the three\ngeneric diffusion modelling frameworks: diffusion probabilistic models,\nnoise-conditioned score networks, and stochastic differential equations. Then,\nwe provide a systematic taxonomy of diffusion models in the medical domain and\npropose a multi-perspective categorization based on their application, imaging\nmodality, organ of interest, and algorithms. To this end, we cover extensive\napplications of diffusion models in the medical domain. Furthermore, we\nemphasize the practical use case of some selected approaches, and then we\ndiscuss the limitations of the diffusion models in the medical domain and\npropose several directions to fulfill the demands of this field. Finally, we\ngather the overviewed studies with their available open-source implementations\nat\nhttps://github.com/amirhossein-kz/Awesome-Diffusion-Models-in-Medical-Imaging.",
+                    "authors": "Amirhossein Kazerouni, Ehsan Khodapanah Aghdam, Moein Heidari, Reza Azad, Mohsen Fayyaz, Ilker Hacihaliloglu, Dorit Merhof",
+                    "published": "2022-11-14",
+                    "updated": "2023-06-03",
+                    "primary_cat": "eess.IV",
+                    "cats": [
+                        "eess.IV",
+                        "cs.CV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/0805.0647v1",
+                    "title": "Scaling of Rough Surfaces: Effects of Surface Diffusion on Growth and Roughness Exponents",
+                    "abstract": "Random deposition model with surface diffusion over several next nearest\nneighbours is studied. The results agree with the results obtained by Family\nfor the case of nearest neighbour diffusion [F. Family, J. Phys. A 19(8), L441,\n1986]. However for larger diffusion steps, the growth exponent and the\nroughness exponent show interesting dependence on diffusion length.",
+                    "authors": "Baisakhi Mal, Subhankar Ray, J. Shamanna",
+                    "published": "2008-05-06",
+                    "updated": "2008-05-06",
+                    "primary_cat": "cond-mat.soft",
+                    "cats": [
+                        "cond-mat.soft",
+                        "cond-mat.stat-mech"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1807.03744v2",
+                    "title": "Enhanced Diffusivity in Perturbed Senile Reinforced Random Walk Models",
+                    "abstract": "We consider diffusivity of random walks with transition probabilities\ndepending on the number of consecutive traversals of the last traversed edge,\nthe so called senile reinforced random walk (SeRW). In one dimension, the walk\nis known to be sub-diffusive with identity reinforcement function. We perturb\nthe model by introducing a small probability $\\delta$ of escaping the last\ntraversed edge at each step. The perturbed SeRW model is diffusive for any\n$\\delta >0 $, with enhanced diffusivity ($\\gg O(\\delta^2)$) in the small\n$\\delta$ regime. We further study stochastically perturbed SeRW models by\nhaving the last edge escape probability of the form $\\delta\\, \\xi_n$ with\n$\\xi_n$'s being independent random variables. Enhanced diffusivity in such\nmodels are logarithmically close to the so called residual diffusivity\n(positive in the zero $\\delta$ limit), with diffusivity between\n$O\\left(\\frac{1}{|\\log\\delta |}\\right)$ and\n$O\\left(\\frac{1}{\\log|\\log\\delta|}\\right)$. Finally, we generalize our results\nto higher dimensions where the unperturbed model is already diffusive. The\nenhanced diffusivity can be as much as $O(\\log^{-2}\\delta)$.",
+                    "authors": "Thu Dinh, Jack Xin",
+                    "published": "2018-07-10",
+                    "updated": "2020-03-16",
+                    "primary_cat": "math.PR",
+                    "cats": [
+                        "math.PR",
+                        "60G50, 60H30, 58J37"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2211.08892v2",
+                    "title": "Fast Graph Generation via Spectral Diffusion",
+                    "abstract": "Generating graph-structured data is a challenging problem, which requires\nlearning the underlying distribution of graphs. Various models such as graph\nVAE, graph GANs, and graph diffusion models have been proposed to generate\nmeaningful and reliable graphs, among which the diffusion models have achieved\nstate-of-the-art performance. In this paper, we argue that running full-rank\ndiffusion SDEs on the whole graph adjacency matrix space hinders diffusion\nmodels from learning graph topology generation, and hence significantly\ndeteriorates the quality of generated graph data. To address this limitation,\nwe propose an efficient yet effective Graph Spectral Diffusion Model (GSDM),\nwhich is driven by low-rank diffusion SDEs on the graph spectrum space. Our\nspectral diffusion model is further proven to enjoy a substantially stronger\ntheoretical guarantee than standard diffusion models. Extensive experiments\nacross various datasets demonstrate that, our proposed GSDM turns out to be the\nSOTA model, by exhibiting both significantly higher generation quality and much\nless computational consumption than the baselines.",
+                    "authors": "Tianze Luo, Zhanfeng Mo, Sinno Jialin Pan",
+                    "published": "2022-11-16",
+                    "updated": "2022-11-19",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2305.10028v1",
+                    "title": "Pyramid Diffusion Models For Low-light Image Enhancement",
+                    "abstract": "Recovering noise-covered details from low-light images is challenging, and\nthe results given by previous methods leave room for improvement. Recent\ndiffusion models show realistic and detailed image generation through a\nsequence of denoising refinements and motivate us to introduce them to\nlow-light image enhancement for recovering realistic details. However, we found\ntwo problems when doing this, i.e., 1) diffusion models keep constant\nresolution in one reverse process, which limits the speed; 2) diffusion models\nsometimes result in global degradation (e.g., RGB shift). To address the above\nproblems, this paper proposes a Pyramid Diffusion model (PyDiff) for low-light\nimage enhancement. PyDiff uses a novel pyramid diffusion method to perform\nsampling in a pyramid resolution style (i.e., progressively increasing\nresolution in one reverse process). Pyramid diffusion makes PyDiff much faster\nthan vanilla diffusion models and introduces no performance degradation.\nFurthermore, PyDiff uses a global corrector to alleviate the global degradation\nthat may occur in the reverse process, significantly improving the performance\nand making the training of diffusion models easier with little additional\ncomputational consumption. Extensive experiments on popular benchmarks show\nthat PyDiff achieves superior performance and efficiency. Moreover, PyDiff can\ngeneralize well to unseen noise and illumination distributions.",
+                    "authors": "Dewei Zhou, Zongxin Yang, Yi Yang",
+                    "published": "2023-05-17",
+                    "updated": "2023-05-17",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1907.09989v1",
+                    "title": "Rogue Heat and Diffusion Waves",
+                    "abstract": "In this paper, we numerically show and discuss the existence and\ncharacteristics of rogue heat and diffusion waves. More specifically, we use\ntwo different nonlinear heat (diffusion) models and show that modulation\ninstability leads to the generation of unexpected and large fluctuations in the\nframe of these models. These fluctuations can be named as rogue heat\n(diffusion) waves. We discuss the properties and statistics of such rogue\nwaves. Our results can find many important applications in many branches such\nas the nonlinear heat transfer, turbulence, financial mathematics, chemical or\nbiological diffusion, nuclear reactions, subsurface water infiltration, and\npore water pressure diffusion modeled in the frame of nonlinear Terzaghi\nconsolidation models, just to name a few.",
+                    "authors": "Cihan Bayindir",
+                    "published": "2019-07-18",
+                    "updated": "2019-07-18",
+                    "primary_cat": "nlin.PS",
+                    "cats": [
+                        "nlin.PS",
+                        "physics.flu-dyn"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2312.08873v1",
+                    "title": "Diffusion Cocktail: Fused Generation from Diffusion Models",
+                    "abstract": "Diffusion models excel at generating high-quality images and are easy to\nextend, making them extremely popular among active users who have created an\nextensive collection of diffusion models with various styles by fine-tuning\nbase models such as Stable Diffusion. Recent work has focused on uncovering\nsemantic and visual information encoded in various components of a diffusion\nmodel, enabling better generation quality and more fine-grained control.\nHowever, those methods target improving a single model and overlook the vastly\navailable collection of fine-tuned diffusion models. In this work, we study the\ncombinations of diffusion models. We propose Diffusion Cocktail (Ditail), a\ntraining-free method that can accurately transfer content information between\ntwo diffusion models. This allows us to perform diverse generations using a set\nof diffusion models, resulting in novel images that are unlikely to be obtained\nby a single model alone. We also explore utilizing Ditail for style transfer,\nwith the target style set by a diffusion model instead of an image. Ditail\noffers a more detailed manipulation of the diffusion generation, thereby\nenabling the vast community to integrate various styles and contents seamlessly\nand generate any content of any style.",
+                    "authors": "Haoming Liu, Yuanhe Guo, Shengjie Wang, Hongyi Wen",
+                    "published": "2023-12-12",
+                    "updated": "2023-12-12",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.AI"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1906.02405v1",
+                    "title": "Indirect interactions influence contact network structure and diffusion dynamics",
+                    "abstract": "Interaction patterns at the individual level influence the behaviour of\ndiffusion over contact networks. Most of the current diffusion models only\nconsider direct interactions among individuals to build underlying infectious\nitems transmission networks. However, delayed indirect interactions, where a\nsusceptible individual interacts with infectious items after the infected\nindividual has left the interaction space, can also cause transmission events.\nWe define a diffusion model called the same place different time transmission\n(SPDT) based diffusion that considers transmission links for these indirect\ninteractions. Our SPDT model changes the network dynamics where the\nconnectivity among individuals varies with the decay rates of link infectivity.\nWe investigate SPDT diffusion behaviours by simulating airborne disease\nspreading on data-driven contact networks. The SPDT model significantly\nincreases diffusion dynamics (particularly for networks with low link densities\nwhere indirect interactions create new infection pathways) and is capable of\nproducing realistic disease reproduction number. Our results show that the SPDT\nmodel is significantly more likely to lead to outbreaks compared to current\ndiffusion models with direct interactions. We find that the diffusion dynamics\nwith including indirect links are not reproducible by the current models,\nhighlighting the importance of the indirect links for predicting outbreaks.",
+                    "authors": "Md Shahzamal, Raja Jurdak, Bernard Mans, Frank de Hoog",
+                    "published": "2019-06-06",
+                    "updated": "2019-06-06",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "physics.soc-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2301.00059v2",
+                    "title": "Describing NMR chemical exchange by effective phase diffusion approach",
+                    "abstract": "This paper proposes an effective phase diffusion method to analyze chemical\nexchange in nuclear magnetic resonance (NMR). The chemical exchange involves\nspin jumps around different sites where the spin angular frequencies vary,\nwhich leads to a random phase walk viewed from the rotating frame reference.\nTherefore, the random walk in phase space can be treated by the effective phase\ndiffusion method. Both the coupled and uncoupled phase diffusions are\nconsidered; additionally, it includes normal diffusion as well as fractional\ndiffusion. Based on these phase diffusion equations, the line shape of NMR\nexchange spectrum can be analyzed. By comparing these theoretical results with\nthe conventional theory, this phase diffusion approach works for fast exchange,\nranging from slightly faster than intermediate exchange to very fast exchange.\nFor normal diffusion models, the theoretically predicted curves agree with\nthose predicted from traditional models in the literature, and the\ncharacteristic exchange time obtained from phase diffusion with a fixed jump\ntime is the same as that obtained from the conventional model. However, the\nphase diffusion with a monoexponential time distribution gives a characteristic\nexchange time constant which is half of that obtained from the traditional\nmodel. Additionally, the fractional diffusion obtains a significantly different\nline shape than that predicted based on normal diffusion.",
+                    "authors": "Guoxing Lin",
+                    "published": "2022-12-30",
+                    "updated": "2023-05-17",
+                    "primary_cat": "physics.chem-ph",
+                    "cats": [
+                        "physics.chem-ph",
+                        "cond-mat.stat-mech"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/physics/0403039v1",
+                    "title": "Non-diffusive transport in plasma turbulence: a fractional diffusion approach",
+                    "abstract": "Numerical evidence of non-diffusive transport in three-dimensional, resistive\npressure-gradient-driven plasma turbulence is presented. It is shown that the\nprobability density function (pdf) of test particles' radial displacements is\nstrongly non-Gaussian and exhibits algebraic decaying tails. To model these\nresults we propose a macroscopic transport model for the pdf based on the use\nof fractional derivatives in space and time, that incorporate in a unified way\nspace-time non-locality (non-Fickian transport), non-Gaussianity, and\nnon-diffusive scaling. The fractional diffusion model reproduces the shape, and\nspace-time scaling of the non-Gaussian pdf of turbulent transport calculations.\nThe model also reproduces the observed super-diffusive scaling.",
+                    "authors": "D. del-Castillo-Negrete, B. A. Carreras, V. E. Lynch",
+                    "published": "2004-03-04",
+                    "updated": "2004-03-04",
+                    "primary_cat": "physics.plasm-ph",
+                    "cats": [
+                        "physics.plasm-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/nlin/0212039v2",
+                    "title": "Front dynamics in reaction-diffusion systems with Levy flights: a fractional diffusion approach",
+                    "abstract": "The use of reaction-diffusion models rests on the key assumption that the\nunderlying diffusive process is Gaussian. However, a growing number of studies\nhave pointed out the prevalence of anomalous diffusion, and there is a need to\nunderstand the dynamics of reactive systems in the presence of this type of\nnon-Gaussian diffusion. Here we present a study of front dynamics in\nreaction-diffusion systems where anomalous diffusion is due to the presence of\nasymmetric Levy flights. Our approach consists of replacing the Laplacian\ndiffusion operator by a fractional diffusion operator, whose fundamental\nsolutions are Levy $\\alpha$-stable distributions. Numerical simulation of the\nfractional Fisher-Kolmogorov equation, and analytical arguments show that\nanomalous diffusion leads to the exponential acceleration of fronts and a\nuniversal power law decay, $x^{-\\alpha}$, of the tail, where $\\alpha$, the\nindex of the Levy distribution, is the order of the fractional derivative.",
+                    "authors": "D. del-Castillo-Negrete, B. A. Carreras, V. E. Lynch",
+                    "published": "2002-12-17",
+                    "updated": "2003-06-30",
+                    "primary_cat": "nlin.PS",
+                    "cats": [
+                        "nlin.PS",
+                        "nlin.CD"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2304.01565v1",
+                    "title": "A Survey on Graph Diffusion Models: Generative AI in Science for Molecule, Protein and Material",
+                    "abstract": "Diffusion models have become a new SOTA generative modeling method in various\nfields, for which there are multiple survey works that provide an overall\nsurvey. With the number of articles on diffusion models increasing\nexponentially in the past few years, there is an increasing need for surveys of\ndiffusion models on specific fields. In this work, we are committed to\nconducting a survey on the graph diffusion models. Even though our focus is to\ncover the progress of diffusion models in graphs, we first briefly summarize\nhow other generative modeling methods are used for graphs. After that, we\nintroduce the mechanism of diffusion models in various forms, which facilitates\nthe discussion on the graph diffusion models. The applications of graph\ndiffusion models mainly fall into the category of AI-generated content (AIGC)\nin science, for which we mainly focus on how graph diffusion models are\nutilized for generating molecules and proteins but also cover other cases,\nincluding materials design. Moreover, we discuss the issue of evaluating\ndiffusion models in the graph domain and the existing challenges.",
+                    "authors": "Mengchun Zhang, Maryam Qamar, Taegoo Kang, Yuna Jung, Chenshuang Zhang, Sung-Ho Bae, Chaoning Zhang",
+                    "published": "2023-04-04",
+                    "updated": "2023-04-04",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.CV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1712.02290v2",
+                    "title": "Effects of nongaussian diffusion on \"isotropic diffusion measurements'': an ex-vivo microimaging and simulation study",
+                    "abstract": "Designing novel diffusion-weighted pulse sequences to probe tissue\nmicrostructure beyond the conventional Stejskal-Tanner family is currently of\nbroad interest. One such technique, multidimensional diffusion MRI, has been\nrecently proposed to afford model-free decomposition of diffusion signal\nkurtosis into terms originating from either ensemble variance of isotropic\ndiffusivity or microscopic diffusion anisotropy. This ability rests on the\nassumption that diffusion can be described as a sum of multiple Gaussian\ncompartments, but this is often not strictly fulfilled. The effects of\nnongaussian diffusion on single shot isotropic diffusion sequences were first\nconsidered in detail by de Swiet and Mitra in 1996. They showed theoretically\nthat anisotropic compartments lead to anisotropic time dependence of the\ndiffusion tensors, which causes the measured isotropic diffusivity to depend on\ngradient frame orientation. Here we show how such deviations from the multiple\nGaussian compartments assumption conflates orientation dispersion with ensemble\nvariance in isotropic diffusivity. Second, we consider additional contributions\nto the apparent variance in isotropic diffusivity arising due to\nintracompartmental kurtosis. These will likewise depend on gradient frame\norientation. We illustrate the potential importance of these confounds with\nanalytical expressions, numerical simulations in simple model geometries, and\nmicroimaging experiments in fixed spinal cord using isotropic diffusion\nencoding waveforms with 7.5 ms duration and 3000 mT/m maximum amplitude.",
+                    "authors": "Sune N\u00f8rh\u00f8j Jespersen, Jonas Lynge Olesen, Andrada Ianu\u015f, Noam Shemesh",
+                    "published": "2017-12-06",
+                    "updated": "2019-02-04",
+                    "primary_cat": "physics.bio-ph",
+                    "cats": [
+                        "physics.bio-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1906.02856v1",
+                    "title": "Diffusion on dynamic contact networks with indirect transmission links",
+                    "abstract": "Modelling diffusion processes on dynamic contact networks is an important\nresearch area for epidemiology, marketing, cybersecurity, and ecology. However,\ncurrent diffusion models cannot capture transmissions occurring for indirect\ninteractions. For example, an airborne infected individual releases infectious\nparticles at locations that can suspend in the air and infect susceptible\nindividuals arriving even after the infected individual left. Thus, current\ndiffusion models miss transmissions during indirect interactions. In this\nthesis, a novel diffusion model called the same place different time\ntransmission based diffusion (SPDT) is introduced to take into account the\ntransmissions through indirect interactions. The behaviour of SPDT diffusion is\nanalysed on real dynamic contact networks and a significant amplification in\ndiffusion dynamics is observed. The SPDT model also introduces some novel\nbehaviours different from current diffusion models. In this work, a new SPDT\ngraph model is also developed to generate synthetic traces to explore SPDT\ndiffusion in several scenarios. The analysis shows that the emergence of new\ndiffusion becomes common thanks to the inclusion of indirect transmissions\nwithin the SPDT model. This work finally investigates how diffusion can be\ncontrolled and develops new methods to hinder diffusion.",
+                    "authors": "Md Shahzamal",
+                    "published": "2019-06-07",
+                    "updated": "2019-06-07",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "physics.soc-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1609.09697v1",
+                    "title": "Anomalous diffusion in time-fluctuating non-stationary diffusivity landscapes",
+                    "abstract": "We investigate the ensemble and time averaged mean squared displacements for\nparticle diffusion in a simple model for disordered media by assuming that the\nlocal diffusivity is both fluctuating in time and has a deterministic average\ngrowth or decay in time. In this study we compare computer simulations of the\nstochastic Langevin equation for this random diffusion process with analytical\nresults. We explore the regimes of normal Brownian motion as well as anomalous\ndiffusion in the sub- and superdiffusive regimes. We also consider effects of\nthe inertial term on the particle motion. The investigation of the resulting\ndiffusion is performed for unconfined and confined motion.",
+                    "authors": "A. G. Cherstvy, R. Metzler",
+                    "published": "2016-09-30",
+                    "updated": "2016-09-30",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1905.04004v2",
+                    "title": "Well-posedness of a cross-diffusion population model with nonlocal diffusion",
+                    "abstract": "We prove the existence and uniqueness of solution of a nonlocal\ncross-diffusion competitive population model for two species. The model may be\nconsidered as a version, or even an approximation, of the paradigmatic\nShigesada-Kawasaki-Teramoto cross-diffusion model, in which the usual diffusion\ndifferential operator is replaced by an integral diffusion operator. The proof\nof existence of solutions is based on a compactness argument, while the\nuniqueness of solution is achieved through a duality technique.",
+                    "authors": "Gonzalo Galiano, Juli\u00e1n Velasco",
+                    "published": "2019-05-10",
+                    "updated": "2024-01-24",
+                    "primary_cat": "math.AP",
+                    "cats": [
+                        "math.AP"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1506.05574v1",
+                    "title": "Information Diffusion issues",
+                    "abstract": "In this report there will be a discussion for Information Diffusion. There\nwill be discussions on what information diffusion is, its key characteristics\nand on several other aspects of these kinds of networks. This report will focus\non peer to peer models in information diffusion. There will be discussions on\nepidemic model, OSN and other details related to information diffusion.",
+                    "authors": "Jonathan Helmigh",
+                    "published": "2015-06-18",
+                    "updated": "2015-06-18",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1404.3573v1",
+                    "title": "\"Diffusing diffusivity\": A model for anomalous and \"anomalous yet Brownian\" diffusion",
+                    "abstract": "Wang et al. [PNAS 106 (2009) 15160] have found that in several systems the\nlinear time dependence of the mean-square displacement (MSD) of diffusing\ncolloidal particles, typical of normal diffusion, is accompanied by a\nnon-Gaussian displacement distribution (DisD), with roughly exponential tails\nat short times, a situation they termed \"anomalous yet Brownian\" diffusion. The\ndiversity of systems in which this is observed calls for a generic model. We\npresent such a model where there is \"diffusivity memory\" but no \"direction\nmemory\" in the particle trajectory, and we show that it leads to both a linear\nMSD and a non-Gaussian DisD at short times. In our model, the diffusivity is\nundergoing a (perhaps biased) random walk, hence the expression \"diffusing\ndiffusivity\". The DisD is predicted to be exactly exponential at short times if\nthe distribution of diffusivities is itself exponential, but an exponential\nremains a good fit to the DisD for a variety of diffusivity distributions.\nMoreover, our generic model can be modified to produce subdiffusion.",
+                    "authors": "Mykyta V. Chubynsky, Gary W. Slater",
+                    "published": "2014-04-14",
+                    "updated": "2014-04-14",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech",
+                        "cond-mat.soft"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2402.13144v1",
+                    "title": "Neural Network Diffusion",
+                    "abstract": "Diffusion models have achieved remarkable success in image and video\ngeneration. In this work, we demonstrate that diffusion models can also\n\\textit{generate high-performing neural network parameters}. Our approach is\nsimple, utilizing an autoencoder and a standard latent diffusion model. The\nautoencoder extracts latent representations of a subset of the trained network\nparameters. A diffusion model is then trained to synthesize these latent\nparameter representations from random noise. It then generates new\nrepresentations that are passed through the autoencoder's decoder, whose\noutputs are ready to use as new subsets of network parameters. Across various\narchitectures and datasets, our diffusion process consistently generates models\nof comparable or improved performance over trained networks, with minimal\nadditional cost. Notably, we empirically find that the generated models perform\ndifferently with the trained networks. Our results encourage more exploration\non the versatile use of diffusion models.",
+                    "authors": "Kai Wang, Zhaopan Xu, Yukun Zhou, Zelin Zang, Trevor Darrell, Zhuang Liu, Yang You",
+                    "published": "2024-02-20",
+                    "updated": "2024-02-20",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.CV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/0801.3436v1",
+                    "title": "Model for Diffusion-Induced Ramsey Narrowing",
+                    "abstract": "Diffusion-induced Ramsey narrowing that appears when atoms can leave the\ninteraction region and repeatedly return without lost of coherence is\ninvestigated using strong collisions approximation. The effective diffusion\nequation is obtained and solved for low-dimensional model configurations and\nthree-dimensional real one.",
+                    "authors": "Alexander Romanenko, Leonid Yatsenko",
+                    "published": "2008-01-22",
+                    "updated": "2008-01-22",
+                    "primary_cat": "quant-ph",
+                    "cats": [
+                        "quant-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2308.06342v2",
+                    "title": "Mirror Diffusion Models",
+                    "abstract": "Diffusion models have successfully been applied to generative tasks in\nvarious continuous domains. However, applying diffusion to discrete categorical\ndata remains a non-trivial task. Moreover, generation in continuous domains\noften requires clipping in practice, which motivates the need for a theoretical\nframework for adapting diffusion to constrained domains. Inspired by the mirror\nLangevin algorithm for the constrained sampling problem, in this theoretical\nreport we propose Mirror Diffusion Models (MDMs). We demonstrate MDMs in the\ncontext of simplex diffusion and propose natural extensions to popular domains\nsuch as image and text generation.",
+                    "authors": "Jaesung Tae",
+                    "published": "2023-08-11",
+                    "updated": "2023-08-18",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1210.5101v1",
+                    "title": "Global well-posedness and zero-diffusion limit of classical solutions to the 3D conservation laws arising in chemotaxis",
+                    "abstract": "In this paper, we study the relationship between a diffusive model and a\nnon-diffusive model which are both derived from the well-known Keller-Segel\nmodel, as a coefficient of diffusion $\\varepsilon$ goes to zero. First, we\nestablish the global well-posedness of classical solutions to the Cauchy\nproblem for the diffusive model with smooth initial data which is of small\n$L^2$ norm, together with some {\\it a priori} estimates uniform for $t$ and\n$\\varepsilon$. Then we investigate the zero-diffusion limit, and get the global\nwell-posedness of classical solutions to the Cauchy problem for the\nnon-diffusive model. Finally, we derive the convergence rate of the diffusive\nmodel toward the non-diffusive model. It is shown that the convergence rate in\n$L^\\infty$ norm is of the order $O(\\varepsilon^{1/2})$. It should be noted that\nthe initial data is small in $L^2$-norm but can be of large oscillations with\nconstant state at far field. As a byproduct, we improve the corresponding\nresult on the well-posedness of the non-difussive model which requires small\noscillations.",
+                    "authors": "Hongyun Peng, Huanyao Wen, Changjiang Zhu",
+                    "published": "2012-10-18",
+                    "updated": "2012-10-18",
+                    "primary_cat": "math.AP",
+                    "cats": [
+                        "math.AP"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1911.11645v1",
+                    "title": "Effects of different discretisations of the Laplacian upon stochastic simulations of reaction-diffusion systems on both static and growing domains",
+                    "abstract": "By discretising space into compartments and letting system dynamics be\ngoverned by the reaction-diffusion master equation, it is possible to derive\nand simulate a stochastic model of reaction and diffusion on an arbitrary\ndomain. However, there are many implementation choices involved in this\nprocess, such as the choice of discretisation and method of derivation of the\ndiffusive jump rates, and it is not clear a priori how these affect model\npredictions. To shed light on this issue, in this work we explore how a variety\nof discretisations and method for derivation of the diffusive jump rates affect\nthe outputs of stochastic simulations of reaction-diffusion models, in\nparticular using Turing's model of pattern formation as a key example. We\nconsider both static and uniformly growing domains and demonstrate that, while\nonly minor differences are observed for simple reaction-diffusion systems,\nthere can be vast differences in model predictions for systems that include\ncomplicated reaction kinetics, such as Turing's model of pattern formation. Our\nwork highlights that care must be taken in using the reaction-diffusion master\nequation to make predictions as to the dynamics of stochastic\nreaction-diffusion systems.",
+                    "authors": "Bartosz J. Bartmanski, Ruth E. Baker",
+                    "published": "2019-11-26",
+                    "updated": "2019-11-26",
+                    "primary_cat": "physics.comp-ph",
+                    "cats": [
+                        "physics.comp-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/0907.0417v1",
+                    "title": "Microscopic origin of the jump diffusion model",
+                    "abstract": "The present paper is aimed at studying the microscopic origin of the jump\ndiffusion. Starting from the $N$-body Liouville equation and making only the\nassumption that molecular reorientation is overdamped, we derive and solve the\nnew (hereafter generalized diffusion) equation. This is the most general\nequation which governs orientational relaxation of an equilibrium molecular\nensemble in the hindered rotation limit and in the long time limit. The\ngeneralized diffusion equation is an extension of the small-angle diffusion\nequation beyond the impact approximation. We establish the conditions under\nwhich the generalized diffusion equation can be identified with the jump\ndiffusion equation, and also discuss the similarities and differences between\nthe two approaches.",
+                    "authors": "M. F. Gelin, D. S. Kosov",
+                    "published": "2009-07-02",
+                    "updated": "2009-07-02",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1705.07063v1",
+                    "title": "Double diffusivity model under stochastic forcing",
+                    "abstract": "The \"double diffusivity\" model was proposed in the late 1970s, and reworked\nin the early 1980s, as a continuum counterpart to existing discrete models of\ndiffusion corresponding to high diffusivity paths, such as grain boundaries and\ndislocation lines. Technically, the model pans out as a system of coupled {\\it\nFick type} diffusion equations to represent \"regular\" and \"high\" diffusivity\npaths with \"source terms\" accounting for the mass exchange between the two\npaths. The model remit was extended by analogy to describe flow in porous media\nwith double porosity, as well as to model heat conduction in media with two\nnon-equilibrium local temperature baths e.g. ion and electron baths. Uncoupling\nof the two partial differential equations leads to a higher-ordered diffusion\nequation, solutions of which could be obtained in terms of classical diffusion\nequation solutions. Similar equations could also be derived within an \"internal\nlength\" gradient (ILG) mechanics formulation applied to diffusion problems,\n{\\it i.e.}, by introducing nonlocal effects, together with inertia and\nviscosity, in a mechanics based formulation of diffusion theory. This issue\nbecomes particularly important in the case of diffusion in nanopolycrystals\nwhose deterministic ILG based theoretical calculations predict a relaxation\ntime that is only about one-tenth of the actual experimentally verified\ntimescale. This article provides the \"missing link\" in this estimation by\nadding a vital element in the ILG structure, that of stochasticity, that takes\ninto account all boundary layer fluctuations. Our stochastic-ILG diffusion\ncalculation confirms rapprochement between theory and experiment, thereby\nbenchmarking a new generation of gradient-based continuum models that conform\ncloser to real life fluctuating environments.",
+                    "authors": "Amit K Chattopadhyay, Elias C Aifantis",
+                    "published": "2017-05-19",
+                    "updated": "2017-05-19",
+                    "primary_cat": "cond-mat.soft",
+                    "cats": [
+                        "cond-mat.soft",
+                        "cond-mat.mtrl-sci",
+                        "cond-mat.stat-mech"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2010.02514v1",
+                    "title": "Diffusion model and analysis of diffusion process at lagrangian method",
+                    "abstract": "Based on Fick's 2nd law the development of moving particle semi-implicit\nmethod for predicting diffusion process is proposed in this study",
+                    "authors": "Ziqi Zhou",
+                    "published": "2020-10-06",
+                    "updated": "2020-10-06",
+                    "primary_cat": "physics.flu-dyn",
+                    "cats": [
+                        "physics.flu-dyn"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2306.07491v2",
+                    "title": "Exact sharp-fronted solutions for nonlinear diffusion on evolving domains",
+                    "abstract": "Models of diffusive processes that occur on evolving domains are frequently\nemployed to describe biological and physical phenomena, such as diffusion\nwithin expanding tissues or substrates. Previous investigations into these\nmodels either report numerical solutions or require an assumption of linear\ndiffusion to determine exact solutions. Unfortunately, numerical solutions do\nnot reveal the relationship between the model parameters and the solution\nfeatures. Additionally, experimental observations typically report the presence\nof sharp fronts, which are not captured by linear diffusion. Here we address\nboth limitations by presenting exact sharp-fronted solutions to a model of\ndegenerate nonlinear diffusion on a growing domain. We obtain the solution by\nidentifying a series of transformations that converts the model of a nonlinear\ndiffusive process on an evolving domain to a nonlinear diffusion equation on a\nfixed domain, which admits known exact solutions for certain choices of\ndiffusivity functions. We determine expressions for critical time scales and\ndomain growth rates such that the diffusive population never reaches the domain\nboundaries and hence the solution remains valid.",
+                    "authors": "Stuart T. Johnston, Matthew J. Simpson",
+                    "published": "2023-06-13",
+                    "updated": "2023-10-06",
+                    "primary_cat": "q-bio.PE",
+                    "cats": [
+                        "q-bio.PE"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1611.06202v2",
+                    "title": "Brownian yet non-Gaussian diffusion: from superstatistics to subordination of diffusing diffusivities",
+                    "abstract": "A growing number of biological, soft, and active matter systems are observed\nto exhibit normal diffusive dynamics with a linear growth of the mean squared\ndisplacement, yet with a non-Gaussian distribution of increments. Based on the\nChubinsky-Slater idea of a diffusing diffusivity we here establish and analyze\na minimal model framework of diffusion processes with fluctuating diffusivity.\nIn particular, we demonstrate the equivalence of the diffusing diffusivity\nprocess with a superstatistical approach with a distribution of diffusivities,\nat times shorter than the diffusivity correlation time. At longer times a\ncrossover to a Gaussian distribution with an effective diffusivity emerges.\nSpecifically, we establish a subordination picture of Brownian but non-Gaussian\ndiffusion processes, that can be used for a wide class of diffusivity\nfluctuation statistics. Our results are shown to be in excellent agreement with\nsimulations and numerical evaluations.",
+                    "authors": "A. V. Chechkin, F. Seno, R. Metzler, I. M. Sokolov",
+                    "published": "2016-11-18",
+                    "updated": "2017-03-30",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech",
+                        "physics.bio-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/cond-mat/0208120v1",
+                    "title": "Aging in a Chaotic System",
+                    "abstract": "We demonstrate aging behavior in a simple non-linear system. Our model is a\nchaotic map which generates deterministically sub-diffusion. Asymptotic\nbehaviors of the diffusion process are described using aging continuous time\nrandom walks, introduced previously to model diffusion in glasses.",
+                    "authors": "E. Barkai",
+                    "published": "2002-08-06",
+                    "updated": "2002-08-06",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech",
+                        "nlin.CD"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2111.03914v2",
+                    "title": "A systematic approach for modeling a nonlocal eddy diffusivity",
+                    "abstract": "This study considers advective and diffusive transport of passive scalar\nfields by spatially-varying incompressible flows. Prior studies have shown that\nthe eddy diffusivities governing the mean field transport in such systems can\ngenerally be nonlocal in space and time. While for many flows nonlocal eddy\ndiffusivities are more accurate than commonly-used Boussinesq eddy\ndiffusivities, nonlocal eddy diffusivities are often computationally\ncost-prohibitive to obtain and difficult to implement in practice. We develop a\nsystematic and more cost-effective approach for modeling nonlocal eddy\ndiffusivities using matched moment inverse (MMI) operators. These operators are\nconstructed using only a few leading-order moments of the exact nonlocal eddy\ndiffusivity kernel, which can be easily computed using the inverse macroscopic\nforcing method (IMFM) (Mani and Park (2021)). The resulting reduced-order\nmodels for the mean fields that incorporate the modeled eddy diffusivities\noften improve Boussinesq-limit models since they capture leading-order nonlocal\neffects. But more importantly, these models can be expressed as partial\ndifferential equations that are readily solvable using existing computational\nfluid dynamics capabilities rather than as integro-partial differential\nequations.",
+                    "authors": "Jessie Liu, Hannah Williams, Ali Mani",
+                    "published": "2021-11-06",
+                    "updated": "2023-06-28",
+                    "primary_cat": "physics.flu-dyn",
+                    "cats": [
+                        "physics.flu-dyn"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1009.5965v1",
+                    "title": "Sensitivity of a Babcock-Leighton Flux-Transport Dynamo to Magnetic Diffusivity Profiles",
+                    "abstract": "We study the influence of various magnetic diffusivity profiles on the\nevolution of the poloidal and toroidal magnetic fields in a kinematic flux\ntransport dynamo model for the Sun. The diffusivity is a poorly understood\ningredient in solar dynamo models. We mathematically construct various\ntheoretical profiles of the depth-dependent diffusivity, based on constraints\nfrom mixing length theory and turbulence, and on comparisons of poloidal field\nevolution on the Sun with that from the flux-transport dynamo model.\n  We then study the effect of each diffusivity profile in the cyclic evolution\nof the magnetic fields in the Sun, by solving the mean-field dynamo equations.\nWe investigate effects on the solar cycle periods, the maximum tachocline field\nstrengths, and the evolution of the toroidal and poloidal field structures\ninside the convection zone, due to different diffusivity profiles.\n  We conduct three experiments: (I) comparing very different magnetic\ndiffusivity profiles; (II) comparing different locations of diffusivity\ngradient near the tachocline for the optimal profile; and (III) comparing\ndifferent slopes of diffusivity gradient for an optimal profile.\n  Based on these simulations, we discuss which aspects of depth-dependent\ndiffusivity profiles may be most relevant for magnetic flux evolution in the\nSun, and how certain observations could help improve knowledge of this dynamo\ningredient.",
+                    "authors": "E. J. Zita",
+                    "published": "2010-09-29",
+                    "updated": "2010-09-29",
+                    "primary_cat": "astro-ph.SR",
+                    "cats": [
+                        "astro-ph.SR",
+                        "physics.flu-dyn"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1812.07249v1",
+                    "title": "A unifying approach to first-passage time distributions in diffusing diffusivity and switching diffusion models",
+                    "abstract": "We propose a unifying theoretical framework for the analysis of first-passage\ntime distributions in two important classes of stochastic processes in which\nthe diffusivity of a particle evolves randomly in time. In the first class of\n\"diffusing diffusivity\" models, the diffusivity changes continuously via a\nprescribed stochastic equation. In turn, the diffusivity switches randomly\nbetween discrete values in the second class of \"switching diffusion\" models.\nFor both cases, we quantify the impact of the diffusivity dynamics onto the\nfirst-passage time distribution of a particle via the moment-generating\nfunction of the integrated diffusivity. We provide general formulas and some\nexplicit solutions for some particular cases of practical interest.",
+                    "authors": "D. S. Grebenkov",
+                    "published": "2018-12-18",
+                    "updated": "2018-12-18",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech",
+                        "physics.bio-ph",
+                        "physics.chem-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/astro-ph/0012545v1",
+                    "title": "Diffusion and the occurrence of hydrogen shell flashes in helium white dwarf stars",
+                    "abstract": "We investigate the effects of element diffusion on the structure and\nevolution of low-mass helium white dwarfs (WD). Attention is focused on the\noccurrence of hydrogen shell flashes induced by diffusion processes during\ncooling phases. Initial models from 0.406 to 0.161 solar masses are constructed\nby applying mass loss rates at different stages of the RGB evolution of a solar\nmodel. The multicomponent flow equations describing gravitational settling, and\nchemical and thermal diffusion are solved and the diffusion calculations are\ncoupled to an evolutionary code. In addition, the same sequences are computed\nbut neglecting diffusion. We find that element diffusion strongly affects the\nstructure and cooling history of helium WD. In particular, diffusion induces\nthe occurrence of hydrogen shell flashes in models with masses ranging from\n0.18 to 0.41 solar masses, which is in sharp contrast from the situation when\ndiffusion is neglected. In connection with the further evolution, these\ndiffusion-induced flashes lead to much thinner hydrogen envelopes, preventing\nstable nuclear burning from being an appreciable energy source at advanced\nstages of evolution. This implies much shorter cooling ages than in the case\nwhen diffusion is neglected. These new WD models are discussed in light of\nrecent observational data of some millisecond pulsar systems with WD\ncompanions. We find that age discrepancies between the predictions of standard\nevolutionary models and such observations appear to be the result of ignoring\nelement diffusion in such models. Indeed, such discrepancies vanish when\naccount is made of diffusion.",
+                    "authors": "L. G. Althaus, A. M. Serenelli, O. G. Benvenuto",
+                    "published": "2000-12-29",
+                    "updated": "2000-12-29",
+                    "primary_cat": "astro-ph",
+                    "cats": [
+                        "astro-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1212.2829v1",
+                    "title": "Spin diffusion in one-dimensional classical Heisenberg mode",
+                    "abstract": "The problem of spin diffusion is studied numerically in one-dimensional\nclassical Heisenberg model using a deterministic odd even spin precession\ndynamics. We demonstrate that spin diffusion in this model, like energy\ndiffusion, is normal and one obtains a long time diffusive tail in the decay of\nautocorrelation function (ACF). Some variations of the model with different\ncoupling schemes and with anisotropy are also studied and we find normal\ndiffusion in all of them. A systematic finite size analysis of the Heisenberg\nmodel also suggests diffusive spreading of fluctuation, contrary to previous\nclaims of anomalous diffusion.",
+                    "authors": "Debarshee Bagchi",
+                    "published": "2012-12-12",
+                    "updated": "2012-12-12",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2301.00527v1",
+                    "title": "Diffusion Probabilistic Models for Scene-Scale 3D Categorical Data",
+                    "abstract": "In this paper, we learn a diffusion model to generate 3D data on a\nscene-scale. Specifically, our model crafts a 3D scene consisting of multiple\nobjects, while recent diffusion research has focused on a single object. To\nrealize our goal, we represent a scene with discrete class labels, i.e.,\ncategorical distribution, to assign multiple objects into semantic categories.\nThus, we extend discrete diffusion models to learn scene-scale categorical\ndistributions. In addition, we validate that a latent diffusion model can\nreduce computation costs for training and deploying. To the best of our\nknowledge, our work is the first to apply discrete and latent diffusion for 3D\ncategorical data on a scene-scale. We further propose to perform semantic scene\ncompletion (SSC) by learning a conditional distribution using our diffusion\nmodel, where the condition is a partial observation in a sparse point cloud. In\nexperiments, we empirically show that our diffusion models not only generate\nreasonable scenes, but also perform the scene completion task better than a\ndiscriminative model. Our code and models are available at\nhttps://github.com/zoomin-lee/scene-scale-diffusion",
+                    "authors": "Jumin Lee, Woobin Im, Sebin Lee, Sung-Eui Yoon",
+                    "published": "2023-01-02",
+                    "updated": "2023-01-02",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2209.05557v3",
+                    "title": "Blurring Diffusion Models",
+                    "abstract": "Recently, Rissanen et al., (2022) have presented a new type of diffusion\nprocess for generative modeling based on heat dissipation, or blurring, as an\nalternative to isotropic Gaussian diffusion. Here, we show that blurring can\nequivalently be defined through a Gaussian diffusion process with non-isotropic\nnoise. In making this connection, we bridge the gap between inverse heat\ndissipation and denoising diffusion, and we shed light on the inductive bias\nthat results from this modeling choice. Finally, we propose a generalized class\nof diffusion models that offers the best of both standard Gaussian denoising\ndiffusion and inverse heat dissipation, which we call Blurring Diffusion\nModels.",
+                    "authors": "Emiel Hoogeboom, Tim Salimans",
+                    "published": "2022-09-12",
+                    "updated": "2024-05-01",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.CV",
+                        "stat.ML"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2312.14589v1",
+                    "title": "Non-Denoising Forward-Time Diffusions",
+                    "abstract": "The scope of this paper is generative modeling through diffusion processes.\nAn approach falling within this paradigm is the work of Song et al. (2021),\nwhich relies on a time-reversal argument to construct a diffusion process\ntargeting the desired data distribution. We show that the time-reversal\nargument, common to all denoising diffusion probabilistic modeling proposals,\nis not necessary. We obtain diffusion processes targeting the desired data\ndistribution by taking appropriate mixtures of diffusion bridges. The resulting\ntransport is exact by construction, allows for greater flexibility in choosing\nthe dynamics of the underlying diffusion, and can be approximated by means of a\nneural network via novel training objectives. We develop a unifying view of the\ndrift adjustments corresponding to our and to time-reversal approaches and make\nuse of this representation to inspect the inner workings of diffusion-based\ngenerative models. Finally, we leverage on scalable simulation and inference\ntechniques common in spatial statistics to move beyond fully factorial\ndistributions in the underlying diffusion dynamics. The methodological advances\ncontained in this work contribute toward establishing a general framework for\ngenerative modeling based on diffusion processes.",
+                    "authors": "Stefano Peluchetti",
+                    "published": "2023-12-22",
+                    "updated": "2023-12-22",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "stat.ML"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1202.6521v1",
+                    "title": "Coherence transition in degenerate diffusion equations with mean field coupling",
+                    "abstract": "We introduce non-linear diffusion in a classical diffusion advection model\nwith non local aggregative coupling on the circle, that exhibits a transition\nfrom an uncoherent state to a coherent one when the coupling strength is\nincreased. We show first that all solutions of the equation converge to the set\nof equilibria, second that the set of equilibria undergoes a bifurcation\nrepresenting the transition to coherence when the coupling strength is\nincreased. These two properties are similar to the situation with linear\ndiffusion. Nevertheless nonlinear diffusion alters the transition scenari,\nwhich are different when the diffusion is sub-quadratic and when the diffusion\nis super-quadratic. When the diffusion is super-quadratic, it results in a\nmultistability region that preceeds the pitchfork bifurcation at which the\nuncoherent equilibrium looses stability. When the diffusion is quadratic the\npitchfork bifurcation at the onset of coherence is infinitely degenerate and a\ndisk of equilibria exist for the critical value of the coupling strength.\nAnother impact of nonlinear diffusion is that coherent equilibria become\nlocalized when advection is strong enough, a phenomenon that is preculded when\nthe diffusion is linear.",
+                    "authors": "Khashayar Pakdaman, Xavier Pellegrin",
+                    "published": "2012-02-29",
+                    "updated": "2012-02-29",
+                    "primary_cat": "nlin.AO",
+                    "cats": [
+                        "nlin.AO",
+                        "37N25, 92B25, 35Q35, 35K55, 37B25, 82C26"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2404.07771v1",
+                    "title": "An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimization",
+                    "abstract": "Diffusion models, a powerful and universal generative AI technology, have\nachieved tremendous success in computer vision, audio, reinforcement learning,\nand computational biology. In these applications, diffusion models provide\nflexible high-dimensional data modeling, and act as a sampler for generating\nnew samples under active guidance towards task-desired properties. Despite the\nsignificant empirical success, theory of diffusion models is very limited,\npotentially slowing down principled methodological innovations for further\nharnessing and improving diffusion models. In this paper, we review emerging\napplications of diffusion models, understanding their sample generation under\nvarious controls. Next, we overview the existing theories of diffusion models,\ncovering their statistical properties and sampling capabilities. We adopt a\nprogressive routine, beginning with unconditional diffusion models and\nconnecting to conditional counterparts. Further, we review a new avenue in\nhigh-dimensional structured optimization through conditional diffusion models,\nwhere searching for solutions is reformulated as a conditional sampling problem\nand solved by diffusion models. Lastly, we discuss future directions about\ndiffusion models. The purpose of this paper is to provide a well-rounded\ntheoretical exposure for stimulating forward-looking theories and methods of\ndiffusion models.",
+                    "authors": "Minshuo Chen, Song Mei, Jianqing Fan, Mengdi Wang",
+                    "published": "2024-04-11",
+                    "updated": "2024-04-11",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "math.ST",
+                        "stat.ML",
+                        "stat.TH"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2210.05559v2",
+                    "title": "Unifying Diffusion Models' Latent Space, with Applications to CycleDiffusion and Guidance",
+                    "abstract": "Diffusion models have achieved unprecedented performance in generative\nmodeling. The commonly-adopted formulation of the latent code of diffusion\nmodels is a sequence of gradually denoised samples, as opposed to the simpler\n(e.g., Gaussian) latent space of GANs, VAEs, and normalizing flows. This paper\nprovides an alternative, Gaussian formulation of the latent space of various\ndiffusion models, as well as an invertible DPM-Encoder that maps images into\nthe latent space. While our formulation is purely based on the definition of\ndiffusion models, we demonstrate several intriguing consequences. (1)\nEmpirically, we observe that a common latent space emerges from two diffusion\nmodels trained independently on related domains. In light of this finding, we\npropose CycleDiffusion, which uses DPM-Encoder for unpaired image-to-image\ntranslation. Furthermore, applying CycleDiffusion to text-to-image diffusion\nmodels, we show that large-scale text-to-image diffusion models can be used as\nzero-shot image-to-image editors. (2) One can guide pre-trained diffusion\nmodels and GANs by controlling the latent codes in a unified, plug-and-play\nformulation based on energy-based models. Using the CLIP model and a face\nrecognition model as guidance, we demonstrate that diffusion models have better\ncoverage of low-density sub-populations and individuals than GANs. The code is\npublicly available at https://github.com/ChenWu98/cycle-diffusion.",
+                    "authors": "Chen Henry Wu, Fernando De la Torre",
+                    "published": "2022-10-11",
+                    "updated": "2022-12-07",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.GR",
+                        "cs.LG"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2202.05830v1",
+                    "title": "Learning Fast Samplers for Diffusion Models by Differentiating Through Sample Quality",
+                    "abstract": "Diffusion models have emerged as an expressive family of generative models\nrivaling GANs in sample quality and autoregressive models in likelihood scores.\nStandard diffusion models typically require hundreds of forward passes through\nthe model to generate a single high-fidelity sample. We introduce\nDifferentiable Diffusion Sampler Search (DDSS): a method that optimizes fast\nsamplers for any pre-trained diffusion model by differentiating through sample\nquality scores. We also present Generalized Gaussian Diffusion Models (GGDM), a\nfamily of flexible non-Markovian samplers for diffusion models. We show that\noptimizing the degrees of freedom of GGDM samplers by maximizing sample quality\nscores via gradient descent leads to improved sample quality. Our optimization\nprocedure backpropagates through the sampling process using the\nreparametrization trick and gradient rematerialization. DDSS achieves strong\nresults on unconditional image generation across various datasets (e.g., FID\nscores on LSUN church 128x128 of 11.6 with only 10 inference steps, and 4.82\nwith 20 steps, compared to 51.1 and 14.9 with strongest DDPM/DDIM baselines).\nOur method is compatible with any pre-trained diffusion model without\nfine-tuning or re-training required.",
+                    "authors": "Daniel Watson, William Chan, Jonathan Ho, Mohammad Norouzi",
+                    "published": "2022-02-11",
+                    "updated": "2022-02-11",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2302.07261v2",
+                    "title": "Where to Diffuse, How to Diffuse, and How to Get Back: Automated Learning for Multivariate Diffusions",
+                    "abstract": "Diffusion-based generative models (DBGMs) perturb data to a target noise\ndistribution and reverse this process to generate samples. The choice of\nnoising process, or inference diffusion process, affects both likelihoods and\nsample quality. For example, extending the inference process with auxiliary\nvariables leads to improved sample quality. While there are many such\nmultivariate diffusions to explore, each new one requires significant\nmodel-specific analysis, hindering rapid prototyping and evaluation. In this\nwork, we study Multivariate Diffusion Models (MDMs). For any number of\nauxiliary variables, we provide a recipe for maximizing a lower-bound on the\nMDMs likelihood without requiring any model-specific analysis. We then\ndemonstrate how to parameterize the diffusion for a specified target noise\ndistribution; these two points together enable optimizing the inference\ndiffusion process. Optimizing the diffusion expands easy experimentation from\njust a few well-known processes to an automatic search over all linear\ndiffusions. To demonstrate these ideas, we introduce two new specific\ndiffusions as well as learn a diffusion process on the MNIST, CIFAR10, and\nImageNet32 datasets. We show learned MDMs match or surpass bits-per-dims (BPDs)\nrelative to fixed choices of diffusions for a given dataset and model\narchitecture.",
+                    "authors": "Raghav Singhal, Mark Goldstein, Rajesh Ranganath",
+                    "published": "2023-02-14",
+                    "updated": "2023-03-03",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "stat.ML"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2404.04629v1",
+                    "title": "DifFUSER: Diffusion Model for Robust Multi-Sensor Fusion in 3D Object Detection and BEV Segmentation",
+                    "abstract": "Diffusion models have recently gained prominence as powerful deep generative\nmodels, demonstrating unmatched performance across various domains. However,\ntheir potential in multi-sensor fusion remains largely unexplored. In this\nwork, we introduce DifFUSER, a novel approach that leverages diffusion models\nfor multi-modal fusion in 3D object detection and BEV map segmentation.\nBenefiting from the inherent denoising property of diffusion, DifFUSER is able\nto refine or even synthesize sensor features in case of sensor malfunction,\nthereby improving the quality of the fused output. In terms of architecture,\nour DifFUSER blocks are chained together in a hierarchical BiFPN fashion,\ntermed cMini-BiFPN, offering an alternative architecture for latent diffusion.\nWe further introduce a Gated Self-conditioned Modulated (GSM) latent diffusion\nmodule together with a Progressive Sensor Dropout Training (PSDT) paradigm,\ndesigned to add stronger conditioning to the diffusion process and robustness\nto sensor failures. Our extensive evaluations on the Nuscenes dataset reveal\nthat DifFUSER not only achieves state-of-the-art performance with a 69.1% mIOU\nin BEV map segmentation tasks but also competes effectively with leading\ntransformer-based fusion techniques in 3D object detection.",
+                    "authors": "Duy-Tho Le, Hengcan Shi, Jianfei Cai, Hamid Rezatofighi",
+                    "published": "2024-04-06",
+                    "updated": "2024-04-06",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2401.17181v1",
+                    "title": "Transfer Learning for Text Diffusion Models",
+                    "abstract": "In this report, we explore the potential for text diffusion to replace\nautoregressive (AR) decoding for the training and deployment of large language\nmodels (LLMs). We are particularly interested to see whether pretrained AR\nmodels can be transformed into text diffusion models through a lightweight\nadaptation procedure we call ``AR2Diff''. We begin by establishing a strong\nbaseline setup for training text diffusion models. Comparing across multiple\narchitectures and pretraining objectives, we find that training a decoder-only\nmodel with a prefix LM objective is best or near-best across several tasks.\nBuilding on this finding, we test various transfer learning setups for text\ndiffusion models. On machine translation, we find that text diffusion\nunderperforms the standard AR approach. However, on code synthesis and\nextractive QA, we find diffusion models trained from scratch outperform AR\nmodels in many cases. We also observe quality gains from AR2Diff -- adapting AR\nmodels to use diffusion decoding. These results are promising given that text\ndiffusion is relatively underexplored and can be significantly faster than AR\ndecoding for long text generation.",
+                    "authors": "Kehang Han, Kathleen Kenealy, Aditya Barua, Noah Fiedel, Noah Constant",
+                    "published": "2024-01-30",
+                    "updated": "2024-01-30",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2307.06272v1",
+                    "title": "Exposing the Fake: Effective Diffusion-Generated Images Detection",
+                    "abstract": "Image synthesis has seen significant advancements with the advent of\ndiffusion-based generative models like Denoising Diffusion Probabilistic Models\n(DDPM) and text-to-image diffusion models. Despite their efficacy, there is a\ndearth of research dedicated to detecting diffusion-generated images, which\ncould pose potential security and privacy risks. This paper addresses this gap\nby proposing a novel detection method called Stepwise Error for\nDiffusion-generated Image Detection (SeDID). Comprising statistical-based\n$\\text{SeDID}_{\\text{Stat}}$ and neural network-based\n$\\text{SeDID}_{\\text{NNs}}$, SeDID exploits the unique attributes of diffusion\nmodels, namely deterministic reverse and deterministic denoising computation\nerrors. Our evaluations demonstrate SeDID's superior performance over existing\nmethods when applied to diffusion models. Thus, our work makes a pivotal\ncontribution to distinguishing diffusion model-generated images, marking a\nsignificant step in the domain of artificial intelligence security.",
+                    "authors": "Ruipeng Ma, Jinhao Duan, Fei Kong, Xiaoshuang Shi, Kaidi Xu",
+                    "published": "2023-07-12",
+                    "updated": "2023-07-12",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.CR",
+                        "cs.LG"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2403.05794v2",
+                    "title": "Privacy-Preserving Diffusion Model Using Homomorphic Encryption",
+                    "abstract": "In this paper, we introduce a privacy-preserving stable diffusion framework\nleveraging homomorphic encryption, called HE-Diffusion, which primarily focuses\non protecting the denoising phase of the diffusion process. HE-Diffusion is a\ntailored encryption framework specifically designed to align with the unique\narchitecture of stable diffusion, ensuring both privacy and functionality. To\naddress the inherent computational challenges, we propose a novel\nmin-distortion method that enables efficient partial image encryption,\nsignificantly reducing the overhead without compromising the model's output\nquality. Furthermore, we adopt a sparse tensor representation to expedite\ncomputational operations, enhancing the overall efficiency of the\nprivacy-preserving diffusion process. We successfully implement HE-based\nprivacy-preserving stable diffusion inference. The experimental results show\nthat HE-Diffusion achieves 500 times speedup compared with the baseline method,\nand reduces time cost of the homomorphically encrypted inference to the minute\nlevel. Both the performance and accuracy of the HE-Diffusion are on par with\nthe plaintext counterpart. Our approach marks a significant step towards\nintegrating advanced cryptographic techniques with state-of-the-art generative\nmodels, paving the way for privacy-preserving and efficient image generation in\ncritical applications.",
+                    "authors": "Yaojian Chen, Qiben Yan",
+                    "published": "2024-03-09",
+                    "updated": "2024-05-02",
+                    "primary_cat": "cs.CR",
+                    "cats": [
+                        "cs.CR",
+                        "cs.AI"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2002.02101v1",
+                    "title": "Trace of anomalous diffusion in a biased quenched trap model",
+                    "abstract": "Diffusion on a quenched heterogeneous environment in the presence of bias is\nconsidered analytically. The first-passage-time statistics can be applied to\nobtain the drift and the diffusion coefficient in periodic quenched\nenvironments. We show several transition points at which sample-to-sample\nfluctuations of the drift or the diffusion coefficient remain large even when\nthe system size becomes large, i.e., non-self-averaging. Moreover, we find that\nthe disorder average of the diffusion coefficient diverges or becomes zero when\nthe corresponding annealed model generates superdiffusion or subdiffusion,\nrespectively. This result implies that anomalous diffusion in an annealed model\nis traced by anomaly of the diffusion coefficients in the corresponding\nquenched model.",
+                    "authors": "Takuma Akimoto, Keiji Saito",
+                    "published": "2020-02-06",
+                    "updated": "2020-02-06",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2210.07677v1",
+                    "title": "TransFusion: Transcribing Speech with Multinomial Diffusion",
+                    "abstract": "Diffusion models have shown exceptional scaling properties in the image\nsynthesis domain, and initial attempts have shown similar benefits for applying\ndiffusion to unconditional text synthesis. Denoising diffusion models attempt\nto iteratively refine a sampled noise signal until it resembles a coherent\nsignal (such as an image or written sentence). In this work we aim to see\nwhether the benefits of diffusion models can also be realized for speech\nrecognition. To this end, we propose a new way to perform speech recognition\nusing a diffusion model conditioned on pretrained speech features.\nSpecifically, we propose TransFusion: a transcribing diffusion model which\niteratively denoises a random character sequence into coherent text\ncorresponding to the transcript of a conditioning utterance. We demonstrate\ncomparable performance to existing high-performing contrastive models on the\nLibriSpeech speech recognition benchmark. To the best of our knowledge, we are\nthe first to apply denoising diffusion to speech recognition. We also propose\nnew techniques for effectively sampling and decoding multinomial diffusion\nmodels. These are required because traditional methods of sampling from\nacoustic models are not possible with our new discrete diffusion approach. Code\nand trained models are available: https://github.com/RF5/transfusion-asr",
+                    "authors": "Matthew Baas, Kevin Eloff, Herman Kamper",
+                    "published": "2022-10-14",
+                    "updated": "2022-10-14",
+                    "primary_cat": "eess.AS",
+                    "cats": [
+                        "eess.AS",
+                        "cs.AI",
+                        "cs.SD"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2303.09295v1",
+                    "title": "DIRE for Diffusion-Generated Image Detection",
+                    "abstract": "Diffusion models have shown remarkable success in visual synthesis, but have\nalso raised concerns about potential abuse for malicious purposes. In this\npaper, we seek to build a detector for telling apart real images from\ndiffusion-generated images. We find that existing detectors struggle to detect\nimages generated by diffusion models, even if we include generated images from\na specific diffusion model in their training data. To address this issue, we\npropose a novel image representation called DIffusion Reconstruction Error\n(DIRE), which measures the error between an input image and its reconstruction\ncounterpart by a pre-trained diffusion model. We observe that\ndiffusion-generated images can be approximately reconstructed by a diffusion\nmodel while real images cannot. It provides a hint that DIRE can serve as a\nbridge to distinguish generated and real images. DIRE provides an effective way\nto detect images generated by most diffusion models, and it is general for\ndetecting generated images from unseen diffusion models and robust to various\nperturbations. Furthermore, we establish a comprehensive diffusion-generated\nbenchmark including images generated by eight diffusion models to evaluate the\nperformance of diffusion-generated image detectors. Extensive experiments on\nour collected benchmark demonstrate that DIRE exhibits superiority over\nprevious generated-image detectors. The code and dataset are available at\nhttps://github.com/ZhendongWang6/DIRE.",
+                    "authors": "Zhendong Wang, Jianmin Bao, Wengang Zhou, Weilun Wang, Hezhen Hu, Hong Chen, Houqiang Li",
+                    "published": "2023-03-16",
+                    "updated": "2023-03-16",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1304.0925v1",
+                    "title": "A new approach to multi-modal diffusions with applications to protein folding",
+                    "abstract": "This article demonstrates that flexible and statistically tractable\nmulti-modal diffusion models can be attained by transformation of simple\nwell-known diffusion models such as the Ornstein-Uhlenbeck model, or more\ngenerally a Pearson diffusion. The transformed diffusion inherits many\nproperties of the underlying simple diffusion including its mixing rates and\ndistributions of first passage times. Likelihood inference and martingale\nestimating functions are considered in the case of a discretely observed\nbimodal diffusion. It is further demonstrated that model parameters can be\nidentified and estimated when the diffusion is observed with additional\nmeasurement error. The new approach is applied to molecular dynamics data in\nform of a reaction coordinate of the small Trp-zipper protein, for which the\nfolding and unfolding rates are estimated. The new models provide a better fit\nto this type of protein folding data than previous models because the diffusion\ncoefficient is state-dependent.",
+                    "authors": "Julie Forman, Michael S\u00f8rensen",
+                    "published": "2013-04-03",
+                    "updated": "2013-04-03",
+                    "primary_cat": "stat.ME",
+                    "cats": [
+                        "stat.ME"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2212.10805v1",
+                    "title": "Beyond Information Exchange: An Approach to Deploy Network Properties for Information Diffusion",
+                    "abstract": "Information diffusion in Online Social Networks is a new and crucial problem\nin social network analysis field and requires significant research attention.\nEfficient diffusion of information are of critical importance in diverse\nsituations such as; pandemic prevention, advertising, marketing etc. Although\nseveral mathematical models have been developed till date, but previous works\nlacked systematic analysis and exploration of the influence of neighborhood for\ninformation diffusion. In this paper, we have proposed Common Neighborhood\nStrategy (CNS) algorithm for information diffusion that demonstrates the role\nof common neighborhood in information propagation throughout the network. The\nperformance of CNS algorithm is evaluated on several real-world datasets in\nterms of diffusion speed and diffusion outspread and compared with several\nwidely used information diffusion models. Empirical results show CNS algorithm\nenables better information diffusion both in terms of diffusion speed and\ndiffusion outspread.",
+                    "authors": "Soumita Das, Anupam Biswas, Ravi Kishore Devarapalli",
+                    "published": "2022-12-21",
+                    "updated": "2022-12-21",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "cs.CV",
+                        "cs.IR",
+                        "J.4; G.4; I.6"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2305.01115v2",
+                    "title": "In-Context Learning Unlocked for Diffusion Models",
+                    "abstract": "We present Prompt Diffusion, a framework for enabling in-context learning in\ndiffusion-based generative models. Given a pair of task-specific example\nimages, such as depth from/to image and scribble from/to image, and a text\nguidance, our model automatically understands the underlying task and performs\nthe same task on a new query image following the text guidance. To achieve\nthis, we propose a vision-language prompt that can model a wide range of\nvision-language tasks and a diffusion model that takes it as input. The\ndiffusion model is trained jointly over six different tasks using these\nprompts. The resulting Prompt Diffusion model is the first diffusion-based\nvision-language foundation model capable of in-context learning. It\ndemonstrates high-quality in-context generation on the trained tasks and\ngeneralizes effectively to new, unseen vision tasks with their respective\nprompts. Our model also shows compelling text-guided image editing results. Our\nframework aims to facilitate research into in-context learning for computer\nvision. We share our code and pre-trained models at\nhttps://github.com/Zhendong-Wang/Prompt-Diffusion.",
+                    "authors": "Zhendong Wang, Yifan Jiang, Yadong Lu, Yelong Shen, Pengcheng He, Weizhu Chen, Zhangyang Wang, Mingyuan Zhou",
+                    "published": "2023-05-01",
+                    "updated": "2023-10-18",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2006.00003v1",
+                    "title": "Coupling particle-based reaction-diffusion simulations with reservoirs mediated by reaction-diffusion PDEs",
+                    "abstract": "Open biochemical systems of interacting molecules are ubiquitous in\nlife-related processes. However, established computational methodologies, like\nmolecular dynamics, are still mostly constrained to closed systems and\ntimescales too small to be relevant for life processes. Alternatively,\nparticle-based reaction-diffusion models are currently the most accurate and\ncomputationally feasible approach at these scales. Their efficiency lies in\nmodeling entire molecules as particles that can diffuse and interact with each\nother. In this work, we develop modeling and numerical schemes for\nparticle-based reaction-diffusion in an open setting, where the reservoirs are\nmediated by reaction-diffusion PDEs. We derive two important theoretical\nresults. The first one is the mean-field for open systems of diffusing\nparticles; the second one is the mean-field for a particle-based\nreaction-diffusion system with second-order reactions. We employ these two\nresults to develop a numerical scheme that consistently couples particle-based\nreaction-diffusion processes with reaction-diffusion PDEs. This allows modeling\nopen biochemical systems in contact with reservoirs that are time-dependent and\nspatially inhomogeneous, as in many relevant real-world applications.",
+                    "authors": "Margarita Kostr\u00e9, Christof Sch\u00fctte, Frank No\u00e9, Mauricio J. del Razo",
+                    "published": "2020-05-29",
+                    "updated": "2020-05-29",
+                    "primary_cat": "q-bio.QM",
+                    "cats": [
+                        "q-bio.QM",
+                        "physics.chem-ph",
+                        "physics.comp-ph",
+                        "92C40, 92C45, 60J70, 60Gxx, 70Lxx"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2305.16269v1",
+                    "title": "UDPM: Upsampling Diffusion Probabilistic Models",
+                    "abstract": "In recent years, Denoising Diffusion Probabilistic Models (DDPM) have caught\nsignificant attention. By composing a Markovian process that starts in the data\ndomain and then gradually adds noise until reaching pure white noise, they\nachieve superior performance in learning data distributions. Yet, these models\nrequire a large number of diffusion steps to produce aesthetically pleasing\nsamples, which is inefficient. In addition, unlike common generative\nadversarial networks, the latent space of diffusion models is not\ninterpretable. In this work, we propose to generalize the denoising diffusion\nprocess into an Upsampling Diffusion Probabilistic Model (UDPM), in which we\nreduce the latent variable dimension in addition to the traditional noise level\naddition. As a result, we are able to sample images of size $256\\times 256$\nwith only 7 diffusion steps, which is less than two orders of magnitude\ncompared to standard DDPMs. We formally develop the Markovian diffusion\nprocesses of the UDPM, and demonstrate its generation capabilities on the\npopular FFHQ, LSUN horses, ImageNet, and AFHQv2 datasets. Another favorable\nproperty of UDPM is that it is very easy to interpolate its latent space, which\nis not the case with standard diffusion models. Our code is available online\n\\url{https://github.com/shadyabh/UDPM}",
+                    "authors": "Shady Abu-Hussein, Raja Giryes",
+                    "published": "2023-05-25",
+                    "updated": "2023-05-25",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.LG",
+                        "eess.IV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1602.07007v1",
+                    "title": "Distributional Behaviors of Time-averaged Observables in Langevin Equation with Fluctuating Diffusivity: Normal Diffusion but Anomalous Fluctuations",
+                    "abstract": "We consider Langevin equation with dichotomously fluctuating diffusivity,\nwhere the diffusion coefficient changes dichotomously in time, in order to\nstudy fluctuations of time-averaged observables in temporary heterogeneous\ndiffusion process. We find that occupation time statistics is a powerful tool\nfor calculating the time-averaged mean square displacement in the model. We\nshow that the time-averaged diffusion coefficients are intrinsically random\nwhen the mean sojourn time for one of the states diverges. Our model provides\nanomalous fluctuations of time-averaged diffusivity, which have relevance to\nlarge fluctuations of the diffusion coefficient in single-particle-tracking\nexperiments.",
+                    "authors": "Takuma Akimoto, Eiji Yamamoto",
+                    "published": "2016-02-23",
+                    "updated": "2016-02-23",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech",
+                        "cond-mat.soft"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/math/0204289v1",
+                    "title": "On diffusion approximation with discontinuous coefficients",
+                    "abstract": "Convergence of stochastic processes with jumps to diffusion processes is\ninvestigated in the case when the limit process has discontinuous coefficients.\n  An example is given in which the diffusion approximation of a queueing model\nyields a diffusion process with discontinuous diffusion and drift coefficients.",
+                    "authors": "N. V. Krylov, R. Liptser",
+                    "published": "2002-04-24",
+                    "updated": "2002-04-24",
+                    "primary_cat": "math.PR",
+                    "cats": [
+                        "math.PR",
+                        "math.SG",
+                        "60B10; 60K25}"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2312.04410v1",
+                    "title": "Smooth Diffusion: Crafting Smooth Latent Spaces in Diffusion Models",
+                    "abstract": "Recently, diffusion models have made remarkable progress in text-to-image\n(T2I) generation, synthesizing images with high fidelity and diverse contents.\nDespite this advancement, latent space smoothness within diffusion models\nremains largely unexplored. Smooth latent spaces ensure that a perturbation on\nan input latent corresponds to a steady change in the output image. This\nproperty proves beneficial in downstream tasks, including image interpolation,\ninversion, and editing. In this work, we expose the non-smoothness of diffusion\nlatent spaces by observing noticeable visual fluctuations resulting from minor\nlatent variations. To tackle this issue, we propose Smooth Diffusion, a new\ncategory of diffusion models that can be simultaneously high-performing and\nsmooth. Specifically, we introduce Step-wise Variation Regularization to\nenforce the proportion between the variations of an arbitrary input latent and\nthat of the output image is a constant at any diffusion training step. In\naddition, we devise an interpolation standard deviation (ISTD) metric to\neffectively assess the latent space smoothness of a diffusion model. Extensive\nquantitative and qualitative experiments demonstrate that Smooth Diffusion\nstands out as a more desirable solution not only in T2I generation but also\nacross various downstream tasks. Smooth Diffusion is implemented as a\nplug-and-play Smooth-LoRA to work with various community models. Code is\navailable at https://github.com/SHI-Labs/Smooth-Diffusion.",
+                    "authors": "Jiayi Guo, Xingqian Xu, Yifan Pu, Zanlin Ni, Chaofei Wang, Manushree Vasu, Shiji Song, Gao Huang, Humphrey Shi",
+                    "published": "2023-12-07",
+                    "updated": "2023-12-07",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2307.13949v1",
+                    "title": "How Does Diffusion Influence Pretrained Language Models on Out-of-Distribution Data?",
+                    "abstract": "Transformer-based pretrained language models (PLMs) have achieved great\nsuccess in modern NLP. An important advantage of PLMs is good\nout-of-distribution (OOD) robustness. Recently, diffusion models have attracted\na lot of work to apply diffusion to PLMs. It remains under-explored how\ndiffusion influences PLMs on OOD data. The core of diffusion models is a\nforward diffusion process which gradually applies Gaussian noise to inputs, and\na reverse denoising process which removes noise. The noised input\nreconstruction is a fundamental ability of diffusion models. We directly\nanalyze OOD robustness by measuring the reconstruction loss, including testing\nthe abilities to reconstruct OOD data, and to detect OOD samples. Experiments\nare conducted by analyzing different training parameters and data statistical\nfeatures on eight datasets. It shows that finetuning PLMs with diffusion\ndegrades the reconstruction ability on OOD data. The comparison also shows that\ndiffusion models can effectively detect OOD samples, achieving state-of-the-art\nperformance in most of the datasets with an absolute accuracy improvement up to\n18%. These results indicate that diffusion reduces OOD robustness of PLMs.",
+                    "authors": "Huazheng Wang, Daixuan Cheng, Haifeng Sun, Jingyu Wang, Qi Qi, Jianxin Liao, Jing Wang, Cong Liu",
+                    "published": "2023-07-26",
+                    "updated": "2023-07-26",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL",
+                        "cs.AI"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2310.01221v2",
+                    "title": "Nonlocal diffusion model with maximum principle",
+                    "abstract": "In this paper, we propose nonlocal diffusion models with Dirichlet boundary.\nThese nonlocal diffusion models preserve the maximum principle and also have\ncorresponding variational form. With these good properties, It is relatively\neasy to prove the well-posedness and the vanishing nonlocality convergence.\nFurthermore, by specifically designed weight function, we can get a nonlocal\ndiffusion model with second order convergence which is optimal for nonlocal\ndiffusion models.",
+                    "authors": "Zuoqiang Shi",
+                    "published": "2023-10-02",
+                    "updated": "2023-10-12",
+                    "primary_cat": "math.AP",
+                    "cats": [
+                        "math.AP",
+                        "cs.NA",
+                        "math.NA"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1711.09967v2",
+                    "title": "CO diffusion and desorption kinetics in CO$_2$ ices",
+                    "abstract": "Diffusion of species in icy dust grain mantles is a fundamental process that\nshapes the chemistry of interstellar regions; yet measurements of diffusion in\ninterstellar ice analogs are scarce. Here we present measurements of CO\ndiffusion into CO$_2$ ice at low temperatures (T=11--23~K) using CO$_2$\nlongitudinal optical (LO) phonon modes to monitor the level of mixing of\ninitially layered ices. We model the diffusion kinetics using Fick's second law\nand find the temperature dependent diffusion coefficients are well fit by an\nArrhenius equation giving a diffusion barrier of 300 $\\pm$ 40 K. The low\nbarrier along with the diffusion kinetics through isotopically labeled layers\nsuggest that CO diffuses through CO$_2$ along pore surfaces rather than through\nbulk diffusion. In complementary experiments, we measure the desorption energy\nof CO from CO$_2$ ices deposited at 11-50 K by temperature-programmed\ndesorption (TPD) and find that the desorption barrier ranges from 1240 $\\pm$ 90\nK to 1410 $\\pm$ 70 K depending on the CO$_2$ deposition temperature and\nresultant ice porosity. The measured CO-CO$_2$ desorption barriers demonstrate\nthat CO binds equally well to CO$_2$ and H$_2$O ices when both are compact. The\nCO-CO$_2$ diffusion-desorption barrier ratio ranges from 0.21-0.24 dependent on\nthe binding environment during diffusion. The diffusion-desorption ratio is\nconsistent with the above hypothesis that the observed diffusion is a surface\nprocess and adds to previous experimental evidence on diffusion in water ice\nthat suggests surface diffusion is important to the mobility of molecules\nwithin interstellar ices.",
+                    "authors": "Ilsa R. Cooke, Karin I. \u00d6berg, Edith C. Fayolle, Zoe Peeler, Jennifer B. Bergner",
+                    "published": "2017-11-27",
+                    "updated": "2017-12-18",
+                    "primary_cat": "astro-ph.GA",
+                    "cats": [
+                        "astro-ph.GA"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1708.06890v1",
+                    "title": "Collaborative Inference of Coexisting Information Diffusions",
+                    "abstract": "Recently, \\textit{diffusion history inference} has become an emerging\nresearch topic due to its great benefits for various applications, whose\npurpose is to reconstruct the missing histories of information diffusion traces\naccording to incomplete observations. The existing methods, however, often\nfocus only on single information diffusion trace, while in a real-world social\nnetwork, there often coexist multiple information diffusions over the same\nnetwork. In this paper, we propose a novel approach called Collaborative\nInference Model (CIM) for the problem of the inference of coexisting\ninformation diffusions. By exploiting the synergism between the coexisting\ninformation diffusions, CIM holistically models multiple information diffusions\nas a sparse 4th-order tensor called Coexisting Diffusions Tensor (CDT) without\nany prior assumption of diffusion models, and collaboratively infers the\nhistories of the coexisting information diffusions via a low-rank approximation\nof CDT with a fusion of heterogeneous constraints generated from additional\ndata sources. To improve the efficiency, we further propose an optimal\nalgorithm called Time Window based Parallel Decomposition Algorithm (TWPDA),\nwhich can speed up the inference without compromise on the accuracy by\nutilizing the temporal locality of information diffusions. The extensive\nexperiments conducted on real world datasets and synthetic datasets verify the\neffectiveness and efficiency of CIM and TWPDA.",
+                    "authors": "Yanchao Sun, Cong Qian, Ning Yang, Philip S. Yu",
+                    "published": "2017-08-23",
+                    "updated": "2017-08-23",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2401.06046v2",
+                    "title": "Quantifying the contributions to diffusion in complex materials",
+                    "abstract": "Using machine learning with a variational formula for diffusivity, we recast\ndiffusion as a sum of individual contributions to diffusion--called\n\"kinosons\"--and compute their statistical distribution to model a complex\nmulticomponent alloy. Calculating kinosons is orders of magnitude more\nefficient than computing whole trajectories, and elucidates kinetic mechanisms\nfor diffusion. The distribution of kinosons with temperature leads to new\naccurate analytic models for macroscale diffusivity. This combination of\nmachine learning with diffusion theory promises insight into other complex\nmaterials.",
+                    "authors": "Soham Chattopadhyay, Dallas R. Trinkle",
+                    "published": "2024-01-11",
+                    "updated": "2024-03-14",
+                    "primary_cat": "cond-mat.mtrl-sci",
+                    "cats": [
+                        "cond-mat.mtrl-sci"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2305.12377v1",
+                    "title": "The vanishing diffusion limit for an Oldroyd-B model in $\\mathbb{R}^2_+$",
+                    "abstract": "We consider the initial-boundary value problem for an incompressible\nOldroyd-B model with stress diffusion in two-dimensional upper half plane which\ndescribes the motion of viscoelastic polymeric fluids. From the physical point\nof view, the diffusive coefficient is several orders of magnitude smaller than\nother parameters in the model, and is usually assumed to be zero. However, the\nlink between the diffusive model and the standard one (zero diffusion) via\nvanishing diffusion limit is still unknown from the mathematical point of view,\nin particular for the problem with boundary. Some numerical results [13]\nsuggest that this should be true. In this work, we provide a rigorous\njustification for the vanishing diffusion in $L^\\infty$-norm.",
+                    "authors": "Yinghui Wang, Huanyao Wen",
+                    "published": "2023-05-21",
+                    "updated": "2023-05-21",
+                    "primary_cat": "math.AP",
+                    "cats": [
+                        "math.AP",
+                        "35Q35, 76A10, 76D10"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1409.3132v1",
+                    "title": "Front propagation in reaction-diffusion systems with anomalous diffusion",
+                    "abstract": "A numerical study of the role of anomalous diffusion in front propagation in\nreaction-diffusion systems is presented. Three models of anomalous diffusion\nare considered: fractional diffusion, tempered fractional diffusion, and a\nmodel that combines fractional diffusion and regular diffusion. The reaction\nkinetics corresponds to a Fisher-Kolmogorov nonlinearity. The numerical method\nis based on a finite-difference operator splitting algorithm with an explicit\nEuler step for the time advance of the reaction kinetics, and a Crank-Nicholson\nsemi-implicit time step for the transport operator. The anomalous diffusion\noperators are discretized using an upwind, flux-conserving, Grunwald-Letnikov\nfinite-difference scheme applied to the regularized fractional derivatives.\nWith fractional diffusion of order $\\alpha$, fronts exhibit exponential\nacceleration, $a_L(t) \\sim e^{\\gamma t/\\alpha}$, and develop algebraic decaying\ntails, $\\phi \\sim 1/x^{\\alpha}$. In the case of tempered fractional diffusion,\nthis phenomenology prevails in the intermediate asymptotic regime\n  $\\left(\\chi t \\right)^{1/\\alpha} \\ll x \\ll 1/\\lambda$, where $1/\\lambda$ is\nthe scale of the tempering. Outside this regime, i.e. for $x > 1/\\lambda$, the\ntail exhibits the tempered decay $\\phi \\sim e^{-\\lambda x}/x^{\\alpha+1}$, and\nthe front velocity approaches the terminal speed $v_*=\n\\left(\\gamma-\\lambda^\\alpha \\chi\\right)/ \\lambda$. Of particular interest is\nthe study of the interplay of regular and fractional diffusion. It is shown\nthat the main role of regular diffusion is to delay the onset of front\nacceleration. In particular, the crossover time, $t_c$, to transition to the\naccelerated fractional regime exhibits a logarithmic scaling of the form $t_c\n\\sim \\log \\left(\\chi_d/\\chi_f\\right)$ where $\\chi_d$ and $\\chi_f$ are the\nregular and fractional diffusivities.",
+                    "authors": "D. del-Castillo-Negrete",
+                    "published": "2014-09-10",
+                    "updated": "2014-09-10",
+                    "primary_cat": "nlin.PS",
+                    "cats": [
+                        "nlin.PS",
+                        "cond-mat.stat-mech"
+                    ],
+                    "category": "Diffusion AND Model"
+                }
+            ],
+            [
+                {
+                    "url": "http://arxiv.org/abs/2404.14177v1",
+                    "title": "Face2Face: Label-driven Facial Retouching Restoration",
+                    "abstract": "With the popularity of social media platforms such as Instagram and TikTok,\nand the widespread availability and convenience of retouching tools, an\nincreasing number of individuals are utilizing these tools to beautify their\nfacial photographs. This poses challenges for fields that place high demands on\nthe authenticity of photographs, such as identity verification and social\nmedia. By altering facial images, users can easily create deceptive images,\nleading to the dissemination of false information. This may pose challenges to\nthe reliability of identity verification systems and social media, and even\nlead to online fraud. To address this issue, some work has proposed makeup\nremoval methods, but they still lack the ability to restore images involving\ngeometric deformations caused by retouching. To tackle the problem of facial\nretouching restoration, we propose a framework, dubbed Face2Face, which\nconsists of three components: a facial retouching detector, an image\nrestoration model named FaceR, and a color correction module called\nHierarchical Adaptive Instance Normalization (H-AdaIN). Firstly, the facial\nretouching detector predicts a retouching label containing three integers,\nindicating the retouching methods and their corresponding degrees. Then FaceR\nrestores the retouched image based on the predicted retouching label. Finally,\nH-AdaIN is applied to address the issue of color shift arising from diffusion\nmodels. Extensive experiments demonstrate the effectiveness of our framework\nand each module.",
+                    "authors": "Guanhua Zhao, Yu Gu, Xuhan Sheng, Yujie Hu, Jian Zhang",
+                    "published": "2024-04-22",
+                    "updated": "2024-04-22",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "label": "Original Paper",
+                    "paper_cat": "Diffusion AND Model",
+                    "gt": "We conduct a literature review on makeup removal, pinpointing limitations in current methods for makeup removal. Subsequently, we compare different facial retouching detection methods. Finally, we delve into the discussion of diffusion models. 2.1 Makeup Removal Makeup removal is the task of recovering the original facial appearance from facial images with makeup while maintaining consistency. Chen et al. [4] propose a component-based convolution neural network architecture for blind inversion of retouching operations. Li et al. [23] integrate global domain-level loss and local instance-level loss into a dual-input or output GAN network (BeautyGAN) for makeup transfer and removal. Gu et al. [12] introduce a Local Adversarial Disentangling Network (LADN) for facial makeup and makeup removal. Liu et al. [24] propose PSGAN++, which utilizes a makeup distillation network and an identity extraction network for makeup transfer and removal. Sun et al. [35] introduce a Unified Symmetric Semantic-Aware Transformer (SSAT) network, which combines semantic correspondence learning to achieve makeup transfer and removal. The aforementioned works can only handle non-deformative makeup removal tasks and are not applicable to retouching restoration tasks involving deformations. 2.2 Facial Retouching Detection Bharati et al. [1] employ a Supervised Restricted Boltzmann Machine (SRBM)-based algorithm to classify facial images as either original or retouched, while Sharma et al. [33] propose an improvised patch-based deep convolution neural network (IPDCN2) for the same purpose. Rathgeb et al. [27] conduct a qualitative assessment of retouching applications, utilizing Photo Response NonUniformity (PRNU) to distinguish between authentic and retouched images. Jain et al. [18] introduce a hierarchical approach named Digital Alteration Detection using Hierarchical Convolution Neural Network (DAD-HCNN) to differentiate retouched images and original ones. These works can only detect whether an image has been retouched or not, but cannot detect the specific methods and degrees of retouching. [28] proposes a differential facial retouching detection system, which processes pairs of potential reference images of retouched single portraits and corresponding unretouched probe images to detect whether an image has been retouched. [39] is based on a multi-frame dynamic facial detection method. Additionally, there are specialized detection networks designed to detect retouched images [19], as well as detect occluded faces [11]. 2.3 Diffusion Models Starting from the proposal of the denoising diffusion probabilistic models by Ho et al. [14], diffusion models have garnered widespread attention and development in the field of image generation. Song et al. [34] propose a significant reduction in the sampling process, thereby improving the model\u2019s generation speed. Dhariwal et al. [8] utilize classifier gradients to guide the diffusion model during sampling, achieving generation quality superior to the stateof-the-art image generation model, BigGAN [2], at the time. The LDM [30] transforms images from the pixel domain to the latent space, significantly reducing computational costs. Some works efficiently fine-tune diffusion models to accomplish their target tasks. For instance, [10] utilizes text embeddings to guide personalized generation, while [22] notes that fine-tuning a small number of parameters in the cross-attention layer can personalize pre-trained models. In addition to direct fine-tuning of the original network, there are adapter-based fine-tuning methods. [42] suggests freezing the weights of the original U-Net [31] and leveraging an additional U-Net-like structure as an adapter to integrate new features conditioned on text or images into the model. [25] shares the same objective as ControlNet but adopts a different implementation approach. T2I-Adapter [25] integrates features generated by the adapter into the encoder of the U-Net, while ControlNet integrates them into the decoder.",
+                    "pre_questions": [],
+                    "main_content": "INTRODUCTION In contemporary society, we witness the increasing prevalence of photo editing tools and techniques, enabling virtually anyone to digitally construct a version of themselves closer to their ideals with a simple click or swipe [29]. From social media to personal avatars, features such as enlarging eyes, smoothing skin, and slimming faces make facial retouching extremely convenient, turning retouched facial photos into a cultural phenomenon. Undeniably, photo editing technology plays a positive role in satisfying people\u2019s pursuit of beauty and shaping personal brands. However, when retouched photos are applied in contexts requiring authenticity and accuracy, issues arise. Specifically, in fields such as judicial crime investigation, financial services, and security supervision, facial recognition-based identity verification systems are widely used. However, if the provided facial images have been retouched, they may pose a threat to the system\u2019s accuracy, resulting in erroneous identity confirmation and introducing security risks. [7] points out the impact of makeup operations on automatic facial recognition. Similarly, in online social platforms involving interpersonal trust, excessively retouched photos may violate the principles of honest communication, leading to social issues such as identity fraud. In the current research and technological development, the primary objective of facial retouching detection technology is to classify facial photographs to determine whether they have undergone retouching processing [1, 27, 28, 33, 39]. However, these technologies currently only detect whether a photo has been retouched, without being able to determine the specific retouching methods and their degrees, which to a certain extent limits their applicability. Suppose in an identity verification system, we employ facial retouching detection technology to determine whether the photo uploaded by the user has undergone retouching processing. If the detection result indicates that the photo has been retouched, the system can reject the photo and request the user to upload a new one. Although this method can help improve the accuracy and reliability of identity verification, it requires users to upload photos multiple times, increasing the complexity of the operation and inconvenience to the user experience. Therefore, if we could adopt more advanced facial retouching restoration technology, we could directly use the retouched photo for identity verification without requiring users to upload it again. The application of this technology will simplify the identity verification process, enhance user experience, help reduce misjudgments, and improve the reliability of the system. Therefore, the development of facial retouching restoration technology holds significant practical significance and application prospects. Facial retouching restoration aims to revert images that have undergone retouching processes using software such as Photoshop or Meitu to their original states. The range and intensity of retouching methods applied by different software and users vary widely, making it difficult to precisely control the range and intensity of restoration involving retouching methods such as facial lifting and eye enlargement, posing significant challenges for the restoration task. Another significant challenge is that, unlike makeup, retouching operations involve facial geometric transformations while maintaining consistency in facial features. Existing restoration works (Chen et al., 2017; Zheng et al., 2013; Liu et al., 2014) only deal with the reversal of known or linear non-deformation operations. To tackle these challenges, we propose Label-driven Facial Retouching Restoration (Face2Face), including a facial retouching detector, an image restoration model named FaceR, and a color correction module called Hierarchical Adaptive Instance Normalization (H-AdaIN). Firstly, we employ a facial retouching detector capable of identifying the retouching methods and degrees presented in retouched images. RetouchingFFHQ [41] introduces a dataset containing over 500,000 conditioned retouched images with large-scale, high-quality, and high-granularity features, along with a novel facial retouching detector (DenseNet121-MAM) capable of analyzing and identifying the methods and degrees of facial retouching in images, rendering the aforementioned task feasible. As the first endeavor on facial restoration from deformation retouching, we select a modest ensemble of retouching techniques, comprising eye enlargement, face lifting, and smoothing. The facial retouching detector predicts a retouching label containing three integers, indicating the retouching methods employed and their corresponding degrees. Then, the face restoration network (FaceR) restores the retouched image based on the retouching label predicted by the facial retouching detector. [37] points out that pre-trained models on large-scale image datasets excel in extracting image features and maintaining consistency in image-to-image tasks. The Latent Diffusion Models (LDM) [30] trained on the large-scale image dataset ImageNet [32] possess rich pre-trained priors and high-quality generation characteristics. Utilizing LDM, we are able to ensure the fidelity and consistency of the restored images. In order to manipulate the image restoration process using the retouching label predicted by the facial retouching detector, we may directly employ the label as a condition to control the denoising process of LDM. However, the direct fine-tuning of LDM may compromise its robust image priors, thereby impairing the restoration outcomes. Consequently, Face2Face: Label-driven Facial Retouching Restoration we suggest training an additional module ControlNet, while keeping the LDM frozen. The retouching label are exclusively used as conditions within ControlNet. Additionally, we observe color distribution shifts in the generated restored images, which is also mentioned in [6]. Adaptive Instance Normalization (AdaIN) [17], initially proposed for image style transfer, has subsequently been employed in subsequent works [5, 40] to control color and stylistic consistency in images. AdaIN extracts the mean and variance of pixels from an entire source image and then applies these statistical parameters to adjust the distribution of pixels in a target image. However, we find that simply applying AdaIN to the entire image is not effective in addressing the issue of color shift. Therefore, we propose Hierarchical Adaptive Instance Normalization (H-AdaIN), which extends global adaptive normalization to hierarchical adaptive normalization computations, enabling faithful color restoration of generated images to match the original images\u2019 colors. We conduct extensive empirical validation, demonstrating the effectiveness of our method Face2Face in achieving significant restoration quality while preserving facial detail consistency. Additionally, the introduction of H-AdaIN provides a new paradigm for color correction, enabling effective correction even in areas with significant local color deviations. Our contributions can be summarized as follows: 1. We propose a framework, Face2Face, which employs retouching labels generated by facial retouching detector as conditions to accomplish facial retouching restoration. Furthermore, to the best of our knowledge, our Face2Face represents the first endeavor to realize facial restoration from deformation retouching. 2. We introduce Hierarchical Adaptive Instance Normalization (H-AdaIN), effectively addressing color shift issues arising from diffusion models. 3. Extensive analysis and experiments prove the effectiveness of our framework and each module. We introduce a novel approach \u2013 Face2Face, to address the facial retouching restoration task. Face2Face is composed of three parts: 1) a pre-trained facial retouching detector; 2) an image restoration model \u2013 FaceR, which is composed of a pre-trained LDM with fixed parameters and a trainable ControlNet [42]; 3) a color correction module \u2013 Hierarchical Adaptive Instance Normalization (H-AdaIN). Guanhua Zhao, Yu Gu, Xuhan Sheng, Yujie Hu, and Jian Zhang Learnable Frozen + H-AdaIN  \u201c A human face \u201d CLIP Text  Encoder Zero Conv Layer MLP Facial Retouching  Detector DenseNet121 MAM Multi-label Classifier FaceR \ufffd\ufffd \ufffd\ufffd \ufffd\ufffd Retouched image Restored image ControlNet U-Net   Eye. Face. Smo. [ 3 , 1 , 0 ] \ufffd  \ufffd \ufffd 0 \u00d7 (T\uff0d1) Figure 2: Overall framework of the proposed Face2Face. The overall architecture is composed of three parts: 1) a pre-trained facial retouching detector; 2) an image restoration model \u2013 FaceR, which is composed of a pre-trained LDM with fixed parameters and a trained ControlNet [42]; 3) a color correction module \u2013 Hierarchical Adaptive Instance Normalization (H-AdaIN). Our framework utilizes retouching labels generated by a facial retouching detector as conditions for restoring retouched images (as elaborated in Sec. 3.1). As depicted in Figure 2, we first employ a facial retouching detector to obtain the retouching label. Then, we input the retouching label and the retouched image into FaceR to obtain the restored image. Further details and the implementation of the FaceR will be elaborated in Sec. 3.2. Finally, the restored image undergoes color correction using the H-AdaIN module to match the color distribution of the original image. The design details and implementation of our H-AdaIN are elaborated in Sec. 3.3. 3.1 Facial Retouching Detector In the task of retouched image restoration, in order to accurately restore the retouched image, it is necessary to detect the retouching methods and their corresponding degrees, so that the restoration network, FaceR, can follow the guidance of the detection results for restoration, rather than blindly restoring. In Sec. 2.2, we discuss relevant retouching detection methods. Considering that our task requires fine-grained detection of retouching methods and degrees, we choose DenseNet121-MAM [41], as shown in Fig. 2. It is an adaptive token clustering method based on multi-layer CNN networks \u2014 DenseNet121 [16]. It utilizes attention mechanisms and Gumble Softmax [20] to perform token clustering and reduce spatial redundancy through mean projection. Subsequently, a lightweight two-layer Transformer encoder is introduced to analyze and compare multi-granularity information for enhanced multigranularity representation learning. Finally, a multi-granularity attention mechanism is adopted to connect reduced token structures and predict different levels of retouching operations through a multi-label classifier. The entire detection process can be defined as follows: ml = \ud835\udc39\ud835\udc45\ud835\udc37(x0), (1) where ml represents a retouching label with dimensions 1\u00d73, while x0 denotes the input retouched image. For the input x0, it needs to undergo a reshaping operation to adjust its resolution to 512 \u00d7 512, followed by scaling the pixel values from the range of 0-255 to 0-1. 3.2 FaceR FaceR is a key component of the framework Face2Face, aiming to accurately restore a retouched image based on the retouching label ml. One method of fine-tuning neural networks is to directly continue training them, including LDM, using additional training data. However, this approach may result in overfitting and catastrophic forgetting, thereby undermining the robust image priors of the LDM and consequently degrading the quality of the restored images. Therefore, we employ ControlNet to learn the restoration of retouched images, while also leveraging the rich prior knowledge provided by LDM to generate high-quality images. Thus, our FaceR is composed of ControlNet [42] and LDM [30]. LDM is a two-stage diffusion model consisting of an autoencoder and a U-Net noise predictor. In the first stage, LDM trains an autoencoder (E) capable of transforming pixel-space images into latent code z0 = E(x0) and decoding them back into pixel space through Face2Face: Label-driven Facial Retouching Restoration Input Output (a)  (b)  \ufffd\ufffd \ufffdP Overlapping size AdaIN Retouched images Refined images Overlapping size = \ufffd\u00d7 \ufffdp \ufffdp = \ufffd  1 +  \ufffd\u22121 \u00d7  1 \u2212\ufffd   \ufffdp = \ufffd  1 +  \ufffd\u22121 \u00d7  1 \u2212\ufffd   Process order \ufffd\u00a0\u00a0 \u2022\u2022\u2022 \u2022\u2022\u2022 \u2022\u2022\u2022 \ufffd\u00a0\u00a0 \ufffd\u00a0\u00a0 \ufffd  \ufffd\ufffd \u00a0\u00a0, \u00a0\ufffd\ufffd  \ufffd \u00a0 \u00a0 AdaIN AdaIN \ufffd\ufffd  \ufffd \u00a0 \u00a0  \ufffd\ufffd \u00a0\u00a0, \u00a0\ufffd\ufffd  \u00a0\u00a0 \u00a0 \u00a0  \ufffd\ufffd \u00a0\u00a0, \u00a0\ufffd\ufffd  \u00a0\u00a0 \u00a0 \u00a0 2 1 \ufffd \u00a0\u00a0  \u00a0 2 \ufffd \u00a0\u00a0  \u00a0 1 \ufffd \ufffd = \u00a0\ufffd \ufffd \u00a0\u00a0  \u00a0 Figure 3: Hierachical Adaptive Instance Normalization (HAdaIN). (a) The formula for overlapping patches. (b) Overview of H-AdaIN. At level \ud835\udc59, each pair of corresponding \ud835\udc56\ud835\udc61\u210epatches (xi, yl i) from x and yl are input into AdaIN. After this, the current refined result yl-1 is obtained, which is used as input at the next level \ud835\udc59\u22121. The process order of AdaINs is performed from the finest level \ud835\udc3fto the coarsest level 1. the decoder. In the second stage, LDM trains an improved U-Net denoiser to directly denoise in the latent space. The optimization process can be defined by the following equation: L = Ezt,C,\ud835\udc61,\ud835\udf16\u223cN(0,\ud835\udc3c) (||\ud835\udf16\u2212\ud835\udf16\ud835\udf03(zt,\ud835\udc61, C)||2 2), (2) where zt represents the noise sample of z0 after \ud835\udc61time steps, \ud835\udf16 denotes the noise feature map at time step \ud835\udc61, \ud835\udc36denotes the control information, and \ud835\udf16\ud835\udf03represents the function of the U-Net denoiser, used to predict the noise added to zt. During inference, deterministic DDIM sampling is employed to denoise the stochastic noise zt into the latent code z0, which is then decoded into the pixel domain \u02c6 x0 through the VAE Decoder. At each time step \ud835\udc61, to balance sample quality and conditional alignment, a classifier-free guidance method [15] is utilized. \u02dc \ud835\udf16\ud835\udf03(zt,\ud835\udc61, C) = (1 + \ud835\udf14)\ud835\udf16\ud835\udf03(zt,\ud835\udc61, C) \u2212\ud835\udf14\ud835\udf16\ud835\udf03(zt,\ud835\udc61), (3) where \u02dc \ud835\udf16\ud835\udf03represents the score guided by the classifier, used to update zt towards zt-1. \ud835\udf14is a scalar controlling the strength of the guidance by C. The ControlNet is a trainable copy of the encoder block and middle block of U-Net in LDM. Its output is added to the 12 skip connections and 1 middle block of U-Net in LDM. FaceR achieves restoration using the conditions ct, cl, cf. Here, ct is a semantic prompt encoded using the CLIP text encoder [26] (e.g., \"a human face\"), which is input into LDM. We pass the retouching label ml (e.g., [1,0,3] representing the degrees of eye enlarging, face lifting, and smoothing, respectively) through fully connected layers to obtain an embedding cl, with a shape of 3\u00d7768 dimensions, the process of the MLP is as follows: cl = MLP(ml) = reshape(ml \u00b7 W, [\u22121, 3, 768]), (4) where W is the weight matrix of the fully connected layer. cf represents the retouched image in the latent space, obtained by encoding the latent code E(x0) using zero convolution layers. The process of the zero convolution layers is as follows: cf = Z(E(x0); \u0398), (5) where Z(\u00b7; \u00b7) denotes the zero convolution layers, and \u0398 represents its parameters. In the ControlNet component of FaceR, cl and cf are used as inputs, while in the LDM component, ct is used as input. Additionally, noise maps are input into both parts. After processing through FaceR, the latent representation cf results in the restored image y. 3.3 Hierarchical Adaptive Instance Normalization Algorithm 1: Hierarchical Adaptive Instance Normalization Input: \u2022 hierarchical level \ud835\udc3f, \u2022 retouched image x \u2208R\ud835\udc36\u00d7\ud835\udc3b\u00d7\ud835\udc4a, \u2022 restored image y \u2208R\ud835\udc36\u00d7\ud835\udc3b\u00d7\ud835\udc4a, \u2022 overlapping ratio \ud835\udefe. Output: corrected result \u02c6 y 1 \u02c6 y(L) = y 2 for \ud835\udc59= \ud835\udc3fto 1 do 3 \ud835\udc3bp = \u2308 \ud835\udc3b (1+(\ud835\udc59\u22121)\u00d7(1\u2212\ud835\udefe)) \u2309 4 \ud835\udc4ap = \u2308 \ud835\udc4a (1+(\ud835\udc59\u22121)\u00d7(1\u2212\ud835\udefe)) \u2309 5 x(l) p = Patchify(x, \ud835\udc3bp,\ud835\udc4ap,\ud835\udefe) \u2208R\ud835\udc41p\u00d7\ud835\udc36\u00d7\ud835\udc3bp\u00d7\ud835\udc4ap 6 \u02c6 y(l) p = Patchify(\u02c6 y(l), \ud835\udc3bp,\ud835\udc4ap,\ud835\udefe) \u2208R\ud835\udc41p\u00d7\ud835\udc36\u00d7\ud835\udc3bp\u00d7\ud835\udc4ap 7 for \ud835\udc56= 0 to \ud835\udc41p do 8 \u02dc y(l) p [\ud835\udc56] = AdaIN(\u02c6 y(l) p [\ud835\udc56], x(l) p [\ud835\udc56]) \u2208R\ud835\udc36\u00d7\ud835\udc3bp\u00d7\ud835\udc4ap 9 end 10 \u02c6 y(l-1) = DePatchify( \u02dc y(l) p , \ud835\udc3b,\ud835\udc4a,\ud835\udefe) \u2208R\ud835\udc36\u00d7\ud835\udc3b\u00d7\ud835\udc4a 11 end 12 \u02c6 y = \u02c6 y(0) 13 return \u02c6 y Diffusion models often exhibit strong generative capabilities but are frequently plagued by color shifts [6]. To address the color mismatch issue between the restored image and the input conditional image, a straightforward approach is to employ adaptive instance normalization (AdaIN) [36]. Specifically, let x \u2208R\ud835\udc36\u00d7\ud835\udc3b\u00d7\ud835\udc4adenote the input image to FaceR and y \u2208R\ud835\udc36\u00d7\ud835\udc3b\u00d7\ud835\udc4arepresent the restored image from FaceR. Then the calculation formula for AdaIN can be expressed as: \u02c6 y\ud835\udc50= AdaIN(x, y) = \ud835\udf07\ud835\udc50 x + \ud835\udf0e\ud835\udc50 x (y\ud835\udc50\u2212\ud835\udf07\ud835\udc50 y) \ud835\udf0e\ud835\udc50 y , (6) where \ud835\udf07and \ud835\udf0erepresent estimated mean and standard deviation, respectively, and \ud835\udc50\u2208{\ud835\udc45,\ud835\udc3a, \ud835\udc35} denotes the three color channels. AdaIN performs global consistent scaling and shifting of all pixel values by computing the statistical features of the input and output images. Although this simple global color correction technique can mitigate color discrepancies between the generated images and input images to a certain extent, when encountering complex Guanhua Zhao, Yu Gu, Xuhan Sheng, Yujie Hu, and Jian Zhang backgrounds or accessories around the face, the generated images by the restoration network exhibit not only simple global color shifts but also varying degrees of color shifts in different image regions. As illustrated in Figure 5, row 1, column 3, under these circumstances, AdaIN is unable to faithfully restore the color of the earring. To address the aforementioned new issue, we further propose Hierarchical Adaptive Instance Normalization (H-AdaIN), as illustrated in Fig. 3. We perform different levels of overlapping patchification on the retouched image x and the initial generated image y simultaneously. At each level \ud835\udc59, from x and y(l), we find the corresponding pair of patches (xi, y(l) i ), which are fed into AdaIN. The overall process order is from the finest level \ud835\udc3fto the coarsest level 1. The details of H-AdaIN can be referred to Algo. 1. 3.4 Training Strategy For the entire Face2Face framework, we employ a strategy of decoupled training, training the Facial Retouching Detector and FaceR separately. Note that the training of the MLP is included within FaceR. The training of the Facial Retouching Detector followed the method outlined in [41], utilizing ground-truth retouching labels paired with retouched images from the RetouchingFFHQ training set for training. For the training of FaceR, we provide groundtruth retouching labels, retouched images, and ground-truth unretouched images for training. The parameters of the LDM module are frozen, and only the ControlNet part is trained. To enable FaceR to effectively align the semantic information of facial features with retouching labels, we adopt an efficient method by dividing the conditions ct, cl, cf into two distinct groups. One group utilizes the text-to-image prior from a pre-trained LDM model (ct \u2192zt), while the other group consists of conditions that need to be learned from the dataset: image-to-image (cf \u2192zt) and label-to-image (cl \u2192zt). This separating strategy prevents knowledge from forgetting in the pre-trained diffusion model. By providing the conditions from the retouching label embedding cl, it effectively reduces the uncertainty in estimating \ud835\udc5d(cf|zt, cl), thereby avoiding uncontrollable blind restoration and ensuring better alignment with the original image. Initially, the pre-trained latent diffusion U-Net, \ud835\udf16\ud835\udf03(zt,\ud835\udc61, ct), remains fixed during the training process, thereby preserving the text-to-image prior, \u2207zt log\ud835\udc5d(zt|ct). Next, we apply a ControlNet initialized with a partially pre-trained U-Net to take the feature map cf of the retouched image, and the embedding cl of the retouching label. Given the input image z0, image diffusion algorithms gradually introduce noise into the image, resulting in a noisy image zt, which is input into both the ControlNet and added to cf, as well as input into the frozen U-Net. To ensure that the retouched image x0 matches the shape of zt and to prevent adding noise to the network, we apply a zero convolution layer with learnable parameters on E(x0), allowing the model to perceive and adapt to the retouched image. \ud835\udf16\ud835\udf03predicts the noise to be added to the noisy image zt as follows: L = Ezt,ct,cl,cf,\ud835\udc61,\ud835\udf16\u223cN(0,\ud835\udc3c) (||\ud835\udf16\u2212\ud835\udf16\ud835\udf03(zt,\ud835\udc61, ct, cl, cf)||2 2). (7) 4 EXPERIMENTS 4.1 Implementation Details Training details. We choose RetouchingFFHQ [41] as our training dataset. During training, we select 19,757 images from the training set that don\u2019t include facial occlusion, closed eyes or infants. These images cover three retouching techniques (larger eyes, slimmer face, and smoother skin) with different retouching levels (ranging from 0 to 3) and include images with single or mixed retouching operations. The facial retouching detector DenseNet121-MAM is trained for 30 epochs on the entire RetouchingFFHQ training dataset using the Adam optimizer [21], with the learning rate of 2 \u00d7 10\u22124 for CNN-based layers and 1 \u00d7 10\u22125 for Transformer-based layers. For the FaceR, we follow the setting of vanilla ControlNet [42], using the SD V1.5. The retouched image in latent space cf and the groundtruth retouching label embedding cl are fed into ControlNet, while the semantic prompt ct (\"a human face\") is fed into LDM. We train FaceR with a batch size of 20 and a learning rate of 1 \u00d7 10\u22125 for 100 epochs. The training process is conducted on a single NVIDIA A800 GPU (80G) and completed within 7 days. Evaluation setting. We randomly select 1000 pairs of retouched and original images with different retouching methods and levels from the RetouchingFFHQ validation set for evaluation. We set up two sets of retouching labels: ground truth and the detection results from our facial retouching detector. The restored images are then processed through the H-AdaIN module to demonstrate the effectiveness of the facial retouching detector and H-AdaIN. 4.2 Comparison with Other Methods Comparing methods. We select four methods for comparison, including SSAT [35], InstructPix2Pix (IP2P) [3], ControlNet and ControlNet+Text. The first two are pre-existing methods without specific training on our task; the latter two are baseline methods proposed by us, which are specifically trained on our task. Originally designed for makeup transfer, SSAT requires the provision of both a makeup-applied image and a non-makeup image. In our experiments, we supply retouched photos alongside nonretouched photos as input, seeking to enable the model to transition the subject from a \"retouched\" state to a \"non-retouched\" state. IP2P is initially intended for instruction-based image editing; in our case, we introduce retouching degrees via textual prompts. ControlNet performs the blind restoration of retouched images without any prompt. ControlNet+Text introduces the retouching degrees through textual prompts. The approach to incorporating the retouching degrees is discussed in Sec. 4.1. For methods that only support text conditions, we use text prompts instead of retouching labels. For example, \"EyeEnlarging 3; FaceLifting 1; Smoothing 0\" corresponds to the retouching label \"[3, 1, 0]\". Evaluation metrics. We select several commonly used evaluation metrics for image restoration tasks, including traditional metrics such as Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index Measure (SSIM) [38], as well as learning-based metrics, namely Learned Perceptual Image Patch Similarity (LPIPS) [43], Deep Image Structure and Texture Similarity (DISTS) [9] and Fr\u00e9chet Inception Distance (FID) [13]. Face2Face: Label-driven Facial Retouching Restoration Eye Enlarging All Face Lifting Smoothing Retouched Img GT SSAT IP2P ControlNet+Text Ours [3,0,0] [0,2,0] [0,0,1] [3,1,2] Figure 4: Visual comparison with other methods. The labels to the left of the images indicate the types and degrees of retouching, while the captions on the top indicate the different methods, ground truth, or retouched images. In particular, for ControlNet+Text, we utilize text prompts instead of ground-truth retouching labels. For instance, \"EyeEnlarging 3; FaceLifting 1; Smoothing 0\" corresponds to the retouching label \"[3, 1, 0]\". The red dashed line is convenient for observing face lifting. Quantitative experiments. We present a quantitative comparison of various approaches on the RetouchingFFHQ test set. As shown in Tab. 1, our method outperforms various image-to-image methods in multiple perceptual metrics, including FID, SSIM, PSNR, LPIPS, and DISTS. Specifically, our Face2Face with detector achieves an FID score of 23.48, which is 59.43% lower than IP2P based on LDM and 71.89% lower than ControlNet+Text, and 74.16% lower than SSAT. Furthermore, our Face2Face surpasses the compared methods in the remaining metrics, indicating its superiority. The inclusion of the ground-truth label comparison in the experiment with Face2Face using a facial retouching detector aims to highlight the quality upper bound of Face2Face. It is noteworthy that although SSAT and IP2P achieve good LPIPS and DISTS scores, they exhibit poorer performance in other perceptual metrics (i.e., FID, SSIM, PSNR). Qualitative experiments. We conduct qualitative tests on the RetouchingFFHQ test set to demonstrate the effectiveness of our method, as shown in Fig. 4. It is observed that Face2Face is capable of faithfully and naturally restoring images according to the retouching labels, as illustrated in the fifth column of Fig. 4. In contrast, other approaches either exhibit no response to the instructions for retouching restoration or transform styles (as in the case of IP2P) or are capable of following the retouching label for restoration (such as ControlNet+Text) but result in unnatural coloration and details. Particularly, in the case of the smoothing operation, SSAT fails to handle this operation, whereas IP2P and ControlNet+Text, although able to identify and address smoothing, generate details that do not belong to the original image. 4.3 Ablation Study on H-AdaIN To achieve optimal qualitative and quantitative results, we conduct comparative experiments on the hyperparameters involved in Hierarchical Adaptive Instance Normalization (H-AdaIN), including the hierarchical level \ud835\udc3fand overlapping ratio \ud835\udefe(See Algo. 1 for Guanhua Zhao, Yu Gu, Xuhan Sheng, Yujie Hu, and Jian Zhang Table 1: Quantitative results on the RetouchingFFHQ. SSAT and IP2P are pre-existing methods without specific training on our task, while the remaining methods are specifically trained on our task. \"No\" indicates the absence of retouching labels, \"GT\" denotes the usage of real retouching labels, and \"Detector\" indicates the utilization of retouching labels generated through the facial retouching detector. Red and bold signify the optimal values, while blue denotes sub-optimal values. Method Label FID\u2193 SSIM\u2191 PSNR\u2191 LPIPS\u2193 DISTS\u2193 SSAT No 91.30 0.8318 21.84 0.2746 0.1810 IP2P No 58.16 0.7870 21.69 0.2073 0.0995 ControlNet No 199.94 0.4381 21.31 0.6290 0.4395 ControlNet+Text GT 83.95 0.7774 21.92 0.3515 0.1608 Ours w/o H-AdaIN GT 44.83 0.8478 26.88 0.2233 0.0963 Ours w/o H-AdaIN Detector 44.97 0.8440 26.57 0.2285 0.0979 Ours GT 23.48 0.8556 28.24 0.1677 0.0737 Ours Detector 23.60 0.8532 28.19 0.1693 0.0741 GT w/o H-AdaIN L:1    :0 L:100    :0 L:30    :0 L:30    :0.5 L:30    :0.7 L:30    :0.9 \ufffd    \ufffd    \ufffd    \ufffd    \ufffd    \ufffd    Figure 5: The results of applying different hyperparameters to H-AdaIN, where \"\ud835\udc3f\" denotes hierarchical level, and \"\ud835\udefe\" represents the overlapping ratio. Table 2: Ablation of H-AdaIN\u2019s hyperparameters. We compare different hyperparameters, where setting \u201c\ud835\udc3f\u201d equal to 1 is equivalent to directly applying AdaIN. All experiments utilize retouching labels generated through the facial retouching detector. The final line represents the parameters we have ultimately selected. Red and bold signify the optimal values, while blue denotes sub-optimal values. L \ud835\udefe FID\u2193 SSIM\u2191 PSNR\u2191 LPIPS\u2193 DISTS\u2193 1 0 44.06 0.8385 26.09 0.2312 0.0986 30 0 23.83 0.8523 28.15 0.1742 0.0774 100 0 19.71 0.8720 28.51 0.1550 0.0745 30 0.5 23.37 0.8514 28.16 0.1723 0.0752 30 0.9 30.99 0.8501 27.76 0.1862 0.0851 30 0.7 23.60 0.8532 28.19 0.1693 0.0741 the details of algorithm and parameters). The hierarchical level \ud835\udc3fdetermines the maximum number of patches segmented from the original image, whereas the overlapping ratio \ud835\udefegoverns the proportion of edges that overlap between adjacent patches. As a control, we also present the results when not utilizing H-AdaIN and when solely employing AdaIN (wherein H-AdaIN degrades into AdaIN when the parameter \ud835\udc3fis set to 1). Our qualitative and quantitative results are exhibited in Fig. 5 and Tab. 2. Firstly, we determine the optimal value of \ud835\udc3fwhen \ud835\udefe is 0; then with the optimal value of \ud835\udc3fset to 30, we determine the optimal value of \ud835\udefe. When only AdaIN is used (i.e. \ud835\udc3f=1), the earring appears green as opposed to the ground truth of the blue, indicating that the color is not faithfully restored. The first row of Tab. 2 further reveals that the quantitative outcomes derived solely from AdaIN are suboptimal. With \ud835\udc3fset to 100, although the earring\u2019s color is faithfully restored and the quantitative results surpass all other comparative experiments, an erroneous enlargement of small eyes is discernible in Fig. 5 as generated by the restoration network. We hypothesize as follows: given that the restoration network is tasked with reverting images retouched to showcase larger eyes, certain pixels that belong to the eyes before restoration do not after; thus when \ud835\udc3fis excessively large, H-AdaIN extracts pixel information from small patches that are initially part of the eye and erroneously applies it to patches that are not part of the eye post-restoration, leading to the undesired magnification of the eye region. Consequently, for \ud835\udc3f, a moderate value of 30 is selected. Tab. 2 reveals that when \ud835\udc3fis set to 30 and \ud835\udefeis less than 0.9, the differences in quantitative results are negligible. However, additional insights can be gleaned from Fig. 5. When \ud835\udefeis too small, due to the lack of overlap in the processing of adjacent patches, conspicuous patch boundaries are apparent within the image. Conversely, when \ud835\udefeis too large, H-AdaIN tends towards the behavior of AdaIN, thus experiencing similar issues with AdaIN \u2013 non-faithful color restoration. Ultimately, for \ud835\udefe, a moderate value of 0.7 is chosen. 5 CONCLUSION We propose a retouching-label-driven framework for the restoration of retouched facial images. To the best of our knowledge, this is the first framework supporting the restoration of retouched images involving deformations. In addition, we propose a color correction module, Hierarchical Adaptive Instance Normalization (H-AdaIN), Face2Face: Label-driven Facial Retouching Restoration to address the issue of color shift. Extensive experiments demonstrate that our approach outperforms previous methods significantly in both qualitative and quantitative results. Our framework establishes a new paradigm for retouched image restoration, paving the way for further developments. Limitations. As an initial effort to restore facial deformation retouching manipulations, our research is confined to three prevalent retouching techniques. The undertaking to restore a more extensive array of retouching methods is left for future work. Additionally, our approach still falls short of fully restoring retouched images to the exact level of the original images. Precisely controlling the degree of restoration in cases involving deformations remains a significant challenge. Meanwhile, the detection of retouching methods and their degree remains somewhat inaccurate, especially in cases where images undergo multiple types of retouching."
+                },
+                {
+                    "url": "http://arxiv.org/abs/1901.09237v1",
+                    "title": "On Detecting GANs and Retouching based Synthetic Alterations",
+                    "abstract": "Digitally retouching images has become a popular trend, with people posting\naltered images on social media and even magazines posting flawless facial\nimages of celebrities. Further, with advancements in Generative Adversarial\nNetworks (GANs), now changing attributes and retouching have become very easy.\nSuch synthetic alterations have adverse effect on face recognition algorithms.\nWhile researchers have proposed to detect image tampering, detecting GANs\ngenerated images has still not been explored. This paper proposes a supervised\ndeep learning algorithm using Convolutional Neural Networks (CNNs) to detect\nsynthetically altered images. The algorithm yields an accuracy of 99.65% on\ndetecting retouching on the ND-IIITD dataset. It outperforms the previous state\nof the art which reported an accuracy of 87% on the database. For\ndistinguishing between real images and images generated using GANs, the\nproposed algorithm yields an accuracy of 99.83%.",
+                    "authors": "Anubhav Jain, Richa Singh, Mayank Vatsa",
+                    "published": "2019-01-26",
+                    "updated": "2019-01-26",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2212.04488v2",
+                    "title": "Multi-Concept Customization of Text-to-Image Diffusion",
+                    "abstract": "While generative models produce high-quality images of concepts learned from\na large-scale database, a user often wishes to synthesize instantiations of\ntheir own concepts (for example, their family, pets, or items). Can we teach a\nmodel to quickly acquire a new concept, given a few examples? Furthermore, can\nwe compose multiple new concepts together? We propose Custom Diffusion, an\nefficient method for augmenting existing text-to-image models. We find that\nonly optimizing a few parameters in the text-to-image conditioning mechanism is\nsufficiently powerful to represent new concepts while enabling fast tuning (~6\nminutes). Additionally, we can jointly train for multiple concepts or combine\nmultiple fine-tuned models into one via closed-form constrained optimization.\nOur fine-tuned model generates variations of multiple new concepts and\nseamlessly composes them with existing concepts in novel settings. Our method\noutperforms or performs on par with several baselines and concurrent works in\nboth qualitative and quantitative evaluations while being memory and\ncomputationally efficient.",
+                    "authors": "Nupur Kumari, Bingliang Zhang, Richard Zhang, Eli Shechtman, Jun-Yan Zhu",
+                    "published": "2022-12-08",
+                    "updated": "2023-06-20",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.GR",
+                        "cs.LG"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2112.10752v2",
+                    "title": "High-Resolution Image Synthesis with Latent Diffusion Models",
+                    "abstract": "By decomposing the image formation process into a sequential application of\ndenoising autoencoders, diffusion models (DMs) achieve state-of-the-art\nsynthesis results on image data and beyond. Additionally, their formulation\nallows for a guiding mechanism to control the image generation process without\nretraining. However, since these models typically operate directly in pixel\nspace, optimization of powerful DMs often consumes hundreds of GPU days and\ninference is expensive due to sequential evaluations. To enable DM training on\nlimited computational resources while retaining their quality and flexibility,\nwe apply them in the latent space of powerful pretrained autoencoders. In\ncontrast to previous work, training diffusion models on such a representation\nallows for the first time to reach a near-optimal point between complexity\nreduction and detail preservation, greatly boosting visual fidelity. By\nintroducing cross-attention layers into the model architecture, we turn\ndiffusion models into powerful and flexible generators for general conditioning\ninputs such as text or bounding boxes and high-resolution synthesis becomes\npossible in a convolutional manner. Our latent diffusion models (LDMs) achieve\na new state of the art for image inpainting and highly competitive performance\non various tasks, including unconditional image generation, semantic scene\nsynthesis, and super-resolution, while significantly reducing computational\nrequirements compared to pixel-based DMs. Code is available at\nhttps://github.com/CompVis/latent-diffusion .",
+                    "authors": "Robin Rombach, Andreas Blattmann, Dominik Lorenz, Patrick Esser, Bj\u00f6rn Ommer",
+                    "published": "2021-12-20",
+                    "updated": "2022-04-13",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2208.01618v1",
+                    "title": "An Image is Worth One Word: Personalizing Text-to-Image Generation using Textual Inversion",
+                    "abstract": "Text-to-image models offer unprecedented freedom to guide creation through\nnatural language. Yet, it is unclear how such freedom can be exercised to\ngenerate images of specific unique concepts, modify their appearance, or\ncompose them in new roles and novel scenes. In other words, we ask: how can we\nuse language-guided models to turn our cat into a painting, or imagine a new\nproduct based on our favorite toy? Here we present a simple approach that\nallows such creative freedom. Using only 3-5 images of a user-provided concept,\nlike an object or a style, we learn to represent it through new \"words\" in the\nembedding space of a frozen text-to-image model. These \"words\" can be composed\ninto natural language sentences, guiding personalized creation in an intuitive\nway. Notably, we find evidence that a single word embedding is sufficient for\ncapturing unique and varied concepts. We compare our approach to a wide range\nof baselines, and demonstrate that it can more faithfully portray the concepts\nacross a range of applications and tasks.\n  Our code, data and new words will be available at:\nhttps://textual-inversion.github.io",
+                    "authors": "Rinon Gal, Yuval Alaluf, Yuval Atzmon, Or Patashnik, Amit H. Bermano, Gal Chechik, Daniel Cohen-Or",
+                    "published": "2022-08-02",
+                    "updated": "2022-08-02",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.CL",
+                        "cs.GR",
+                        "cs.LG"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2302.08453v2",
+                    "title": "T2I-Adapter: Learning Adapters to Dig out More Controllable Ability for Text-to-Image Diffusion Models",
+                    "abstract": "The incredible generative ability of large-scale text-to-image (T2I) models\nhas demonstrated strong power of learning complex structures and meaningful\nsemantics. However, relying solely on text prompts cannot fully take advantage\nof the knowledge learned by the model, especially when flexible and accurate\ncontrolling (e.g., color and structure) is needed. In this paper, we aim to\n``dig out\" the capabilities that T2I models have implicitly learned, and then\nexplicitly use them to control the generation more granularly. Specifically, we\npropose to learn simple and lightweight T2I-Adapters to align internal\nknowledge in T2I models with external control signals, while freezing the\noriginal large T2I models. In this way, we can train various adapters according\nto different conditions, achieving rich control and editing effects in the\ncolor and structure of the generation results. Further, the proposed\nT2I-Adapters have attractive properties of practical value, such as\ncomposability and generalization ability. Extensive experiments demonstrate\nthat our T2I-Adapter has promising generation quality and a wide range of\napplications.",
+                    "authors": "Chong Mou, Xintao Wang, Liangbin Xie, Yanze Wu, Jian Zhang, Zhongang Qi, Ying Shan, Xiaohu Qie",
+                    "published": "2023-02-16",
+                    "updated": "2023-03-20",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.AI",
+                        "cs.LG",
+                        "cs.MM"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2105.05233v4",
+                    "title": "Diffusion Models Beat GANs on Image Synthesis",
+                    "abstract": "We show that diffusion models can achieve image sample quality superior to\nthe current state-of-the-art generative models. We achieve this on\nunconditional image synthesis by finding a better architecture through a series\nof ablations. For conditional image synthesis, we further improve sample\nquality with classifier guidance: a simple, compute-efficient method for\ntrading off diversity for fidelity using gradients from a classifier. We\nachieve an FID of 2.97 on ImageNet 128$\\times$128, 4.59 on ImageNet\n256$\\times$256, and 7.72 on ImageNet 512$\\times$512, and we match BigGAN-deep\neven with as few as 25 forward passes per sample, all while maintaining better\ncoverage of the distribution. Finally, we find that classifier guidance\ncombines well with upsampling diffusion models, further improving FID to 3.94\non ImageNet 256$\\times$256 and 3.85 on ImageNet 512$\\times$512. We release our\ncode at https://github.com/openai/guided-diffusion",
+                    "authors": "Prafulla Dhariwal, Alex Nichol",
+                    "published": "2021-05-11",
+                    "updated": "2021-06-01",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI",
+                        "cs.CV",
+                        "stat.ML"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2006.11239v2",
+                    "title": "Denoising Diffusion Probabilistic Models",
+                    "abstract": "We present high quality image synthesis results using diffusion probabilistic\nmodels, a class of latent variable models inspired by considerations from\nnonequilibrium thermodynamics. Our best results are obtained by training on a\nweighted variational bound designed according to a novel connection between\ndiffusion probabilistic models and denoising score matching with Langevin\ndynamics, and our models naturally admit a progressive lossy decompression\nscheme that can be interpreted as a generalization of autoregressive decoding.\nOn the unconditional CIFAR10 dataset, we obtain an Inception score of 9.46 and\na state-of-the-art FID score of 3.17. On 256x256 LSUN, we obtain sample quality\nsimilar to ProgressiveGAN. Our implementation is available at\nhttps://github.com/hojonathanho/diffusion",
+                    "authors": "Jonathan Ho, Ajay Jain, Pieter Abbeel",
+                    "published": "2020-06-19",
+                    "updated": "2020-12-16",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "stat.ML"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2105.12324v1",
+                    "title": "PSGAN++: Robust Detail-Preserving Makeup Transfer and Removal",
+                    "abstract": "In this paper, we address the makeup transfer and removal tasks\nsimultaneously, which aim to transfer the makeup from a reference image to a\nsource image and remove the makeup from the with-makeup image respectively.\nExisting methods have achieved much advancement in constrained scenarios, but\nit is still very challenging for them to transfer makeup between images with\nlarge pose and expression differences, or handle makeup details like blush on\ncheeks or highlight on the nose. In addition, they are hardly able to control\nthe degree of makeup during transferring or to transfer a specified part in the\ninput face. In this work, we propose the PSGAN++, which is capable of\nperforming both detail-preserving makeup transfer and effective makeup removal.\nFor makeup transfer, PSGAN++ uses a Makeup Distill Network to extract makeup\ninformation, which is embedded into spatial-aware makeup matrices. We also\ndevise an Attentive Makeup Morphing module that specifies how the makeup in the\nsource image is morphed from the reference image, and a makeup detail loss to\nsupervise the model within the selected makeup detail area. On the other hand,\nfor makeup removal, PSGAN++ applies an Identity Distill Network to embed the\nidentity information from with-makeup images into identity matrices. Finally,\nthe obtained makeup/identity matrices are fed to a Style Transfer Network that\nis able to edit the feature maps to achieve makeup transfer or removal. To\nevaluate the effectiveness of our PSGAN++, we collect a Makeup Transfer In the\nWild dataset that contains images with diverse poses and expressions and a\nMakeup Transfer High-Resolution dataset that contains high-resolution images.\nExperiments demonstrate that PSGAN++ not only achieves state-of-the-art results\nwith fine makeup details even in cases of large pose/expression differences but\nalso can perform partial or degree-controllable makeup transfer.",
+                    "authors": "Si Liu, Wentao Jiang, Chen Gao, Ran He, Jiashi Feng, Bo Li, Shuicheng Yan",
+                    "published": "2021-05-26",
+                    "updated": "2021-05-26",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2112.03631v1",
+                    "title": "SSAT: A Symmetric Semantic-Aware Transformer Network for Makeup Transfer and Removal",
+                    "abstract": "Makeup transfer is not only to extract the makeup style of the reference\nimage, but also to render the makeup style to the semantic corresponding\nposition of the target image. However, most existing methods focus on the\nformer and ignore the latter, resulting in a failure to achieve desired\nresults. To solve the above problems, we propose a unified Symmetric\nSemantic-Aware Transformer (SSAT) network, which incorporates semantic\ncorrespondence learning to realize makeup transfer and removal simultaneously.\nIn SSAT, a novel Symmetric Semantic Corresponding Feature Transfer (SSCFT)\nmodule and a weakly supervised semantic loss are proposed to model and\nfacilitate the establishment of accurate semantic correspondence. In the\ngeneration process, the extracted makeup features are spatially distorted by\nSSCFT to achieve semantic alignment with the target image, then the distorted\nmakeup features are combined with unmodified makeup irrelevant features to\nproduce the final result. Experiments show that our method obtains more\nvisually accurate makeup transfer results, and user study in comparison with\nother state-of-the-art makeup transfer methods reflects the superiority of our\nmethod. Besides, we verify the robustness of the proposed method in the\ndifference of expression and pose, object occlusion scenes, and extend it to\nvideo makeup transfer. Code will be available at\nhttps://gitee.com/sunzhaoyang0304/ssat-msp.",
+                    "authors": "Zhaoyang Sun, Yaxiong Chen, Shengwu Xiong",
+                    "published": "2021-12-07",
+                    "updated": "2021-12-07",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1904.11272v2",
+                    "title": "LADN: Local Adversarial Disentangling Network for Facial Makeup and De-Makeup",
+                    "abstract": "We propose a local adversarial disentangling network (LADN) for facial makeup\nand de-makeup. Central to our method are multiple and overlapping local\nadversarial discriminators in a content-style disentangling network for\nachieving local detail transfer between facial images, with the use of\nasymmetric loss functions for dramatic makeup styles with high-frequency\ndetails. Existing techniques do not demonstrate or fail to transfer\nhigh-frequency details in a global adversarial setting, or train a single local\ndiscriminator only to ensure image structure consistency and thus work only for\nrelatively simple styles. Unlike others, our proposed local adversarial\ndiscriminators can distinguish whether the generated local image details are\nconsistent with the corresponding regions in the given reference image in\ncross-image style transfer in an unsupervised setting. Incorporating these\ntechnical contributions, we achieve not only state-of-the-art results on\nconventional styles but also novel results involving complex and dramatic\nstyles with high-frequency details covering large areas across multiple facial\nfeatures. A carefully designed dataset of unpaired before and after makeup\nimages is released.",
+                    "authors": "Qiao Gu, Guanzhi Wang, Mang Tik Chiu, Yu-Wing Tai, Chi-Keung Tang",
+                    "published": "2019-04-25",
+                    "updated": "2019-08-09",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.AI",
+                        "cs.LG"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2003.08061v1",
+                    "title": "Deep Spatial Gradient and Temporal Depth Learning for Face Anti-spoofing",
+                    "abstract": "Face anti-spoofing is critical to the security of face recognition systems.\nDepth supervised learning has been proven as one of the most effective methods\nfor face anti-spoofing. Despite the great success, most previous works still\nformulate the problem as a single-frame multi-task one by simply augmenting the\nloss with depth, while neglecting the detailed fine-grained information and the\ninterplay between facial depths and moving patterns. In contrast, we design a\nnew approach to detect presentation attacks from multiple frames based on two\ninsights: 1) detailed discriminative clues (e.g., spatial gradient magnitude)\nbetween living and spoofing face may be discarded through stacked vanilla\nconvolutions, and 2) the dynamics of 3D moving faces provide important clues in\ndetecting the spoofing faces. The proposed method is able to capture\ndiscriminative details via Residual Spatial Gradient Block (RSGB) and encode\nspatio-temporal information from Spatio-Temporal Propagation Module (STPM)\nefficiently. Moreover, a novel Contrastive Depth Loss is presented for more\naccurate depth supervision. To assess the efficacy of our method, we also\ncollect a Double-modal Anti-spoofing Dataset (DMAD) which provides actual depth\nfor each sample. The experiments demonstrate that the proposed approach\nachieves state-of-the-art results on five benchmark datasets including\nOULU-NPU, SiW, CASIA-MFSD, Replay-Attack, and the new DMAD. Codes will be\navailable at https://github.com/clks-wzz/FAS-SGTD.",
+                    "authors": "Zezheng Wang, Zitong Yu, Chenxu Zhao, Xiangyu Zhu, Yunxiao Qin, Qiusheng Zhou, Feng Zhou, Zhen Lei",
+                    "published": "2020-03-18",
+                    "updated": "2020-03-18",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2011.13456v2",
+                    "title": "Score-Based Generative Modeling through Stochastic Differential Equations",
+                    "abstract": "Creating noise from data is easy; creating data from noise is generative\nmodeling. We present a stochastic differential equation (SDE) that smoothly\ntransforms a complex data distribution to a known prior distribution by slowly\ninjecting noise, and a corresponding reverse-time SDE that transforms the prior\ndistribution back into the data distribution by slowly removing the noise.\nCrucially, the reverse-time SDE depends only on the time-dependent gradient\nfield (\\aka, score) of the perturbed data distribution. By leveraging advances\nin score-based generative modeling, we can accurately estimate these scores\nwith neural networks, and use numerical SDE solvers to generate samples. We\nshow that this framework encapsulates previous approaches in score-based\ngenerative modeling and diffusion probabilistic modeling, allowing for new\nsampling procedures and new modeling capabilities. In particular, we introduce\na predictor-corrector framework to correct errors in the evolution of the\ndiscretized reverse-time SDE. We also derive an equivalent neural ODE that\nsamples from the same distribution as the SDE, but additionally enables exact\nlikelihood computation, and improved sampling efficiency. In addition, we\nprovide a new way to solve inverse problems with score-based models, as\ndemonstrated with experiments on class-conditional generation, image\ninpainting, and colorization. Combined with multiple architectural\nimprovements, we achieve record-breaking performance for unconditional image\ngeneration on CIFAR-10 with an Inception score of 9.89 and FID of 2.20, a\ncompetitive likelihood of 2.99 bits/dim, and demonstrate high fidelity\ngeneration of 1024 x 1024 images for the first time from a score-based\ngenerative model.",
+                    "authors": "Yang Song, Jascha Sohl-Dickstein, Diederik P. Kingma, Abhishek Kumar, Stefano Ermon, Ben Poole",
+                    "published": "2020-11-26",
+                    "updated": "2021-02-10",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "stat.ML"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2302.05543v3",
+                    "title": "Adding Conditional Control to Text-to-Image Diffusion Models",
+                    "abstract": "We present ControlNet, a neural network architecture to add spatial\nconditioning controls to large, pretrained text-to-image diffusion models.\nControlNet locks the production-ready large diffusion models, and reuses their\ndeep and robust encoding layers pretrained with billions of images as a strong\nbackbone to learn a diverse set of conditional controls. The neural\narchitecture is connected with \"zero convolutions\" (zero-initialized\nconvolution layers) that progressively grow the parameters from zero and ensure\nthat no harmful noise could affect the finetuning. We test various conditioning\ncontrols, eg, edges, depth, segmentation, human pose, etc, with Stable\nDiffusion, using single or multiple conditions, with or without prompts. We\nshow that the training of ControlNets is robust with small (<50k) and large\n(>1m) datasets. Extensive results show that ControlNet may facilitate wider\napplications to control image diffusion models.",
+                    "authors": "Lvmin Zhang, Anyi Rao, Maneesh Agrawala",
+                    "published": "2023-02-10",
+                    "updated": "2023-11-26",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.AI",
+                        "cs.GR",
+                        "cs.HC",
+                        "cs.MM"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1809.11096v2",
+                    "title": "Large Scale GAN Training for High Fidelity Natural Image Synthesis",
+                    "abstract": "Despite recent progress in generative image modeling, successfully generating\nhigh-resolution, diverse samples from complex datasets such as ImageNet remains\nan elusive goal. To this end, we train Generative Adversarial Networks at the\nlargest scale yet attempted, and study the instabilities specific to such\nscale. We find that applying orthogonal regularization to the generator renders\nit amenable to a simple \"truncation trick,\" allowing fine control over the\ntrade-off between sample fidelity and variety by reducing the variance of the\nGenerator's input. Our modifications lead to models which set the new state of\nthe art in class-conditional image synthesis. When trained on ImageNet at\n128x128 resolution, our models (BigGANs) achieve an Inception Score (IS) of\n166.5 and Frechet Inception Distance (FID) of 7.4, improving over the previous\nbest IS of 52.52 and FID of 18.6.",
+                    "authors": "Andrew Brock, Jeff Donahue, Karen Simonyan",
+                    "published": "2018-09-28",
+                    "updated": "2019-02-25",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "stat.ML"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2404.08926v2",
+                    "title": "Diffusion Models Meet Remote Sensing: Principles, Methods, and Perspectives",
+                    "abstract": "As a newly emerging advance in deep generative models, diffusion models have\nachieved state-of-the-art results in many fields, including computer vision,\nnatural language processing, and molecule design. The remote sensing community\nhas also noticed the powerful ability of diffusion models and quickly applied\nthem to a variety of tasks for image processing. Given the rapid increase in\nresearch on diffusion models in the field of remote sensing, it is necessary to\nconduct a comprehensive review of existing diffusion model-based remote sensing\npapers, to help researchers recognize the potential of diffusion models and\nprovide some directions for further exploration. Specifically, this paper first\nintroduces the theoretical background of diffusion models, and then\nsystematically reviews the applications of diffusion models in remote sensing,\nincluding image generation, enhancement, and interpretation. Finally, the\nlimitations of existing remote sensing diffusion models and worthy research\ndirections for further exploration are discussed and summarized.",
+                    "authors": "Yidan Liu, Jun Yue, Shaobo Xia, Pedram Ghamisi, Weiying Xie, Leyuan Fang",
+                    "published": "2024-04-13",
+                    "updated": "2024-04-17",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1911.11645v1",
+                    "title": "Effects of different discretisations of the Laplacian upon stochastic simulations of reaction-diffusion systems on both static and growing domains",
+                    "abstract": "By discretising space into compartments and letting system dynamics be\ngoverned by the reaction-diffusion master equation, it is possible to derive\nand simulate a stochastic model of reaction and diffusion on an arbitrary\ndomain. However, there are many implementation choices involved in this\nprocess, such as the choice of discretisation and method of derivation of the\ndiffusive jump rates, and it is not clear a priori how these affect model\npredictions. To shed light on this issue, in this work we explore how a variety\nof discretisations and method for derivation of the diffusive jump rates affect\nthe outputs of stochastic simulations of reaction-diffusion models, in\nparticular using Turing's model of pattern formation as a key example. We\nconsider both static and uniformly growing domains and demonstrate that, while\nonly minor differences are observed for simple reaction-diffusion systems,\nthere can be vast differences in model predictions for systems that include\ncomplicated reaction kinetics, such as Turing's model of pattern formation. Our\nwork highlights that care must be taken in using the reaction-diffusion master\nequation to make predictions as to the dynamics of stochastic\nreaction-diffusion systems.",
+                    "authors": "Bartosz J. Bartmanski, Ruth E. Baker",
+                    "published": "2019-11-26",
+                    "updated": "2019-11-26",
+                    "primary_cat": "physics.comp-ph",
+                    "cats": [
+                        "physics.comp-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2308.06342v2",
+                    "title": "Mirror Diffusion Models",
+                    "abstract": "Diffusion models have successfully been applied to generative tasks in\nvarious continuous domains. However, applying diffusion to discrete categorical\ndata remains a non-trivial task. Moreover, generation in continuous domains\noften requires clipping in practice, which motivates the need for a theoretical\nframework for adapting diffusion to constrained domains. Inspired by the mirror\nLangevin algorithm for the constrained sampling problem, in this theoretical\nreport we propose Mirror Diffusion Models (MDMs). We demonstrate MDMs in the\ncontext of simplex diffusion and propose natural extensions to popular domains\nsuch as image and text generation.",
+                    "authors": "Jaesung Tae",
+                    "published": "2023-08-11",
+                    "updated": "2023-08-18",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2012.06816v1",
+                    "title": "Evaluation and Comparison of Diffusion Models with Motif Features",
+                    "abstract": "Diffusion models simulate the propagation of influence in networks. The\ndesign and evaluation of diffusion models has been subjective and empirical.\nWhen being applied to a network represented by a graph, the diffusion model\ngenerates a sequence of edges on which the influence flows, such sequence forms\na temporal network. In most scenarios, the statistical properties or the\ncharacteristics of a network are inferred by analyzing the temporal networks\ngenerated by diffusion models. To analyze real temporal networks, the motif has\nbeen proposed as a reliable feature. However, it is unclear how the network\ntopology and the diffusion model affect the motif feature of a generated\ntemporal network. In this paper, we adopt the motif feature to evaluate the\ntemporal graph generated by a diffusion model, thence the diffusion model\nitself. Two benchmarks for quantitively evaluating diffusion models with motif,\nstability and separability, are proposed and measured on numerous diffusion\nmodels. One motif-based metric is proposed to measure the similarity between\ndiffusion models. The experiments suggest that the motif of a generated\ntemporal network is dominated by the diffusion model, while the network\ntopology is almost ignored. This result indicates that more practical and\nreliable diffusion models have to be designed with delicacy in order to capture\nthe propagation patterns of real temporal networks.",
+                    "authors": "Fangqi Li",
+                    "published": "2020-12-12",
+                    "updated": "2020-12-12",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "cs.NI"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1212.2829v1",
+                    "title": "Spin diffusion in one-dimensional classical Heisenberg mode",
+                    "abstract": "The problem of spin diffusion is studied numerically in one-dimensional\nclassical Heisenberg model using a deterministic odd even spin precession\ndynamics. We demonstrate that spin diffusion in this model, like energy\ndiffusion, is normal and one obtains a long time diffusive tail in the decay of\nautocorrelation function (ACF). Some variations of the model with different\ncoupling schemes and with anisotropy are also studied and we find normal\ndiffusion in all of them. A systematic finite size analysis of the Heisenberg\nmodel also suggests diffusive spreading of fluctuation, contrary to previous\nclaims of anomalous diffusion.",
+                    "authors": "Debarshee Bagchi",
+                    "published": "2012-12-12",
+                    "updated": "2012-12-12",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1701.00257v2",
+                    "title": "Analyzing PFG anisotropic anomalous diffusions by instantaneous signal attenuation method",
+                    "abstract": "Anomalous diffusion has been investigated in many systems. Pulsed field\ngradient (PFG) anomalous diffusion is much more complicated than PFG normal\ndiffusion. There have been many theoretical and experimental studies for PFG\nisotropic anomalous diffusion, but there are very few theoretical treatments\nreported for anisotropic anomalous diffusion. Currently, there is not a general\nPFG signal attenuation expression, which includes the finite gradient pulse\neffect and can treat all three types of anisotropic fractional diffusions:\ngeneral fractional diffusion, time fractional diffusion, and space-fractional\ndiffusion. In this paper, the recently developed instantaneous signal\nattenuation (ISA) method was applied to obtain PFG signal attenuation\nexpression for free and restricted anisotropic anomalous diffusion with two\nmodels: fractal derivative and fractional derivative models. The obtained PFG\nsignal attenuation expression for anisotropic anomalous diffusion can reduce to\nthe reported result for PFG anisotropic normal diffusion. The results can also\nreduce to reported PFG isotropic anomalous diffusion results obtained by\neffective phase shift diffusion equation method and instantaneous signal\nattenuation method. For anisotropic space-fractional diffusion, the obtained\nresult agrees with that obtained by the modified Bloch equation method.\nAdditionally, The PFG signal attenuation expressions for free and restricted\nanisotropic curvilinear diffusions were derived by the traditional method, the\nresults of which agree with the PFG anisotropic fractional diffusion results\nbased on the fractional derivative model. The powder pattern of PFG anisotropic\ndiffusion was also discussed. The results here improve our understanding of PFG\nanomalous diffusion, and provide new formalisms for PFG anisotropic anomalous\ndiffusion in NMR and MRI.",
+                    "authors": "Guoxing Lin",
+                    "published": "2017-01-01",
+                    "updated": "2017-01-05",
+                    "primary_cat": "physics.chem-ph",
+                    "cats": [
+                        "physics.chem-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/0907.0417v1",
+                    "title": "Microscopic origin of the jump diffusion model",
+                    "abstract": "The present paper is aimed at studying the microscopic origin of the jump\ndiffusion. Starting from the $N$-body Liouville equation and making only the\nassumption that molecular reorientation is overdamped, we derive and solve the\nnew (hereafter generalized diffusion) equation. This is the most general\nequation which governs orientational relaxation of an equilibrium molecular\nensemble in the hindered rotation limit and in the long time limit. The\ngeneralized diffusion equation is an extension of the small-angle diffusion\nequation beyond the impact approximation. We establish the conditions under\nwhich the generalized diffusion equation can be identified with the jump\ndiffusion equation, and also discuss the similarities and differences between\nthe two approaches.",
+                    "authors": "M. F. Gelin, D. S. Kosov",
+                    "published": "2009-07-02",
+                    "updated": "2009-07-02",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2305.10028v1",
+                    "title": "Pyramid Diffusion Models For Low-light Image Enhancement",
+                    "abstract": "Recovering noise-covered details from low-light images is challenging, and\nthe results given by previous methods leave room for improvement. Recent\ndiffusion models show realistic and detailed image generation through a\nsequence of denoising refinements and motivate us to introduce them to\nlow-light image enhancement for recovering realistic details. However, we found\ntwo problems when doing this, i.e., 1) diffusion models keep constant\nresolution in one reverse process, which limits the speed; 2) diffusion models\nsometimes result in global degradation (e.g., RGB shift). To address the above\nproblems, this paper proposes a Pyramid Diffusion model (PyDiff) for low-light\nimage enhancement. PyDiff uses a novel pyramid diffusion method to perform\nsampling in a pyramid resolution style (i.e., progressively increasing\nresolution in one reverse process). Pyramid diffusion makes PyDiff much faster\nthan vanilla diffusion models and introduces no performance degradation.\nFurthermore, PyDiff uses a global corrector to alleviate the global degradation\nthat may occur in the reverse process, significantly improving the performance\nand making the training of diffusion models easier with little additional\ncomputational consumption. Extensive experiments on popular benchmarks show\nthat PyDiff achieves superior performance and efficiency. Moreover, PyDiff can\ngeneralize well to unseen noise and illumination distributions.",
+                    "authors": "Dewei Zhou, Zongxin Yang, Yi Yang",
+                    "published": "2023-05-17",
+                    "updated": "2023-05-17",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1812.07249v1",
+                    "title": "A unifying approach to first-passage time distributions in diffusing diffusivity and switching diffusion models",
+                    "abstract": "We propose a unifying theoretical framework for the analysis of first-passage\ntime distributions in two important classes of stochastic processes in which\nthe diffusivity of a particle evolves randomly in time. In the first class of\n\"diffusing diffusivity\" models, the diffusivity changes continuously via a\nprescribed stochastic equation. In turn, the diffusivity switches randomly\nbetween discrete values in the second class of \"switching diffusion\" models.\nFor both cases, we quantify the impact of the diffusivity dynamics onto the\nfirst-passage time distribution of a particle via the moment-generating\nfunction of the integrated diffusivity. We provide general formulas and some\nexplicit solutions for some particular cases of practical interest.",
+                    "authors": "D. S. Grebenkov",
+                    "published": "2018-12-18",
+                    "updated": "2018-12-18",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech",
+                        "physics.bio-ph",
+                        "physics.chem-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2111.03914v2",
+                    "title": "A systematic approach for modeling a nonlocal eddy diffusivity",
+                    "abstract": "This study considers advective and diffusive transport of passive scalar\nfields by spatially-varying incompressible flows. Prior studies have shown that\nthe eddy diffusivities governing the mean field transport in such systems can\ngenerally be nonlocal in space and time. While for many flows nonlocal eddy\ndiffusivities are more accurate than commonly-used Boussinesq eddy\ndiffusivities, nonlocal eddy diffusivities are often computationally\ncost-prohibitive to obtain and difficult to implement in practice. We develop a\nsystematic and more cost-effective approach for modeling nonlocal eddy\ndiffusivities using matched moment inverse (MMI) operators. These operators are\nconstructed using only a few leading-order moments of the exact nonlocal eddy\ndiffusivity kernel, which can be easily computed using the inverse macroscopic\nforcing method (IMFM) (Mani and Park (2021)). The resulting reduced-order\nmodels for the mean fields that incorporate the modeled eddy diffusivities\noften improve Boussinesq-limit models since they capture leading-order nonlocal\neffects. But more importantly, these models can be expressed as partial\ndifferential equations that are readily solvable using existing computational\nfluid dynamics capabilities rather than as integro-partial differential\nequations.",
+                    "authors": "Jessie Liu, Hannah Williams, Ali Mani",
+                    "published": "2021-11-06",
+                    "updated": "2023-06-28",
+                    "primary_cat": "physics.flu-dyn",
+                    "cats": [
+                        "physics.flu-dyn"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2312.04410v1",
+                    "title": "Smooth Diffusion: Crafting Smooth Latent Spaces in Diffusion Models",
+                    "abstract": "Recently, diffusion models have made remarkable progress in text-to-image\n(T2I) generation, synthesizing images with high fidelity and diverse contents.\nDespite this advancement, latent space smoothness within diffusion models\nremains largely unexplored. Smooth latent spaces ensure that a perturbation on\nan input latent corresponds to a steady change in the output image. This\nproperty proves beneficial in downstream tasks, including image interpolation,\ninversion, and editing. In this work, we expose the non-smoothness of diffusion\nlatent spaces by observing noticeable visual fluctuations resulting from minor\nlatent variations. To tackle this issue, we propose Smooth Diffusion, a new\ncategory of diffusion models that can be simultaneously high-performing and\nsmooth. Specifically, we introduce Step-wise Variation Regularization to\nenforce the proportion between the variations of an arbitrary input latent and\nthat of the output image is a constant at any diffusion training step. In\naddition, we devise an interpolation standard deviation (ISTD) metric to\neffectively assess the latent space smoothness of a diffusion model. Extensive\nquantitative and qualitative experiments demonstrate that Smooth Diffusion\nstands out as a more desirable solution not only in T2I generation but also\nacross various downstream tasks. Smooth Diffusion is implemented as a\nplug-and-play Smooth-LoRA to work with various community models. Code is\navailable at https://github.com/SHI-Labs/Smooth-Diffusion.",
+                    "authors": "Jiayi Guo, Xingqian Xu, Yifan Pu, Zanlin Ni, Chaofei Wang, Manushree Vasu, Shiji Song, Gao Huang, Humphrey Shi",
+                    "published": "2023-12-07",
+                    "updated": "2023-12-07",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1602.07007v1",
+                    "title": "Distributional Behaviors of Time-averaged Observables in Langevin Equation with Fluctuating Diffusivity: Normal Diffusion but Anomalous Fluctuations",
+                    "abstract": "We consider Langevin equation with dichotomously fluctuating diffusivity,\nwhere the diffusion coefficient changes dichotomously in time, in order to\nstudy fluctuations of time-averaged observables in temporary heterogeneous\ndiffusion process. We find that occupation time statistics is a powerful tool\nfor calculating the time-averaged mean square displacement in the model. We\nshow that the time-averaged diffusion coefficients are intrinsically random\nwhen the mean sojourn time for one of the states diverges. Our model provides\nanomalous fluctuations of time-averaged diffusivity, which have relevance to\nlarge fluctuations of the diffusion coefficient in single-particle-tracking\nexperiments.",
+                    "authors": "Takuma Akimoto, Eiji Yamamoto",
+                    "published": "2016-02-23",
+                    "updated": "2016-02-23",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech",
+                        "cond-mat.soft"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2002.02101v1",
+                    "title": "Trace of anomalous diffusion in a biased quenched trap model",
+                    "abstract": "Diffusion on a quenched heterogeneous environment in the presence of bias is\nconsidered analytically. The first-passage-time statistics can be applied to\nobtain the drift and the diffusion coefficient in periodic quenched\nenvironments. We show several transition points at which sample-to-sample\nfluctuations of the drift or the diffusion coefficient remain large even when\nthe system size becomes large, i.e., non-self-averaging. Moreover, we find that\nthe disorder average of the diffusion coefficient diverges or becomes zero when\nthe corresponding annealed model generates superdiffusion or subdiffusion,\nrespectively. This result implies that anomalous diffusion in an annealed model\nis traced by anomaly of the diffusion coefficients in the corresponding\nquenched model.",
+                    "authors": "Takuma Akimoto, Keiji Saito",
+                    "published": "2020-02-06",
+                    "updated": "2020-02-06",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1409.3132v1",
+                    "title": "Front propagation in reaction-diffusion systems with anomalous diffusion",
+                    "abstract": "A numerical study of the role of anomalous diffusion in front propagation in\nreaction-diffusion systems is presented. Three models of anomalous diffusion\nare considered: fractional diffusion, tempered fractional diffusion, and a\nmodel that combines fractional diffusion and regular diffusion. The reaction\nkinetics corresponds to a Fisher-Kolmogorov nonlinearity. The numerical method\nis based on a finite-difference operator splitting algorithm with an explicit\nEuler step for the time advance of the reaction kinetics, and a Crank-Nicholson\nsemi-implicit time step for the transport operator. The anomalous diffusion\noperators are discretized using an upwind, flux-conserving, Grunwald-Letnikov\nfinite-difference scheme applied to the regularized fractional derivatives.\nWith fractional diffusion of order $\\alpha$, fronts exhibit exponential\nacceleration, $a_L(t) \\sim e^{\\gamma t/\\alpha}$, and develop algebraic decaying\ntails, $\\phi \\sim 1/x^{\\alpha}$. In the case of tempered fractional diffusion,\nthis phenomenology prevails in the intermediate asymptotic regime\n  $\\left(\\chi t \\right)^{1/\\alpha} \\ll x \\ll 1/\\lambda$, where $1/\\lambda$ is\nthe scale of the tempering. Outside this regime, i.e. for $x > 1/\\lambda$, the\ntail exhibits the tempered decay $\\phi \\sim e^{-\\lambda x}/x^{\\alpha+1}$, and\nthe front velocity approaches the terminal speed $v_*=\n\\left(\\gamma-\\lambda^\\alpha \\chi\\right)/ \\lambda$. Of particular interest is\nthe study of the interplay of regular and fractional diffusion. It is shown\nthat the main role of regular diffusion is to delay the onset of front\nacceleration. In particular, the crossover time, $t_c$, to transition to the\naccelerated fractional regime exhibits a logarithmic scaling of the form $t_c\n\\sim \\log \\left(\\chi_d/\\chi_f\\right)$ where $\\chi_d$ and $\\chi_f$ are the\nregular and fractional diffusivities.",
+                    "authors": "D. del-Castillo-Negrete",
+                    "published": "2014-09-10",
+                    "updated": "2014-09-10",
+                    "primary_cat": "nlin.PS",
+                    "cats": [
+                        "nlin.PS",
+                        "cond-mat.stat-mech"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2312.14589v1",
+                    "title": "Non-Denoising Forward-Time Diffusions",
+                    "abstract": "The scope of this paper is generative modeling through diffusion processes.\nAn approach falling within this paradigm is the work of Song et al. (2021),\nwhich relies on a time-reversal argument to construct a diffusion process\ntargeting the desired data distribution. We show that the time-reversal\nargument, common to all denoising diffusion probabilistic modeling proposals,\nis not necessary. We obtain diffusion processes targeting the desired data\ndistribution by taking appropriate mixtures of diffusion bridges. The resulting\ntransport is exact by construction, allows for greater flexibility in choosing\nthe dynamics of the underlying diffusion, and can be approximated by means of a\nneural network via novel training objectives. We develop a unifying view of the\ndrift adjustments corresponding to our and to time-reversal approaches and make\nuse of this representation to inspect the inner workings of diffusion-based\ngenerative models. Finally, we leverage on scalable simulation and inference\ntechniques common in spatial statistics to move beyond fully factorial\ndistributions in the underlying diffusion dynamics. The methodological advances\ncontained in this work contribute toward establishing a general framework for\ngenerative modeling based on diffusion processes.",
+                    "authors": "Stefano Peluchetti",
+                    "published": "2023-12-22",
+                    "updated": "2023-12-22",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "stat.ML"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2307.06272v1",
+                    "title": "Exposing the Fake: Effective Diffusion-Generated Images Detection",
+                    "abstract": "Image synthesis has seen significant advancements with the advent of\ndiffusion-based generative models like Denoising Diffusion Probabilistic Models\n(DDPM) and text-to-image diffusion models. Despite their efficacy, there is a\ndearth of research dedicated to detecting diffusion-generated images, which\ncould pose potential security and privacy risks. This paper addresses this gap\nby proposing a novel detection method called Stepwise Error for\nDiffusion-generated Image Detection (SeDID). Comprising statistical-based\n$\\text{SeDID}_{\\text{Stat}}$ and neural network-based\n$\\text{SeDID}_{\\text{NNs}}$, SeDID exploits the unique attributes of diffusion\nmodels, namely deterministic reverse and deterministic denoising computation\nerrors. Our evaluations demonstrate SeDID's superior performance over existing\nmethods when applied to diffusion models. Thus, our work makes a pivotal\ncontribution to distinguishing diffusion model-generated images, marking a\nsignificant step in the domain of artificial intelligence security.",
+                    "authors": "Ruipeng Ma, Jinhao Duan, Fei Kong, Xiaoshuang Shi, Kaidi Xu",
+                    "published": "2023-07-12",
+                    "updated": "2023-07-12",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.CR",
+                        "cs.LG"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2304.01565v1",
+                    "title": "A Survey on Graph Diffusion Models: Generative AI in Science for Molecule, Protein and Material",
+                    "abstract": "Diffusion models have become a new SOTA generative modeling method in various\nfields, for which there are multiple survey works that provide an overall\nsurvey. With the number of articles on diffusion models increasing\nexponentially in the past few years, there is an increasing need for surveys of\ndiffusion models on specific fields. In this work, we are committed to\nconducting a survey on the graph diffusion models. Even though our focus is to\ncover the progress of diffusion models in graphs, we first briefly summarize\nhow other generative modeling methods are used for graphs. After that, we\nintroduce the mechanism of diffusion models in various forms, which facilitates\nthe discussion on the graph diffusion models. The applications of graph\ndiffusion models mainly fall into the category of AI-generated content (AIGC)\nin science, for which we mainly focus on how graph diffusion models are\nutilized for generating molecules and proteins but also cover other cases,\nincluding materials design. Moreover, we discuss the issue of evaluating\ndiffusion models in the graph domain and the existing challenges.",
+                    "authors": "Mengchun Zhang, Maryam Qamar, Taegoo Kang, Yuna Jung, Chenshuang Zhang, Sung-Ho Bae, Chaoning Zhang",
+                    "published": "2023-04-04",
+                    "updated": "2023-04-04",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.CV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2404.12761v1",
+                    "title": "Universality of giant diffusion in tilted periodic potentials",
+                    "abstract": "Giant diffusion, where the diffusion coefficient of a Brownian particle in a\nperiodic potential with an external force is significantly enhanced by the\nexternal force, is a non-trivial non-equilibrium phenomenon. We propose a\nsimple stochastic model of giant diffusion, which is based on a biased\ncontinuous-time random walk (CTRW). In this model, we introduce a flight time\nin the biased CTRW. We derive the diffusion coefficients of this model by the\nrenewal theory and find that there is a maximum diffusion coefficient when the\nbias is changed. Giant diffusion is universally observed in the sense that\nthere is a peak of the diffusion coefficient for any tilted periodic potentials\nand the degree of the diffusivity is greatly enhanced especially for\nlow-temperature regimes. The biased CTRW models with flight times are applied\nto diffusion under three tilted periodic potentials. Furthermore, the\ntemperature dependence of the maximum diffusion coefficient and the external\nforce that attains the maximum are presented for diffusion under a tilted\nsawtooth potential.",
+                    "authors": "Kento Iida, Andreas Dechant, Takuma Akimoto",
+                    "published": "2024-04-19",
+                    "updated": "2024-04-19",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/nlin/0212039v2",
+                    "title": "Front dynamics in reaction-diffusion systems with Levy flights: a fractional diffusion approach",
+                    "abstract": "The use of reaction-diffusion models rests on the key assumption that the\nunderlying diffusive process is Gaussian. However, a growing number of studies\nhave pointed out the prevalence of anomalous diffusion, and there is a need to\nunderstand the dynamics of reactive systems in the presence of this type of\nnon-Gaussian diffusion. Here we present a study of front dynamics in\nreaction-diffusion systems where anomalous diffusion is due to the presence of\nasymmetric Levy flights. Our approach consists of replacing the Laplacian\ndiffusion operator by a fractional diffusion operator, whose fundamental\nsolutions are Levy $\\alpha$-stable distributions. Numerical simulation of the\nfractional Fisher-Kolmogorov equation, and analytical arguments show that\nanomalous diffusion leads to the exponential acceleration of fronts and a\nuniversal power law decay, $x^{-\\alpha}$, of the tail, where $\\alpha$, the\nindex of the Levy distribution, is the order of the fractional derivative.",
+                    "authors": "D. del-Castillo-Negrete, B. A. Carreras, V. E. Lynch",
+                    "published": "2002-12-17",
+                    "updated": "2003-06-30",
+                    "primary_cat": "nlin.PS",
+                    "cats": [
+                        "nlin.PS",
+                        "nlin.CD"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1304.0925v1",
+                    "title": "A new approach to multi-modal diffusions with applications to protein folding",
+                    "abstract": "This article demonstrates that flexible and statistically tractable\nmulti-modal diffusion models can be attained by transformation of simple\nwell-known diffusion models such as the Ornstein-Uhlenbeck model, or more\ngenerally a Pearson diffusion. The transformed diffusion inherits many\nproperties of the underlying simple diffusion including its mixing rates and\ndistributions of first passage times. Likelihood inference and martingale\nestimating functions are considered in the case of a discretely observed\nbimodal diffusion. It is further demonstrated that model parameters can be\nidentified and estimated when the diffusion is observed with additional\nmeasurement error. The new approach is applied to molecular dynamics data in\nform of a reaction coordinate of the small Trp-zipper protein, for which the\nfolding and unfolding rates are estimated. The new models provide a better fit\nto this type of protein folding data than previous models because the diffusion\ncoefficient is state-dependent.",
+                    "authors": "Julie Forman, Michael S\u00f8rensen",
+                    "published": "2013-04-03",
+                    "updated": "2013-04-03",
+                    "primary_cat": "stat.ME",
+                    "cats": [
+                        "stat.ME"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1503.03201v2",
+                    "title": "Fractional Diffusion Equations for Lattice and Continuum: Grunwald-Letnikov Differences and Derivatives Approach",
+                    "abstract": "Fractional diffusion equations for three-dimensional lattice models based on\nfractional-order differences of the Grunwald-Letnikov type are suggested. These\nlattice fractional diffusion equations contain difference operators that\ndescribe long-range jumps from one lattice site to other. In continuum limit,\nthe suggested lattice diffusion equations with non-integer order differences\ngive the diffusion equations with the Grunwald-Letnikov fractional derivatives\nfor continuum. We propose a consistent derivation of the fractional diffusion\nequation with the fractional derivatives of Grunwald-Letnikov type. The\nsuggested lattice diffusion equations can be considered as a new\nmicrostructural basis of space-fractional diffusion in nonlocal media.",
+                    "authors": "Vasily E. Tarasov",
+                    "published": "2015-03-11",
+                    "updated": "2015-03-12",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2404.04629v1",
+                    "title": "DifFUSER: Diffusion Model for Robust Multi-Sensor Fusion in 3D Object Detection and BEV Segmentation",
+                    "abstract": "Diffusion models have recently gained prominence as powerful deep generative\nmodels, demonstrating unmatched performance across various domains. However,\ntheir potential in multi-sensor fusion remains largely unexplored. In this\nwork, we introduce DifFUSER, a novel approach that leverages diffusion models\nfor multi-modal fusion in 3D object detection and BEV map segmentation.\nBenefiting from the inherent denoising property of diffusion, DifFUSER is able\nto refine or even synthesize sensor features in case of sensor malfunction,\nthereby improving the quality of the fused output. In terms of architecture,\nour DifFUSER blocks are chained together in a hierarchical BiFPN fashion,\ntermed cMini-BiFPN, offering an alternative architecture for latent diffusion.\nWe further introduce a Gated Self-conditioned Modulated (GSM) latent diffusion\nmodule together with a Progressive Sensor Dropout Training (PSDT) paradigm,\ndesigned to add stronger conditioning to the diffusion process and robustness\nto sensor failures. Our extensive evaluations on the Nuscenes dataset reveal\nthat DifFUSER not only achieves state-of-the-art performance with a 69.1% mIOU\nin BEV map segmentation tasks but also competes effectively with leading\ntransformer-based fusion techniques in 3D object detection.",
+                    "authors": "Duy-Tho Le, Hengcan Shi, Jianfei Cai, Hamid Rezatofighi",
+                    "published": "2024-04-06",
+                    "updated": "2024-04-06",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2305.08379v2",
+                    "title": "TESS: Text-to-Text Self-Conditioned Simplex Diffusion",
+                    "abstract": "Diffusion models have emerged as a powerful paradigm for generation,\nobtaining strong performance in various continuous domains. However, applying\ncontinuous diffusion models to natural language remains challenging due to its\ndiscrete nature and the need for a large number of diffusion steps to generate\ntext, making diffusion-based generation expensive. In this work, we propose\nText-to-text Self-conditioned Simplex Diffusion (TESS), a text diffusion model\nthat is fully non-autoregressive, employs a new form of self-conditioning, and\napplies the diffusion process on the logit simplex space rather than the\nlearned embedding space. Through extensive experiments on natural language\nunderstanding and generation tasks including summarization, text\nsimplification, paraphrase generation, and question generation, we demonstrate\nthat TESS outperforms state-of-the-art non-autoregressive models, requires\nfewer diffusion steps with minimal drop in performance, and is competitive with\npretrained autoregressive sequence-to-sequence models. We publicly release our\ncodebase at https://github.com/allenai/tess-diffusion.",
+                    "authors": "Rabeeh Karimi Mahabadi, Hamish Ivison, Jaesung Tae, James Henderson, Iz Beltagy, Matthew E. Peters, Arman Cohan",
+                    "published": "2023-05-15",
+                    "updated": "2024-02-21",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL",
+                        "cs.LG"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1711.09967v2",
+                    "title": "CO diffusion and desorption kinetics in CO$_2$ ices",
+                    "abstract": "Diffusion of species in icy dust grain mantles is a fundamental process that\nshapes the chemistry of interstellar regions; yet measurements of diffusion in\ninterstellar ice analogs are scarce. Here we present measurements of CO\ndiffusion into CO$_2$ ice at low temperatures (T=11--23~K) using CO$_2$\nlongitudinal optical (LO) phonon modes to monitor the level of mixing of\ninitially layered ices. We model the diffusion kinetics using Fick's second law\nand find the temperature dependent diffusion coefficients are well fit by an\nArrhenius equation giving a diffusion barrier of 300 $\\pm$ 40 K. The low\nbarrier along with the diffusion kinetics through isotopically labeled layers\nsuggest that CO diffuses through CO$_2$ along pore surfaces rather than through\nbulk diffusion. In complementary experiments, we measure the desorption energy\nof CO from CO$_2$ ices deposited at 11-50 K by temperature-programmed\ndesorption (TPD) and find that the desorption barrier ranges from 1240 $\\pm$ 90\nK to 1410 $\\pm$ 70 K depending on the CO$_2$ deposition temperature and\nresultant ice porosity. The measured CO-CO$_2$ desorption barriers demonstrate\nthat CO binds equally well to CO$_2$ and H$_2$O ices when both are compact. The\nCO-CO$_2$ diffusion-desorption barrier ratio ranges from 0.21-0.24 dependent on\nthe binding environment during diffusion. The diffusion-desorption ratio is\nconsistent with the above hypothesis that the observed diffusion is a surface\nprocess and adds to previous experimental evidence on diffusion in water ice\nthat suggests surface diffusion is important to the mobility of molecules\nwithin interstellar ices.",
+                    "authors": "Ilsa R. Cooke, Karin I. \u00d6berg, Edith C. Fayolle, Zoe Peeler, Jennifer B. Bergner",
+                    "published": "2017-11-27",
+                    "updated": "2017-12-18",
+                    "primary_cat": "astro-ph.GA",
+                    "cats": [
+                        "astro-ph.GA"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2110.14851v1",
+                    "title": "Behavior of Spiral Wave Spectra with a Rank-Deficient Diffusion Matrix",
+                    "abstract": "Spiral waves emerge in numerous pattern forming systems and are commonly\nmodeled with reaction-diffusion systems. Some systems used to model biological\nprocesses, such as ion-channel models, fall under the reaction-diffusion\ncategory and often have one or more non-diffusing species which results in a\nrank-deficient diffusion matrix. Previous theoretical research focused on\nspiral spectra for strictly positive diffusion matrices. In this paper, we use\na general two-variable reaction-diffusion system to compare the essential and\nabsolute spectra of spiral waves for strictly positive and rank-deficient\ndiffusion matrices. We show that the essential spectrum is not continuous in\nthe limit of vanishing diffusion in one component. Moreover, we predict\nlocations for the absolute spectrum in the case of a non-diffusing slow\nvariable. Predictions are confirmed numerically for the Barkley and Karma\nmodels.",
+                    "authors": "Stephanie Dodson, Bjorn Sandstede",
+                    "published": "2021-10-28",
+                    "updated": "2021-10-28",
+                    "primary_cat": "math.DS",
+                    "cats": [
+                        "math.DS"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2404.07771v1",
+                    "title": "An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimization",
+                    "abstract": "Diffusion models, a powerful and universal generative AI technology, have\nachieved tremendous success in computer vision, audio, reinforcement learning,\nand computational biology. In these applications, diffusion models provide\nflexible high-dimensional data modeling, and act as a sampler for generating\nnew samples under active guidance towards task-desired properties. Despite the\nsignificant empirical success, theory of diffusion models is very limited,\npotentially slowing down principled methodological innovations for further\nharnessing and improving diffusion models. In this paper, we review emerging\napplications of diffusion models, understanding their sample generation under\nvarious controls. Next, we overview the existing theories of diffusion models,\ncovering their statistical properties and sampling capabilities. We adopt a\nprogressive routine, beginning with unconditional diffusion models and\nconnecting to conditional counterparts. Further, we review a new avenue in\nhigh-dimensional structured optimization through conditional diffusion models,\nwhere searching for solutions is reformulated as a conditional sampling problem\nand solved by diffusion models. Lastly, we discuss future directions about\ndiffusion models. The purpose of this paper is to provide a well-rounded\ntheoretical exposure for stimulating forward-looking theories and methods of\ndiffusion models.",
+                    "authors": "Minshuo Chen, Song Mei, Jianqing Fan, Mengdi Wang",
+                    "published": "2024-04-11",
+                    "updated": "2024-04-11",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "math.ST",
+                        "stat.ML",
+                        "stat.TH"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2306.07491v2",
+                    "title": "Exact sharp-fronted solutions for nonlinear diffusion on evolving domains",
+                    "abstract": "Models of diffusive processes that occur on evolving domains are frequently\nemployed to describe biological and physical phenomena, such as diffusion\nwithin expanding tissues or substrates. Previous investigations into these\nmodels either report numerical solutions or require an assumption of linear\ndiffusion to determine exact solutions. Unfortunately, numerical solutions do\nnot reveal the relationship between the model parameters and the solution\nfeatures. Additionally, experimental observations typically report the presence\nof sharp fronts, which are not captured by linear diffusion. Here we address\nboth limitations by presenting exact sharp-fronted solutions to a model of\ndegenerate nonlinear diffusion on a growing domain. We obtain the solution by\nidentifying a series of transformations that converts the model of a nonlinear\ndiffusive process on an evolving domain to a nonlinear diffusion equation on a\nfixed domain, which admits known exact solutions for certain choices of\ndiffusivity functions. We determine expressions for critical time scales and\ndomain growth rates such that the diffusive population never reaches the domain\nboundaries and hence the solution remains valid.",
+                    "authors": "Stuart T. Johnston, Matthew J. Simpson",
+                    "published": "2023-06-13",
+                    "updated": "2023-10-06",
+                    "primary_cat": "q-bio.PE",
+                    "cats": [
+                        "q-bio.PE"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2403.15766v1",
+                    "title": "BEND: Bagging Deep Learning Training Based on Efficient Neural Network Diffusion",
+                    "abstract": "Bagging has achieved great success in the field of machine learning by\nintegrating multiple base classifiers to build a single strong classifier to\nreduce model variance. The performance improvement of bagging mainly relies on\nthe number and diversity of base classifiers. However, traditional deep\nlearning model training methods are expensive to train individually and\ndifficult to train multiple models with low similarity in a restricted dataset.\nRecently, diffusion models, which have been tremendously successful in the\nfields of imaging and vision, have been found to be effective in generating\nneural network model weights and biases with diversity. We creatively propose a\nBagging deep learning training algorithm based on Efficient Neural network\nDiffusion (BEND). The originality of BEND comes from the first use of a neural\nnetwork diffusion model to efficiently build base classifiers for bagging. Our\napproach is simple but effective, first using multiple trained model weights\nand biases as inputs to train autoencoder and latent diffusion model to realize\na diffusion model from noise to valid neural network parameters. Subsequently,\nwe generate several base classifiers using the trained diffusion model.\nFinally, we integrate these ba se classifiers for various inference tasks using\nthe Bagging method. Resulting experiments on multiple models and datasets show\nthat our proposed BEND algorithm can consistently outperform the mean and\nmedian accuracies of both the original trained model and the diffused model. At\nthe same time, new models diffused using the diffusion model have higher\ndiversity and lower cost than multiple models trained using traditional\nmethods. The BEND approach successfully introduces diffusion models into the\nnew deep learning training domain and provides a new paradigm for future deep\nlearning training and inference.",
+                    "authors": "Jia Wei, Xingjun Zhang, Witold Pedrycz",
+                    "published": "2024-03-23",
+                    "updated": "2024-03-23",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2305.12377v1",
+                    "title": "The vanishing diffusion limit for an Oldroyd-B model in $\\mathbb{R}^2_+$",
+                    "abstract": "We consider the initial-boundary value problem for an incompressible\nOldroyd-B model with stress diffusion in two-dimensional upper half plane which\ndescribes the motion of viscoelastic polymeric fluids. From the physical point\nof view, the diffusive coefficient is several orders of magnitude smaller than\nother parameters in the model, and is usually assumed to be zero. However, the\nlink between the diffusive model and the standard one (zero diffusion) via\nvanishing diffusion limit is still unknown from the mathematical point of view,\nin particular for the problem with boundary. Some numerical results [13]\nsuggest that this should be true. In this work, we provide a rigorous\njustification for the vanishing diffusion in $L^\\infty$-norm.",
+                    "authors": "Yinghui Wang, Huanyao Wen",
+                    "published": "2023-05-21",
+                    "updated": "2023-05-21",
+                    "primary_cat": "math.AP",
+                    "cats": [
+                        "math.AP",
+                        "35Q35, 76A10, 76D10"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/math/0204289v1",
+                    "title": "On diffusion approximation with discontinuous coefficients",
+                    "abstract": "Convergence of stochastic processes with jumps to diffusion processes is\ninvestigated in the case when the limit process has discontinuous coefficients.\n  An example is given in which the diffusion approximation of a queueing model\nyields a diffusion process with discontinuous diffusion and drift coefficients.",
+                    "authors": "N. V. Krylov, R. Liptser",
+                    "published": "2002-04-24",
+                    "updated": "2002-04-24",
+                    "primary_cat": "math.PR",
+                    "cats": [
+                        "math.PR",
+                        "math.SG",
+                        "60B10; 60K25}"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2312.08873v1",
+                    "title": "Diffusion Cocktail: Fused Generation from Diffusion Models",
+                    "abstract": "Diffusion models excel at generating high-quality images and are easy to\nextend, making them extremely popular among active users who have created an\nextensive collection of diffusion models with various styles by fine-tuning\nbase models such as Stable Diffusion. Recent work has focused on uncovering\nsemantic and visual information encoded in various components of a diffusion\nmodel, enabling better generation quality and more fine-grained control.\nHowever, those methods target improving a single model and overlook the vastly\navailable collection of fine-tuned diffusion models. In this work, we study the\ncombinations of diffusion models. We propose Diffusion Cocktail (Ditail), a\ntraining-free method that can accurately transfer content information between\ntwo diffusion models. This allows us to perform diverse generations using a set\nof diffusion models, resulting in novel images that are unlikely to be obtained\nby a single model alone. We also explore utilizing Ditail for style transfer,\nwith the target style set by a diffusion model instead of an image. Ditail\noffers a more detailed manipulation of the diffusion generation, thereby\nenabling the vast community to integrate various styles and contents seamlessly\nand generate any content of any style.",
+                    "authors": "Haoming Liu, Yuanhe Guo, Shengjie Wang, Hongyi Wen",
+                    "published": "2023-12-12",
+                    "updated": "2023-12-12",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.AI"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1611.06202v2",
+                    "title": "Brownian yet non-Gaussian diffusion: from superstatistics to subordination of diffusing diffusivities",
+                    "abstract": "A growing number of biological, soft, and active matter systems are observed\nto exhibit normal diffusive dynamics with a linear growth of the mean squared\ndisplacement, yet with a non-Gaussian distribution of increments. Based on the\nChubinsky-Slater idea of a diffusing diffusivity we here establish and analyze\na minimal model framework of diffusion processes with fluctuating diffusivity.\nIn particular, we demonstrate the equivalence of the diffusing diffusivity\nprocess with a superstatistical approach with a distribution of diffusivities,\nat times shorter than the diffusivity correlation time. At longer times a\ncrossover to a Gaussian distribution with an effective diffusivity emerges.\nSpecifically, we establish a subordination picture of Brownian but non-Gaussian\ndiffusion processes, that can be used for a wide class of diffusivity\nfluctuation statistics. Our results are shown to be in excellent agreement with\nsimulations and numerical evaluations.",
+                    "authors": "A. V. Chechkin, F. Seno, R. Metzler, I. M. Sokolov",
+                    "published": "2016-11-18",
+                    "updated": "2017-03-30",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech",
+                        "physics.bio-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2207.09786v1",
+                    "title": "Non-Uniform Diffusion Models",
+                    "abstract": "Diffusion models have emerged as one of the most promising frameworks for\ndeep generative modeling. In this work, we explore the potential of non-uniform\ndiffusion models. We show that non-uniform diffusion leads to multi-scale\ndiffusion models which have similar structure to this of multi-scale\nnormalizing flows. We experimentally find that in the same or less training\ntime, the multi-scale diffusion model achieves better FID score than the\nstandard uniform diffusion model. More importantly, it generates samples $4.4$\ntimes faster in $128\\times 128$ resolution. The speed-up is expected to be\nhigher in higher resolutions where more scales are used. Moreover, we show that\nnon-uniform diffusion leads to a novel estimator for the conditional score\nfunction which achieves on par performance with the state-of-the-art\nconditional denoising estimator. Our theoretical and experimental findings are\naccompanied by an open source library MSDiff which can facilitate further\nresearch of non-uniform diffusion models.",
+                    "authors": "Georgios Batzolis, Jan Stanczuk, Carola-Bibiane Sch\u00f6nlieb, Christian Etmann",
+                    "published": "2022-07-20",
+                    "updated": "2022-07-20",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2305.16269v1",
+                    "title": "UDPM: Upsampling Diffusion Probabilistic Models",
+                    "abstract": "In recent years, Denoising Diffusion Probabilistic Models (DDPM) have caught\nsignificant attention. By composing a Markovian process that starts in the data\ndomain and then gradually adds noise until reaching pure white noise, they\nachieve superior performance in learning data distributions. Yet, these models\nrequire a large number of diffusion steps to produce aesthetically pleasing\nsamples, which is inefficient. In addition, unlike common generative\nadversarial networks, the latent space of diffusion models is not\ninterpretable. In this work, we propose to generalize the denoising diffusion\nprocess into an Upsampling Diffusion Probabilistic Model (UDPM), in which we\nreduce the latent variable dimension in addition to the traditional noise level\naddition. As a result, we are able to sample images of size $256\\times 256$\nwith only 7 diffusion steps, which is less than two orders of magnitude\ncompared to standard DDPMs. We formally develop the Markovian diffusion\nprocesses of the UDPM, and demonstrate its generation capabilities on the\npopular FFHQ, LSUN horses, ImageNet, and AFHQv2 datasets. Another favorable\nproperty of UDPM is that it is very easy to interpolate its latent space, which\nis not the case with standard diffusion models. Our code is available online\n\\url{https://github.com/shadyabh/UDPM}",
+                    "authors": "Shady Abu-Hussein, Raja Giryes",
+                    "published": "2023-05-25",
+                    "updated": "2023-05-25",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.LG",
+                        "eess.IV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1906.02405v1",
+                    "title": "Indirect interactions influence contact network structure and diffusion dynamics",
+                    "abstract": "Interaction patterns at the individual level influence the behaviour of\ndiffusion over contact networks. Most of the current diffusion models only\nconsider direct interactions among individuals to build underlying infectious\nitems transmission networks. However, delayed indirect interactions, where a\nsusceptible individual interacts with infectious items after the infected\nindividual has left the interaction space, can also cause transmission events.\nWe define a diffusion model called the same place different time transmission\n(SPDT) based diffusion that considers transmission links for these indirect\ninteractions. Our SPDT model changes the network dynamics where the\nconnectivity among individuals varies with the decay rates of link infectivity.\nWe investigate SPDT diffusion behaviours by simulating airborne disease\nspreading on data-driven contact networks. The SPDT model significantly\nincreases diffusion dynamics (particularly for networks with low link densities\nwhere indirect interactions create new infection pathways) and is capable of\nproducing realistic disease reproduction number. Our results show that the SPDT\nmodel is significantly more likely to lead to outbreaks compared to current\ndiffusion models with direct interactions. We find that the diffusion dynamics\nwith including indirect links are not reproducible by the current models,\nhighlighting the importance of the indirect links for predicting outbreaks.",
+                    "authors": "Md Shahzamal, Raja Jurdak, Bernard Mans, Frank de Hoog",
+                    "published": "2019-06-06",
+                    "updated": "2019-06-06",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "physics.soc-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2306.03436v2",
+                    "title": "Intellectual Property Protection of Diffusion Models via the Watermark Diffusion Process",
+                    "abstract": "Diffusion models have rapidly become a vital part of deep generative\narchitectures, given today's increasing demands. Obtaining large,\nhigh-performance diffusion models demands significant resources, highlighting\ntheir importance as intellectual property worth protecting. However, existing\nwatermarking techniques for ownership verification are insufficient when\napplied to diffusion models. Very recent research in watermarking diffusion\nmodels either exposes watermarks during task generation, which harms the\nimperceptibility, or is developed for conditional diffusion models that require\nprompts to trigger the watermark. This paper introduces WDM, a novel\nwatermarking solution for diffusion models without imprinting the watermark\nduring task generation. It involves training a model to concurrently learn a\nWatermark Diffusion Process (WDP) for embedding watermarks alongside the\nstandard diffusion process for task generation. We provide a detailed\ntheoretical analysis of WDP training and sampling, relating it to a shifted\nGaussian diffusion process via the same reverse noise. Extensive experiments\nare conducted to validate the effectiveness and robustness of our approach in\nvarious trigger and watermark data configurations.",
+                    "authors": "Sen Peng, Yufei Chen, Cong Wang, Xiaohua Jia",
+                    "published": "2023-06-06",
+                    "updated": "2023-11-29",
+                    "primary_cat": "cs.CR",
+                    "cats": [
+                        "cs.CR",
+                        "cs.LG"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2106.04745v2",
+                    "title": "Evaluation of diffuse mismatch model for phonon scattering at disordered interfaces",
+                    "abstract": "Diffuse phonon scattering strongly affects the phonon transport through a\ndisordered interface. The often-used diffuse mismatch model assumes that\nphonons lose memory of their origin after being scattered by the interface.\nUsing mode-resolved atomic Green's function simulation, we demonstrate that\ndiffuse phonon scattering by a single disordered interface cannot make a phonon\nlose its memory and thus the applicability of diffusive mismatch model is\nlimited. An analytical expression for diffuse scattering probability based on\nthe continuum approximation is also derived and shown to work reasonably well\nat low frequencies.",
+                    "authors": "Qichen Song, Gang Chen",
+                    "published": "2021-06-09",
+                    "updated": "2021-08-04",
+                    "primary_cat": "cond-mat.mes-hall",
+                    "cats": [
+                        "cond-mat.mes-hall"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2210.05559v2",
+                    "title": "Unifying Diffusion Models' Latent Space, with Applications to CycleDiffusion and Guidance",
+                    "abstract": "Diffusion models have achieved unprecedented performance in generative\nmodeling. The commonly-adopted formulation of the latent code of diffusion\nmodels is a sequence of gradually denoised samples, as opposed to the simpler\n(e.g., Gaussian) latent space of GANs, VAEs, and normalizing flows. This paper\nprovides an alternative, Gaussian formulation of the latent space of various\ndiffusion models, as well as an invertible DPM-Encoder that maps images into\nthe latent space. While our formulation is purely based on the definition of\ndiffusion models, we demonstrate several intriguing consequences. (1)\nEmpirically, we observe that a common latent space emerges from two diffusion\nmodels trained independently on related domains. In light of this finding, we\npropose CycleDiffusion, which uses DPM-Encoder for unpaired image-to-image\ntranslation. Furthermore, applying CycleDiffusion to text-to-image diffusion\nmodels, we show that large-scale text-to-image diffusion models can be used as\nzero-shot image-to-image editors. (2) One can guide pre-trained diffusion\nmodels and GANs by controlling the latent codes in a unified, plug-and-play\nformulation based on energy-based models. Using the CLIP model and a face\nrecognition model as guidance, we demonstrate that diffusion models have better\ncoverage of low-density sub-populations and individuals than GANs. The code is\npublicly available at https://github.com/ChenWu98/cycle-diffusion.",
+                    "authors": "Chen Henry Wu, Fernando De la Torre",
+                    "published": "2022-10-11",
+                    "updated": "2022-12-07",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.GR",
+                        "cs.LG"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1411.2007v1",
+                    "title": "On large time behavior and selection principle for a diffusive Carr-Penrose Model",
+                    "abstract": "This paper is concerned with the study of a diffusive perturbation of the\nlinear LSW model introduced by Carr and Penrose. A main subject of interest is\nto understand how the presence of diffusion acts as a selection principle,\nwhich singles out a particular self-similar solution of the linear LSW model as\ndetermining the large time behavior of the diffusive model. A selection\nprinciple is rigorously proven for a model which is a semi-classical\napproximation to the diffusive model. Upper bounds on the rate of coarsening\nare also obtained for the full diffusive model.",
+                    "authors": "Joseph G. Conlon, Michael Dabkowski, Jingchen Wu",
+                    "published": "2014-11-07",
+                    "updated": "2014-11-07",
+                    "primary_cat": "math.AP",
+                    "cats": [
+                        "math.AP",
+                        "35F05"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1712.02290v2",
+                    "title": "Effects of nongaussian diffusion on \"isotropic diffusion measurements'': an ex-vivo microimaging and simulation study",
+                    "abstract": "Designing novel diffusion-weighted pulse sequences to probe tissue\nmicrostructure beyond the conventional Stejskal-Tanner family is currently of\nbroad interest. One such technique, multidimensional diffusion MRI, has been\nrecently proposed to afford model-free decomposition of diffusion signal\nkurtosis into terms originating from either ensemble variance of isotropic\ndiffusivity or microscopic diffusion anisotropy. This ability rests on the\nassumption that diffusion can be described as a sum of multiple Gaussian\ncompartments, but this is often not strictly fulfilled. The effects of\nnongaussian diffusion on single shot isotropic diffusion sequences were first\nconsidered in detail by de Swiet and Mitra in 1996. They showed theoretically\nthat anisotropic compartments lead to anisotropic time dependence of the\ndiffusion tensors, which causes the measured isotropic diffusivity to depend on\ngradient frame orientation. Here we show how such deviations from the multiple\nGaussian compartments assumption conflates orientation dispersion with ensemble\nvariance in isotropic diffusivity. Second, we consider additional contributions\nto the apparent variance in isotropic diffusivity arising due to\nintracompartmental kurtosis. These will likewise depend on gradient frame\norientation. We illustrate the potential importance of these confounds with\nanalytical expressions, numerical simulations in simple model geometries, and\nmicroimaging experiments in fixed spinal cord using isotropic diffusion\nencoding waveforms with 7.5 ms duration and 3000 mT/m maximum amplitude.",
+                    "authors": "Sune N\u00f8rh\u00f8j Jespersen, Jonas Lynge Olesen, Andrada Ianu\u015f, Noam Shemesh",
+                    "published": "2017-12-06",
+                    "updated": "2019-02-04",
+                    "primary_cat": "physics.bio-ph",
+                    "cats": [
+                        "physics.bio-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2303.16203v3",
+                    "title": "Your Diffusion Model is Secretly a Zero-Shot Classifier",
+                    "abstract": "The recent wave of large-scale text-to-image diffusion models has\ndramatically increased our text-based image generation abilities. These models\ncan generate realistic images for a staggering variety of prompts and exhibit\nimpressive compositional generalization abilities. Almost all use cases thus\nfar have solely focused on sampling; however, diffusion models can also provide\nconditional density estimates, which are useful for tasks beyond image\ngeneration. In this paper, we show that the density estimates from large-scale\ntext-to-image diffusion models like Stable Diffusion can be leveraged to\nperform zero-shot classification without any additional training. Our\ngenerative approach to classification, which we call Diffusion Classifier,\nattains strong results on a variety of benchmarks and outperforms alternative\nmethods of extracting knowledge from diffusion models. Although a gap remains\nbetween generative and discriminative approaches on zero-shot recognition\ntasks, our diffusion-based approach has significantly stronger multimodal\ncompositional reasoning ability than competing discriminative approaches.\nFinally, we use Diffusion Classifier to extract standard classifiers from\nclass-conditional diffusion models trained on ImageNet. Our models achieve\nstrong classification performance using only weak augmentations and exhibit\nqualitatively better \"effective robustness\" to distribution shift. Overall, our\nresults are a step toward using generative over discriminative models for\ndownstream tasks. Results and visualizations at\nhttps://diffusion-classifier.github.io/",
+                    "authors": "Alexander C. Li, Mihir Prabhudesai, Shivam Duggal, Ellis Brown, Deepak Pathak",
+                    "published": "2023-03-28",
+                    "updated": "2023-09-13",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI",
+                        "cs.CV",
+                        "cs.NE",
+                        "cs.RO"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2305.01115v2",
+                    "title": "In-Context Learning Unlocked for Diffusion Models",
+                    "abstract": "We present Prompt Diffusion, a framework for enabling in-context learning in\ndiffusion-based generative models. Given a pair of task-specific example\nimages, such as depth from/to image and scribble from/to image, and a text\nguidance, our model automatically understands the underlying task and performs\nthe same task on a new query image following the text guidance. To achieve\nthis, we propose a vision-language prompt that can model a wide range of\nvision-language tasks and a diffusion model that takes it as input. The\ndiffusion model is trained jointly over six different tasks using these\nprompts. The resulting Prompt Diffusion model is the first diffusion-based\nvision-language foundation model capable of in-context learning. It\ndemonstrates high-quality in-context generation on the trained tasks and\ngeneralizes effectively to new, unseen vision tasks with their respective\nprompts. Our model also shows compelling text-guided image editing results. Our\nframework aims to facilitate research into in-context learning for computer\nvision. We share our code and pre-trained models at\nhttps://github.com/Zhendong-Wang/Prompt-Diffusion.",
+                    "authors": "Zhendong Wang, Yifan Jiang, Yadong Lu, Yelong Shen, Pengcheng He, Weizhu Chen, Zhangyang Wang, Mingyuan Zhou",
+                    "published": "2023-05-01",
+                    "updated": "2023-10-18",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2310.01221v2",
+                    "title": "Nonlocal diffusion model with maximum principle",
+                    "abstract": "In this paper, we propose nonlocal diffusion models with Dirichlet boundary.\nThese nonlocal diffusion models preserve the maximum principle and also have\ncorresponding variational form. With these good properties, It is relatively\neasy to prove the well-posedness and the vanishing nonlocality convergence.\nFurthermore, by specifically designed weight function, we can get a nonlocal\ndiffusion model with second order convergence which is optimal for nonlocal\ndiffusion models.",
+                    "authors": "Zuoqiang Shi",
+                    "published": "2023-10-02",
+                    "updated": "2023-10-12",
+                    "primary_cat": "math.AP",
+                    "cats": [
+                        "math.AP",
+                        "cs.NA",
+                        "math.NA"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2006.00003v1",
+                    "title": "Coupling particle-based reaction-diffusion simulations with reservoirs mediated by reaction-diffusion PDEs",
+                    "abstract": "Open biochemical systems of interacting molecules are ubiquitous in\nlife-related processes. However, established computational methodologies, like\nmolecular dynamics, are still mostly constrained to closed systems and\ntimescales too small to be relevant for life processes. Alternatively,\nparticle-based reaction-diffusion models are currently the most accurate and\ncomputationally feasible approach at these scales. Their efficiency lies in\nmodeling entire molecules as particles that can diffuse and interact with each\nother. In this work, we develop modeling and numerical schemes for\nparticle-based reaction-diffusion in an open setting, where the reservoirs are\nmediated by reaction-diffusion PDEs. We derive two important theoretical\nresults. The first one is the mean-field for open systems of diffusing\nparticles; the second one is the mean-field for a particle-based\nreaction-diffusion system with second-order reactions. We employ these two\nresults to develop a numerical scheme that consistently couples particle-based\nreaction-diffusion processes with reaction-diffusion PDEs. This allows modeling\nopen biochemical systems in contact with reservoirs that are time-dependent and\nspatially inhomogeneous, as in many relevant real-world applications.",
+                    "authors": "Margarita Kostr\u00e9, Christof Sch\u00fctte, Frank No\u00e9, Mauricio J. del Razo",
+                    "published": "2020-05-29",
+                    "updated": "2020-05-29",
+                    "primary_cat": "q-bio.QM",
+                    "cats": [
+                        "q-bio.QM",
+                        "physics.chem-ph",
+                        "physics.comp-ph",
+                        "92C40, 92C45, 60J70, 60Gxx, 70Lxx"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1609.04658v1",
+                    "title": "Analyzing Signal Attenuation in PFG Anomalous Diffusion via a Modified Gaussian Phase Distribution Approximation Based on Fractal Derivative Model",
+                    "abstract": "Pulsed field gradient (PFG) has been increasingly employed to study anomalous\ndiffusions in Nuclear Magnetic Resonance (NMR) and Magnetic Resonance Imaging\n(MRI). However, the analysis of PFG anomalous diffusion is complicated. In this\npaper, a fractal derivative model based modified Gaussian phase distribution\nmethod is proposed to describe PFG anomalous diffusion. By using the phase\ndistribution obtained from the effective phase shift diffusion method based on\nfractal derivatives, and employing some of the traditional Gaussian phase\ndistribution approximation techniques, a general signal attenuation expression\nfor free fractional diffusion is derived. This expression describes a stretched\nexponential function based attenuation, which is distinct from both the\nexponential attenuation for normal diffusion obtained from conventional\nGaussian phase distribution approximation, and the Mittag-Leffler function\nbased attenuation for anomalous diffusion obtained from fractional derivative.\nThe obtained signal attenuation expression can analyze the finite gradient\npulse width (FGPW) effect. Additionally, it can generally be applied to all\nthree types of PFG fractional diffusions classified based on time derivative\norder alpha and space derivative order beta. These three types of fractional\ndiffusions include time-fractional diffusion, space-fractional diffusion, and\ngeneral fractional diffusion. The results in this paper are consistent with\nreported results based on effective phase shift diffusion equation method and\ninstantaneous signal attenuation method. This method provides a new, convenient\napproximation formalism for analyzing PFG anomalous diffusion experiments.",
+                    "authors": "Guoxing Lin",
+                    "published": "2016-09-15",
+                    "updated": "2016-09-15",
+                    "primary_cat": "physics.chem-ph",
+                    "cats": [
+                        "physics.chem-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2403.01742v2",
+                    "title": "Diffusion-TS: Interpretable Diffusion for General Time Series Generation",
+                    "abstract": "Denoising diffusion probabilistic models (DDPMs) are becoming the leading\nparadigm for generative models. It has recently shown breakthroughs in audio\nsynthesis, time series imputation and forecasting. In this paper, we propose\nDiffusion-TS, a novel diffusion-based framework that generates multivariate\ntime series samples of high quality by using an encoder-decoder transformer\nwith disentangled temporal representations, in which the decomposition\ntechnique guides Diffusion-TS to capture the semantic meaning of time series\nwhile transformers mine detailed sequential information from the noisy model\ninput. Different from existing diffusion-based approaches, we train the model\nto directly reconstruct the sample instead of the noise in each diffusion step,\ncombining a Fourier-based loss term. Diffusion-TS is expected to generate time\nseries satisfying both interpretablity and realness. In addition, it is shown\nthat the proposed Diffusion-TS can be easily extended to conditional generation\ntasks, such as forecasting and imputation, without any model changes. This also\nmotivates us to further explore the performance of Diffusion-TS under irregular\nsettings. Finally, through qualitative and quantitative experiments, results\nshow that Diffusion-TS achieves the state-of-the-art results on various\nrealistic analyses of time series.",
+                    "authors": "Xinyu Yuan, Yan Qiao",
+                    "published": "2024-03-04",
+                    "updated": "2024-03-14",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1906.02856v1",
+                    "title": "Diffusion on dynamic contact networks with indirect transmission links",
+                    "abstract": "Modelling diffusion processes on dynamic contact networks is an important\nresearch area for epidemiology, marketing, cybersecurity, and ecology. However,\ncurrent diffusion models cannot capture transmissions occurring for indirect\ninteractions. For example, an airborne infected individual releases infectious\nparticles at locations that can suspend in the air and infect susceptible\nindividuals arriving even after the infected individual left. Thus, current\ndiffusion models miss transmissions during indirect interactions. In this\nthesis, a novel diffusion model called the same place different time\ntransmission based diffusion (SPDT) is introduced to take into account the\ntransmissions through indirect interactions. The behaviour of SPDT diffusion is\nanalysed on real dynamic contact networks and a significant amplification in\ndiffusion dynamics is observed. The SPDT model also introduces some novel\nbehaviours different from current diffusion models. In this work, a new SPDT\ngraph model is also developed to generate synthetic traces to explore SPDT\ndiffusion in several scenarios. The analysis shows that the emergence of new\ndiffusion becomes common thanks to the inclusion of indirect transmissions\nwithin the SPDT model. This work finally investigates how diffusion can be\ncontrolled and develops new methods to hinder diffusion.",
+                    "authors": "Md Shahzamal",
+                    "published": "2019-06-07",
+                    "updated": "2019-06-07",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "physics.soc-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1708.06890v1",
+                    "title": "Collaborative Inference of Coexisting Information Diffusions",
+                    "abstract": "Recently, \\textit{diffusion history inference} has become an emerging\nresearch topic due to its great benefits for various applications, whose\npurpose is to reconstruct the missing histories of information diffusion traces\naccording to incomplete observations. The existing methods, however, often\nfocus only on single information diffusion trace, while in a real-world social\nnetwork, there often coexist multiple information diffusions over the same\nnetwork. In this paper, we propose a novel approach called Collaborative\nInference Model (CIM) for the problem of the inference of coexisting\ninformation diffusions. By exploiting the synergism between the coexisting\ninformation diffusions, CIM holistically models multiple information diffusions\nas a sparse 4th-order tensor called Coexisting Diffusions Tensor (CDT) without\nany prior assumption of diffusion models, and collaboratively infers the\nhistories of the coexisting information diffusions via a low-rank approximation\nof CDT with a fusion of heterogeneous constraints generated from additional\ndata sources. To improve the efficiency, we further propose an optimal\nalgorithm called Time Window based Parallel Decomposition Algorithm (TWPDA),\nwhich can speed up the inference without compromise on the accuracy by\nutilizing the temporal locality of information diffusions. The extensive\nexperiments conducted on real world datasets and synthetic datasets verify the\neffectiveness and efficiency of CIM and TWPDA.",
+                    "authors": "Yanchao Sun, Cong Qian, Ning Yang, Philip S. Yu",
+                    "published": "2017-08-23",
+                    "updated": "2017-08-23",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2305.13122v1",
+                    "title": "Policy Representation via Diffusion Probability Model for Reinforcement Learning",
+                    "abstract": "Popular reinforcement learning (RL) algorithms tend to produce a unimodal\npolicy distribution, which weakens the expressiveness of complicated policy and\ndecays the ability of exploration. The diffusion probability model is powerful\nto learn complicated multimodal distributions, which has shown promising and\npotential applications to RL. In this paper, we formally build a theoretical\nfoundation of policy representation via the diffusion probability model and\nprovide practical implementations of diffusion policy for online model-free RL.\nConcretely, we character diffusion policy as a stochastic process, which is a\nnew approach to representing a policy. Then we present a convergence guarantee\nfor diffusion policy, which provides a theory to understand the multimodality\nof diffusion policy. Furthermore, we propose the DIPO which is an\nimplementation for model-free online RL with DIffusion POlicy. To the best of\nour knowledge, DIPO is the first algorithm to solve model-free online RL\nproblems with the diffusion model. Finally, extensive empirical results show\nthe effectiveness and superiority of DIPO on the standard continuous control\nMujoco benchmark.",
+                    "authors": "Long Yang, Zhixiong Huang, Fenghao Lei, Yucun Zhong, Yiming Yang, Cong Fang, Shiting Wen, Binbin Zhou, Zhouchen Lin",
+                    "published": "2023-05-22",
+                    "updated": "2023-05-22",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2212.10805v1",
+                    "title": "Beyond Information Exchange: An Approach to Deploy Network Properties for Information Diffusion",
+                    "abstract": "Information diffusion in Online Social Networks is a new and crucial problem\nin social network analysis field and requires significant research attention.\nEfficient diffusion of information are of critical importance in diverse\nsituations such as; pandemic prevention, advertising, marketing etc. Although\nseveral mathematical models have been developed till date, but previous works\nlacked systematic analysis and exploration of the influence of neighborhood for\ninformation diffusion. In this paper, we have proposed Common Neighborhood\nStrategy (CNS) algorithm for information diffusion that demonstrates the role\nof common neighborhood in information propagation throughout the network. The\nperformance of CNS algorithm is evaluated on several real-world datasets in\nterms of diffusion speed and diffusion outspread and compared with several\nwidely used information diffusion models. Empirical results show CNS algorithm\nenables better information diffusion both in terms of diffusion speed and\ndiffusion outspread.",
+                    "authors": "Soumita Das, Anupam Biswas, Ravi Kishore Devarapalli",
+                    "published": "2022-12-21",
+                    "updated": "2022-12-21",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "cs.CV",
+                        "cs.IR",
+                        "J.4; G.4; I.6"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1506.05574v1",
+                    "title": "Information Diffusion issues",
+                    "abstract": "In this report there will be a discussion for Information Diffusion. There\nwill be discussions on what information diffusion is, its key characteristics\nand on several other aspects of these kinds of networks. This report will focus\non peer to peer models in information diffusion. There will be discussions on\nepidemic model, OSN and other details related to information diffusion.",
+                    "authors": "Jonathan Helmigh",
+                    "published": "2015-06-18",
+                    "updated": "2015-06-18",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2402.13144v1",
+                    "title": "Neural Network Diffusion",
+                    "abstract": "Diffusion models have achieved remarkable success in image and video\ngeneration. In this work, we demonstrate that diffusion models can also\n\\textit{generate high-performing neural network parameters}. Our approach is\nsimple, utilizing an autoencoder and a standard latent diffusion model. The\nautoencoder extracts latent representations of a subset of the trained network\nparameters. A diffusion model is then trained to synthesize these latent\nparameter representations from random noise. It then generates new\nrepresentations that are passed through the autoencoder's decoder, whose\noutputs are ready to use as new subsets of network parameters. Across various\narchitectures and datasets, our diffusion process consistently generates models\nof comparable or improved performance over trained networks, with minimal\nadditional cost. Notably, we empirically find that the generated models perform\ndifferently with the trained networks. Our results encourage more exploration\non the versatile use of diffusion models.",
+                    "authors": "Kai Wang, Zhaopan Xu, Yukun Zhou, Zelin Zang, Trevor Darrell, Zhuang Liu, Yang You",
+                    "published": "2024-02-20",
+                    "updated": "2024-02-20",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.CV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2211.08892v2",
+                    "title": "Fast Graph Generation via Spectral Diffusion",
+                    "abstract": "Generating graph-structured data is a challenging problem, which requires\nlearning the underlying distribution of graphs. Various models such as graph\nVAE, graph GANs, and graph diffusion models have been proposed to generate\nmeaningful and reliable graphs, among which the diffusion models have achieved\nstate-of-the-art performance. In this paper, we argue that running full-rank\ndiffusion SDEs on the whole graph adjacency matrix space hinders diffusion\nmodels from learning graph topology generation, and hence significantly\ndeteriorates the quality of generated graph data. To address this limitation,\nwe propose an efficient yet effective Graph Spectral Diffusion Model (GSDM),\nwhich is driven by low-rank diffusion SDEs on the graph spectrum space. Our\nspectral diffusion model is further proven to enjoy a substantially stronger\ntheoretical guarantee than standard diffusion models. Extensive experiments\nacross various datasets demonstrate that, our proposed GSDM turns out to be the\nSOTA model, by exhibiting both significantly higher generation quality and much\nless computational consumption than the baselines.",
+                    "authors": "Tianze Luo, Zhanfeng Mo, Sinno Jialin Pan",
+                    "published": "2022-11-16",
+                    "updated": "2022-11-19",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1202.6521v1",
+                    "title": "Coherence transition in degenerate diffusion equations with mean field coupling",
+                    "abstract": "We introduce non-linear diffusion in a classical diffusion advection model\nwith non local aggregative coupling on the circle, that exhibits a transition\nfrom an uncoherent state to a coherent one when the coupling strength is\nincreased. We show first that all solutions of the equation converge to the set\nof equilibria, second that the set of equilibria undergoes a bifurcation\nrepresenting the transition to coherence when the coupling strength is\nincreased. These two properties are similar to the situation with linear\ndiffusion. Nevertheless nonlinear diffusion alters the transition scenari,\nwhich are different when the diffusion is sub-quadratic and when the diffusion\nis super-quadratic. When the diffusion is super-quadratic, it results in a\nmultistability region that preceeds the pitchfork bifurcation at which the\nuncoherent equilibrium looses stability. When the diffusion is quadratic the\npitchfork bifurcation at the onset of coherence is infinitely degenerate and a\ndisk of equilibria exist for the critical value of the coupling strength.\nAnother impact of nonlinear diffusion is that coherent equilibria become\nlocalized when advection is strong enough, a phenomenon that is preculded when\nthe diffusion is linear.",
+                    "authors": "Khashayar Pakdaman, Xavier Pellegrin",
+                    "published": "2012-02-29",
+                    "updated": "2012-02-29",
+                    "primary_cat": "nlin.AO",
+                    "cats": [
+                        "nlin.AO",
+                        "37N25, 92B25, 35Q35, 35K55, 37B25, 82C26"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1603.05605v1",
+                    "title": "Multiscale modeling of diffusion in a crowded environment",
+                    "abstract": "We present a multiscale approach to model diffusion in a crowded environment\nand its effect on the reaction rates. Diffusion in biological systems is often\nmodeled by a discrete space jump process in order to capture the inherent noise\nof biological systems, which becomes important in the low copy number regime.\nTo model diffusion in the crowded cell environment efficiently, we compute the\njump rates in this mesoscopic model from local first exit times, which account\nfor the microscopic positions of the crowding molecules, while the diffusing\nmolecules jump on a coarser Cartesian grid. We then extract a macroscopic\ndescription from the resulting jump rates, where the excluded volume effect is\nmodeled by a diffusion equation with space dependent diffusion coefficient. The\ncrowding molecules can be of arbitrary shape and size and numerical experiments\ndemonstrate that those factors together with the size of the diffusing molecule\nplay a crucial role on the magnitude of the decrease in diffusive motion. When\ncorrecting the reaction rates for the altered diffusion we can show that\nmolecular crowding either enhances or inhibits chemical reactions depending on\nlocal fluctuations of the obstacle density.",
+                    "authors": "Lina Meinecke",
+                    "published": "2016-03-12",
+                    "updated": "2016-03-12",
+                    "primary_cat": "q-bio.SC",
+                    "cats": [
+                        "q-bio.SC",
+                        "math.NA",
+                        "92-08"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/0801.3436v1",
+                    "title": "Model for Diffusion-Induced Ramsey Narrowing",
+                    "abstract": "Diffusion-induced Ramsey narrowing that appears when atoms can leave the\ninteraction region and repeatedly return without lost of coherence is\ninvestigated using strong collisions approximation. The effective diffusion\nequation is obtained and solved for low-dimensional model configurations and\nthree-dimensional real one.",
+                    "authors": "Alexander Romanenko, Leonid Yatsenko",
+                    "published": "2008-01-22",
+                    "updated": "2008-01-22",
+                    "primary_cat": "quant-ph",
+                    "cats": [
+                        "quant-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2301.00527v1",
+                    "title": "Diffusion Probabilistic Models for Scene-Scale 3D Categorical Data",
+                    "abstract": "In this paper, we learn a diffusion model to generate 3D data on a\nscene-scale. Specifically, our model crafts a 3D scene consisting of multiple\nobjects, while recent diffusion research has focused on a single object. To\nrealize our goal, we represent a scene with discrete class labels, i.e.,\ncategorical distribution, to assign multiple objects into semantic categories.\nThus, we extend discrete diffusion models to learn scene-scale categorical\ndistributions. In addition, we validate that a latent diffusion model can\nreduce computation costs for training and deploying. To the best of our\nknowledge, our work is the first to apply discrete and latent diffusion for 3D\ncategorical data on a scene-scale. We further propose to perform semantic scene\ncompletion (SSC) by learning a conditional distribution using our diffusion\nmodel, where the condition is a partial observation in a sparse point cloud. In\nexperiments, we empirically show that our diffusion models not only generate\nreasonable scenes, but also perform the scene completion task better than a\ndiscriminative model. Our code and models are available at\nhttps://github.com/zoomin-lee/scene-scale-diffusion",
+                    "authors": "Jumin Lee, Woobin Im, Sebin Lee, Sung-Eui Yoon",
+                    "published": "2023-01-02",
+                    "updated": "2023-01-02",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2305.09605v1",
+                    "title": "Expressiveness Remarks for Denoising Diffusion Models and Samplers",
+                    "abstract": "Denoising diffusion models are a class of generative models which have\nrecently achieved state-of-the-art results across many domains. Gradual noise\nis added to the data using a diffusion process, which transforms the data\ndistribution into a Gaussian. Samples from the generative model are then\nobtained by simulating an approximation of the time reversal of this diffusion\ninitialized by Gaussian samples. Recent research has explored adapting\ndiffusion models for sampling and inference tasks. In this paper, we leverage\nknown connections to stochastic control akin to the F\\\"ollmer drift to extend\nestablished neural network approximation results for the F\\\"ollmer drift to\ndenoising diffusion models and samplers.",
+                    "authors": "Francisco Vargas, Teodora Reu, Anna Kerekes",
+                    "published": "2023-05-16",
+                    "updated": "2023-05-16",
+                    "primary_cat": "stat.ML",
+                    "cats": [
+                        "stat.ML",
+                        "cs.LG"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2310.05264v3",
+                    "title": "The Emergence of Reproducibility and Consistency in Diffusion Models",
+                    "abstract": "In this work, we investigate an intriguing and prevalent phenomenon of\ndiffusion models which we term as \"consistent model reproducibility\": given the\nsame starting noise input and a deterministic sampler, different diffusion\nmodels often yield remarkably similar outputs. We confirm this phenomenon\nthrough comprehensive experiments, implying that different diffusion models\nconsistently reach the same data distribution and scoring function regardless\nof diffusion model frameworks, model architectures, or training procedures.\nMore strikingly, our further investigation implies that diffusion models are\nlearning distinct distributions affected by the training data size. This is\nsupported by the fact that the model reproducibility manifests in two distinct\ntraining regimes: (i) \"memorization regime\", where the diffusion model overfits\nto the training data distribution, and (ii) \"generalization regime\", where the\nmodel learns the underlying data distribution. Our study also finds that this\nvaluable property generalizes to many variants of diffusion models, including\nthose for conditional use, solving inverse problems, and model fine-tuning.\nFinally, our work raises numerous intriguing theoretical questions for future\ninvestigation and highlights practical implications regarding training\nefficiency, model privacy, and the controlled generation of diffusion models.",
+                    "authors": "Huijie Zhang, Jinfan Zhou, Yifu Lu, Minzhe Guo, Peng Wang, Liyue Shen, Qing Qu",
+                    "published": "2023-10-08",
+                    "updated": "2024-02-21",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.CV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1807.03744v2",
+                    "title": "Enhanced Diffusivity in Perturbed Senile Reinforced Random Walk Models",
+                    "abstract": "We consider diffusivity of random walks with transition probabilities\ndepending on the number of consecutive traversals of the last traversed edge,\nthe so called senile reinforced random walk (SeRW). In one dimension, the walk\nis known to be sub-diffusive with identity reinforcement function. We perturb\nthe model by introducing a small probability $\\delta$ of escaping the last\ntraversed edge at each step. The perturbed SeRW model is diffusive for any\n$\\delta >0 $, with enhanced diffusivity ($\\gg O(\\delta^2)$) in the small\n$\\delta$ regime. We further study stochastically perturbed SeRW models by\nhaving the last edge escape probability of the form $\\delta\\, \\xi_n$ with\n$\\xi_n$'s being independent random variables. Enhanced diffusivity in such\nmodels are logarithmically close to the so called residual diffusivity\n(positive in the zero $\\delta$ limit), with diffusivity between\n$O\\left(\\frac{1}{|\\log\\delta |}\\right)$ and\n$O\\left(\\frac{1}{\\log|\\log\\delta|}\\right)$. Finally, we generalize our results\nto higher dimensions where the unperturbed model is already diffusive. The\nenhanced diffusivity can be as much as $O(\\log^{-2}\\delta)$.",
+                    "authors": "Thu Dinh, Jack Xin",
+                    "published": "2018-07-10",
+                    "updated": "2020-03-16",
+                    "primary_cat": "math.PR",
+                    "cats": [
+                        "math.PR",
+                        "60G50, 60H30, 58J37"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2206.12327v1",
+                    "title": "Source Localization of Graph Diffusion via Variational Autoencoders for Graph Inverse Problems",
+                    "abstract": "Graph diffusion problems such as the propagation of rumors, computer viruses,\nor smart grid failures are ubiquitous and societal. Hence it is usually crucial\nto identify diffusion sources according to the current graph diffusion\nobservations. Despite its tremendous necessity and significance in practice,\nsource localization, as the inverse problem of graph diffusion, is extremely\nchallenging as it is ill-posed: different sources may lead to the same graph\ndiffusion patterns. Different from most traditional source localization\nmethods, this paper focuses on a probabilistic manner to account for the\nuncertainty of different candidate sources. Such endeavors require overcoming\nchallenges including 1) the uncertainty in graph diffusion source localization\nis hard to be quantified; 2) the complex patterns of the graph diffusion\nsources are difficult to be probabilistically characterized; 3) the\ngeneralization under any underlying diffusion patterns is hard to be imposed.\nTo solve the above challenges, this paper presents a generic framework: Source\nLocalization Variational AutoEncoder (SL-VAE) for locating the diffusion\nsources under arbitrary diffusion patterns. Particularly, we propose a\nprobabilistic model that leverages the forward diffusion estimation model along\nwith deep generative models to approximate the diffusion source distribution\nfor quantifying the uncertainty. SL-VAE further utilizes prior knowledge of the\nsource-observation pairs to characterize the complex patterns of diffusion\nsources by a learned generative prior. Lastly, a unified objective that\nintegrates the forward diffusion estimation model is derived to enforce the\nmodel to generalize under arbitrary diffusion patterns. Extensive experiments\nare conducted on 7 real-world datasets to demonstrate the superiority of SL-VAE\nin reconstructing the diffusion sources by excelling other methods on average\n20% in AUC score.",
+                    "authors": "Chen Ling, Junji Jiang, Junxiang Wang, Liang Zhao",
+                    "published": "2022-06-24",
+                    "updated": "2022-06-24",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.IT",
+                        "math.IT"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1907.09989v1",
+                    "title": "Rogue Heat and Diffusion Waves",
+                    "abstract": "In this paper, we numerically show and discuss the existence and\ncharacteristics of rogue heat and diffusion waves. More specifically, we use\ntwo different nonlinear heat (diffusion) models and show that modulation\ninstability leads to the generation of unexpected and large fluctuations in the\nframe of these models. These fluctuations can be named as rogue heat\n(diffusion) waves. We discuss the properties and statistics of such rogue\nwaves. Our results can find many important applications in many branches such\nas the nonlinear heat transfer, turbulence, financial mathematics, chemical or\nbiological diffusion, nuclear reactions, subsurface water infiltration, and\npore water pressure diffusion modeled in the frame of nonlinear Terzaghi\nconsolidation models, just to name a few.",
+                    "authors": "Cihan Bayindir",
+                    "published": "2019-07-18",
+                    "updated": "2019-07-18",
+                    "primary_cat": "nlin.PS",
+                    "cats": [
+                        "nlin.PS",
+                        "physics.flu-dyn"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1908.03076v3",
+                    "title": "The strategy of survival for a competition between normal and anomalous diffusion",
+                    "abstract": "In this paper, we study the competition of two diffusion processes for\nachieving the maximum possible diffusion in an area. This competition, however,\ndoes not occur in the same circumstance; one of these processes is a normal\ndiffusion with a higher growth rate, and another one is an anomalous diffusion\nwith a lower growth rate. The trivial solution of the proposed model suggests\nthat the winner is the one with the higher growth rate. But, the question is:\nwhat characteristics and strategies should the second diffusion include to\nprolong the survival in such a competition? The studied diffusion equations\ncorrespond to the SI model such that the anomalous diffusion has memory\ndescribed by a fractional order derivative. The strategy promise that anomalous\ndiffusion reaches maximum survival in case of forgetting some parts of the\nmemory. This model can represent some of real phenomena, such as the contest of\ntwo companies in a market share, the spreading of two epidemic diseases, the\ndiffusion of two species, or any reaction-diffusion related to real-world\ncompetition.",
+                    "authors": "Moein Khalighi, Jamshid Ardalankia, Abbas Karimi Rizi, Haleh Ebadi, Gholamreza Jafari",
+                    "published": "2019-08-07",
+                    "updated": "2020-10-18",
+                    "primary_cat": "physics.soc-ph",
+                    "cats": [
+                        "physics.soc-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2212.10777v4",
+                    "title": "Hierarchically branched diffusion models leverage dataset structure for class-conditional generation",
+                    "abstract": "Class-labeled datasets, particularly those common in scientific domains, are\nrife with internal structure, yet current class-conditional diffusion models\nignore these relationships and implicitly diffuse on all classes in a flat\nfashion. To leverage this structure, we propose hierarchically branched\ndiffusion models as a novel framework for class-conditional generation.\nBranched diffusion models rely on the same diffusion process as traditional\nmodels, but learn reverse diffusion separately for each branch of a hierarchy.\nWe highlight several advantages of branched diffusion models over the current\nstate-of-the-art methods for class-conditional diffusion, including extension\nto novel classes in a continual-learning setting, a more sophisticated form of\nanalogy-based conditional generation (i.e. transmutation), and a novel\ninterpretability into the generation process. We extensively evaluate branched\ndiffusion models on several benchmark and large real-world scientific datasets\nspanning many data modalities.",
+                    "authors": "Alex M. Tseng, Max Shen, Tommaso Biancalani, Gabriele Scalia",
+                    "published": "2022-12-21",
+                    "updated": "2024-02-01",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2302.07261v2",
+                    "title": "Where to Diffuse, How to Diffuse, and How to Get Back: Automated Learning for Multivariate Diffusions",
+                    "abstract": "Diffusion-based generative models (DBGMs) perturb data to a target noise\ndistribution and reverse this process to generate samples. The choice of\nnoising process, or inference diffusion process, affects both likelihoods and\nsample quality. For example, extending the inference process with auxiliary\nvariables leads to improved sample quality. While there are many such\nmultivariate diffusions to explore, each new one requires significant\nmodel-specific analysis, hindering rapid prototyping and evaluation. In this\nwork, we study Multivariate Diffusion Models (MDMs). For any number of\nauxiliary variables, we provide a recipe for maximizing a lower-bound on the\nMDMs likelihood without requiring any model-specific analysis. We then\ndemonstrate how to parameterize the diffusion for a specified target noise\ndistribution; these two points together enable optimizing the inference\ndiffusion process. Optimizing the diffusion expands easy experimentation from\njust a few well-known processes to an automatic search over all linear\ndiffusions. To demonstrate these ideas, we introduce two new specific\ndiffusions as well as learn a diffusion process on the MNIST, CIFAR10, and\nImageNet32 datasets. We show learned MDMs match or surpass bits-per-dims (BPDs)\nrelative to fixed choices of diffusions for a given dataset and model\narchitecture.",
+                    "authors": "Raghav Singhal, Mark Goldstein, Rajesh Ranganath",
+                    "published": "2023-02-14",
+                    "updated": "2023-03-03",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "stat.ML"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1801.09352v1",
+                    "title": "Distributed order Hausdorff derivative diffusion model to characterize non-Fickian diffusion in porous media",
+                    "abstract": "Many theoretical and experimental results show that solute transport in\nheterogeneous porous media exhibits multi-scaling behaviors. To describe such\nnon-Fickian diffusions, this work provides a distributed order Hausdorff\ndiffusion model to describe the tracer transport in porous media. This model is\nproved to be equivalent with the diffusion equation model with a nonlinear time\ndependent diffusion coefficient. In conjunction with the structural derivative,\nits mean squared displacement (MSD) of the tracer particles is explicitly\nderived as a dilogarithm function when the weight function of the order\ndistribution is a linear function of the time derivative order. This model can\ncapture both accelerating and decelerating anomalous and ultraslow diffusions\nby varying the weight parameter c. In this study, the tracer transport in\nwater-filled pore spaces of two-dimensional Euclidean is demonstrated as a\ndecelerating sub-diffusion, and can well be described by the distributed order\nHausdorff diffusion model with c = 1.73. While the Hausdorff diffusion model\ncan accurately fit the sub-diffusion experimental data of the tracer transport\nin the pore-solid prefractal porous media.",
+                    "authors": "Yingjie Liang, Wen Chen, Wei Xu, HongGuang Sun",
+                    "published": "2018-01-29",
+                    "updated": "2018-01-29",
+                    "primary_cat": "physics.flu-dyn",
+                    "cats": [
+                        "physics.flu-dyn"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2211.07804v3",
+                    "title": "Diffusion Models for Medical Image Analysis: A Comprehensive Survey",
+                    "abstract": "Denoising diffusion models, a class of generative models, have garnered\nimmense interest lately in various deep-learning problems. A diffusion\nprobabilistic model defines a forward diffusion stage where the input data is\ngradually perturbed over several steps by adding Gaussian noise and then learns\nto reverse the diffusion process to retrieve the desired noise-free data from\nnoisy data samples. Diffusion models are widely appreciated for their strong\nmode coverage and quality of the generated samples despite their known\ncomputational burdens. Capitalizing on the advances in computer vision, the\nfield of medical imaging has also observed a growing interest in diffusion\nmodels. To help the researcher navigate this profusion, this survey intends to\nprovide a comprehensive overview of diffusion models in the discipline of\nmedical image analysis. Specifically, we introduce the solid theoretical\nfoundation and fundamental concepts behind diffusion models and the three\ngeneric diffusion modelling frameworks: diffusion probabilistic models,\nnoise-conditioned score networks, and stochastic differential equations. Then,\nwe provide a systematic taxonomy of diffusion models in the medical domain and\npropose a multi-perspective categorization based on their application, imaging\nmodality, organ of interest, and algorithms. To this end, we cover extensive\napplications of diffusion models in the medical domain. Furthermore, we\nemphasize the practical use case of some selected approaches, and then we\ndiscuss the limitations of the diffusion models in the medical domain and\npropose several directions to fulfill the demands of this field. Finally, we\ngather the overviewed studies with their available open-source implementations\nat\nhttps://github.com/amirhossein-kz/Awesome-Diffusion-Models-in-Medical-Imaging.",
+                    "authors": "Amirhossein Kazerouni, Ehsan Khodapanah Aghdam, Moein Heidari, Reza Azad, Mohsen Fayyaz, Ilker Hacihaliloglu, Dorit Merhof",
+                    "published": "2022-11-14",
+                    "updated": "2023-06-03",
+                    "primary_cat": "eess.IV",
+                    "cats": [
+                        "eess.IV",
+                        "cs.CV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1210.5101v1",
+                    "title": "Global well-posedness and zero-diffusion limit of classical solutions to the 3D conservation laws arising in chemotaxis",
+                    "abstract": "In this paper, we study the relationship between a diffusive model and a\nnon-diffusive model which are both derived from the well-known Keller-Segel\nmodel, as a coefficient of diffusion $\\varepsilon$ goes to zero. First, we\nestablish the global well-posedness of classical solutions to the Cauchy\nproblem for the diffusive model with smooth initial data which is of small\n$L^2$ norm, together with some {\\it a priori} estimates uniform for $t$ and\n$\\varepsilon$. Then we investigate the zero-diffusion limit, and get the global\nwell-posedness of classical solutions to the Cauchy problem for the\nnon-diffusive model. Finally, we derive the convergence rate of the diffusive\nmodel toward the non-diffusive model. It is shown that the convergence rate in\n$L^\\infty$ norm is of the order $O(\\varepsilon^{1/2})$. It should be noted that\nthe initial data is small in $L^2$-norm but can be of large oscillations with\nconstant state at far field. As a byproduct, we improve the corresponding\nresult on the well-posedness of the non-difussive model which requires small\noscillations.",
+                    "authors": "Hongyun Peng, Huanyao Wen, Changjiang Zhu",
+                    "published": "2012-10-18",
+                    "updated": "2012-10-18",
+                    "primary_cat": "math.AP",
+                    "cats": [
+                        "math.AP"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1609.09697v1",
+                    "title": "Anomalous diffusion in time-fluctuating non-stationary diffusivity landscapes",
+                    "abstract": "We investigate the ensemble and time averaged mean squared displacements for\nparticle diffusion in a simple model for disordered media by assuming that the\nlocal diffusivity is both fluctuating in time and has a deterministic average\ngrowth or decay in time. In this study we compare computer simulations of the\nstochastic Langevin equation for this random diffusion process with analytical\nresults. We explore the regimes of normal Brownian motion as well as anomalous\ndiffusion in the sub- and superdiffusive regimes. We also consider effects of\nthe inertial term on the particle motion. The investigation of the resulting\ndiffusion is performed for unconfined and confined motion.",
+                    "authors": "A. G. Cherstvy, R. Metzler",
+                    "published": "2016-09-30",
+                    "updated": "2016-09-30",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/physics/0403039v1",
+                    "title": "Non-diffusive transport in plasma turbulence: a fractional diffusion approach",
+                    "abstract": "Numerical evidence of non-diffusive transport in three-dimensional, resistive\npressure-gradient-driven plasma turbulence is presented. It is shown that the\nprobability density function (pdf) of test particles' radial displacements is\nstrongly non-Gaussian and exhibits algebraic decaying tails. To model these\nresults we propose a macroscopic transport model for the pdf based on the use\nof fractional derivatives in space and time, that incorporate in a unified way\nspace-time non-locality (non-Fickian transport), non-Gaussianity, and\nnon-diffusive scaling. The fractional diffusion model reproduces the shape, and\nspace-time scaling of the non-Gaussian pdf of turbulent transport calculations.\nThe model also reproduces the observed super-diffusive scaling.",
+                    "authors": "D. del-Castillo-Negrete, B. A. Carreras, V. E. Lynch",
+                    "published": "2004-03-04",
+                    "updated": "2004-03-04",
+                    "primary_cat": "physics.plasm-ph",
+                    "cats": [
+                        "physics.plasm-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/astro-ph/0012545v1",
+                    "title": "Diffusion and the occurrence of hydrogen shell flashes in helium white dwarf stars",
+                    "abstract": "We investigate the effects of element diffusion on the structure and\nevolution of low-mass helium white dwarfs (WD). Attention is focused on the\noccurrence of hydrogen shell flashes induced by diffusion processes during\ncooling phases. Initial models from 0.406 to 0.161 solar masses are constructed\nby applying mass loss rates at different stages of the RGB evolution of a solar\nmodel. The multicomponent flow equations describing gravitational settling, and\nchemical and thermal diffusion are solved and the diffusion calculations are\ncoupled to an evolutionary code. In addition, the same sequences are computed\nbut neglecting diffusion. We find that element diffusion strongly affects the\nstructure and cooling history of helium WD. In particular, diffusion induces\nthe occurrence of hydrogen shell flashes in models with masses ranging from\n0.18 to 0.41 solar masses, which is in sharp contrast from the situation when\ndiffusion is neglected. In connection with the further evolution, these\ndiffusion-induced flashes lead to much thinner hydrogen envelopes, preventing\nstable nuclear burning from being an appreciable energy source at advanced\nstages of evolution. This implies much shorter cooling ages than in the case\nwhen diffusion is neglected. These new WD models are discussed in light of\nrecent observational data of some millisecond pulsar systems with WD\ncompanions. We find that age discrepancies between the predictions of standard\nevolutionary models and such observations appear to be the result of ignoring\nelement diffusion in such models. Indeed, such discrepancies vanish when\naccount is made of diffusion.",
+                    "authors": "L. G. Althaus, A. M. Serenelli, O. G. Benvenuto",
+                    "published": "2000-12-29",
+                    "updated": "2000-12-29",
+                    "primary_cat": "astro-ph",
+                    "cats": [
+                        "astro-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2005.00562v1",
+                    "title": "Unexpected crossovers in correlated random-diffusivity processes",
+                    "abstract": "The passive and active motion of micron-sized tracer particles in crowded\nliquids and inside living biological cells is ubiquitously characterised by\n\"viscoelastic\" anomalous diffusion, in which the increments of the motion\nfeature long-ranged negative and positive correlations. While viscoelastic\nanomalous diffusion is typically modelled by a Gaussian process with correlated\nincrements, so-called fractional Gaussian noise, an increasing number of\nsystems are reported, in which viscoelastic anomalous diffusion is paired with\nnon-Gaussian displacement distributions. Following recent advances in Brownian\nyet non-Gaussian diffusion we here introduce and discuss several possible\nversions of random-diffusivity models with long-ranged correlations. While all\nthese models show a crossover from non-Gaussian to Gaussian distributions\nbeyond some correlation time, their mean squared displacements exhibit\nstrikingly different behaviours: depending on the model crossovers from\nanomalous to normal diffusion are observed, as well as unexpected dependencies\nof the effective diffusion coefficient on the correlation exponent. Our\nobservations of the strong non-universality of random-diffusivity viscoelastic\nanomalous diffusion are important for the analysis of experiments and a better\nunderstanding of the physical origins of \"viscoelastic yet non-Gaussian\"\ndiffusion.",
+                    "authors": "Wei Wang, Flavio Seno, Igor M. Sokolov, Aleksei V. Chechkin, Ralf Metzler",
+                    "published": "2020-05-01",
+                    "updated": "2020-05-01",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech",
+                        "physics.bio-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2210.07677v1",
+                    "title": "TransFusion: Transcribing Speech with Multinomial Diffusion",
+                    "abstract": "Diffusion models have shown exceptional scaling properties in the image\nsynthesis domain, and initial attempts have shown similar benefits for applying\ndiffusion to unconditional text synthesis. Denoising diffusion models attempt\nto iteratively refine a sampled noise signal until it resembles a coherent\nsignal (such as an image or written sentence). In this work we aim to see\nwhether the benefits of diffusion models can also be realized for speech\nrecognition. To this end, we propose a new way to perform speech recognition\nusing a diffusion model conditioned on pretrained speech features.\nSpecifically, we propose TransFusion: a transcribing diffusion model which\niteratively denoises a random character sequence into coherent text\ncorresponding to the transcript of a conditioning utterance. We demonstrate\ncomparable performance to existing high-performing contrastive models on the\nLibriSpeech speech recognition benchmark. To the best of our knowledge, we are\nthe first to apply denoising diffusion to speech recognition. We also propose\nnew techniques for effectively sampling and decoding multinomial diffusion\nmodels. These are required because traditional methods of sampling from\nacoustic models are not possible with our new discrete diffusion approach. Code\nand trained models are available: https://github.com/RF5/transfusion-asr",
+                    "authors": "Matthew Baas, Kevin Eloff, Herman Kamper",
+                    "published": "2022-10-14",
+                    "updated": "2022-10-14",
+                    "primary_cat": "eess.AS",
+                    "cats": [
+                        "eess.AS",
+                        "cs.AI",
+                        "cs.SD"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2402.01965v2",
+                    "title": "Analyzing Neural Network-Based Generative Diffusion Models through Convex Optimization",
+                    "abstract": "Diffusion models are becoming widely used in state-of-the-art image, video\nand audio generation. Score-based diffusion models stand out among these\nmethods, necessitating the estimation of score function of the input data\ndistribution. In this study, we present a theoretical framework to analyze\ntwo-layer neural network-based diffusion models by reframing score matching and\ndenoising score matching as convex optimization. Though existing diffusion\ntheory is mainly asymptotic, we characterize the exact predicted score function\nand establish the convergence result for neural network-based diffusion models\nwith finite data. This work contributes to understanding what neural\nnetwork-based diffusion model learns in non-asymptotic settings.",
+                    "authors": "Fangzhao Zhang, Mert Pilanci",
+                    "published": "2024-02-03",
+                    "updated": "2024-02-06",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "math.OC"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2305.14671v2",
+                    "title": "A Survey of Diffusion Models in Natural Language Processing",
+                    "abstract": "This survey paper provides a comprehensive review of the use of diffusion\nmodels in natural language processing (NLP). Diffusion models are a class of\nmathematical models that aim to capture the diffusion of information or signals\nacross a network or manifold. In NLP, diffusion models have been used in a\nvariety of applications, such as natural language generation, sentiment\nanalysis, topic modeling, and machine translation. This paper discusses the\ndifferent formulations of diffusion models used in NLP, their strengths and\nlimitations, and their applications. We also perform a thorough comparison\nbetween diffusion models and alternative generative models, specifically\nhighlighting the autoregressive (AR) models, while also examining how diverse\narchitectures incorporate the Transformer in conjunction with diffusion models.\nCompared to AR models, diffusion models have significant advantages for\nparallel generation, text interpolation, token-level controls such as syntactic\nstructures and semantic contents, and robustness. Exploring further\npermutations of integrating Transformers into diffusion models would be a\nvaluable pursuit. Also, the development of multimodal diffusion models and\nlarge-scale diffusion language models with notable capabilities for few-shot\nlearning would be important directions for the future advance of diffusion\nmodels in NLP.",
+                    "authors": "Hao Zou, Zae Myung Kim, Dongyeop Kang",
+                    "published": "2023-05-24",
+                    "updated": "2023-06-14",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1308.3393v2",
+                    "title": "Cosmology with matter diffusion",
+                    "abstract": "We construct a viable cosmological model based on velocity diffusion of\nmatter particles. In order to ensure the conservation of the total\nenergy-momentum tensor in the presence of diffusion, we include a cosmological\nscalar field $\\phi$ which we identify with the dark energy component of the\nUniverse. The model is characterized by only one new degree of freedom, the\ndiffusion parameter $\\sigma$. The standard $\\Lambda$CDM model can be recovered\nby setting $\\sigma=0$. If diffusion takes place ($\\sigma >0$) the dynamics of\nthe matter and of the dark energy fields are coupled. We argue that the\nexistence of a diffusion mechanism in the Universe can serve as a theoretical\nmotivation for interacting models. We constrain the background dynamics of the\ndiffusion model with Supernovae, H(z) and BAO data. We also perform a\nperturbative analysis of this model in order to understand structure formation\nin the Universe. We calculate the impact of diffusion both on the CMB spectrum,\nwith particular attention to the integrated Sachs-Wolfe signal, and on the\nmatter power spectrum $P(k)$. The latter analysis places strong constraints on\nthe magnitude of the diffusion mechanism but does not rule out the model.",
+                    "authors": "Simone Calogero, Hermano Velten",
+                    "published": "2013-08-15",
+                    "updated": "2013-10-29",
+                    "primary_cat": "astro-ph.CO",
+                    "cats": [
+                        "astro-ph.CO"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2304.05060v2",
+                    "title": "SPIRiT-Diffusion: Self-Consistency Driven Diffusion Model for Accelerated MRI",
+                    "abstract": "Diffusion models have emerged as a leading methodology for image generation\nand have proven successful in the realm of magnetic resonance imaging (MRI)\nreconstruction. However, existing reconstruction methods based on diffusion\nmodels are primarily formulated in the image domain, making the reconstruction\nquality susceptible to inaccuracies in coil sensitivity maps (CSMs). k-space\ninterpolation methods can effectively address this issue but conventional\ndiffusion models are not readily applicable in k-space interpolation. To\novercome this challenge, we introduce a novel approach called SPIRiT-Diffusion,\nwhich is a diffusion model for k-space interpolation inspired by the iterative\nself-consistent SPIRiT method. Specifically, we utilize the iterative solver of\nthe self-consistent term (i.e., k-space physical prior) in SPIRiT to formulate\na novel stochastic differential equation (SDE) governing the diffusion process.\nSubsequently, k-space data can be interpolated by executing the diffusion\nprocess. This innovative approach highlights the optimization model's role in\ndesigning the SDE in diffusion models, enabling the diffusion process to align\nclosely with the physics inherent in the optimization model, a concept referred\nto as model-driven diffusion. We evaluated the proposed SPIRiT-Diffusion method\nusing a 3D joint intracranial and carotid vessel wall imaging dataset. The\nresults convincingly demonstrate its superiority over image-domain\nreconstruction methods, achieving high reconstruction quality even at a\nsubstantial acceleration rate of 10.",
+                    "authors": "Zhuo-Xu Cui, Chentao Cao, Yue Wang, Sen Jia, Jing Cheng, Xin Liu, Hairong Zheng, Dong Liang, Yanjie Zhu",
+                    "published": "2023-04-11",
+                    "updated": "2024-04-20",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/cond-mat/0208120v1",
+                    "title": "Aging in a Chaotic System",
+                    "abstract": "We demonstrate aging behavior in a simple non-linear system. Our model is a\nchaotic map which generates deterministically sub-diffusion. Asymptotic\nbehaviors of the diffusion process are described using aging continuous time\nrandom walks, introduced previously to model diffusion in glasses.",
+                    "authors": "E. Barkai",
+                    "published": "2002-08-06",
+                    "updated": "2002-08-06",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech",
+                        "nlin.CD"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2104.13565v2",
+                    "title": "Generalisation of continuous time random walk to anomalous diffusion MRI models with an age-related evaluation of human corpus callosum",
+                    "abstract": "Diffusion MRI measures of the human brain provide key insight into\nmicrostructural variations across individuals and into the impact of central\nnervous system diseases and disorders. One approach to extract information from\ndiffusion signals has been to use biologically relevant analytical models to\nlink millimetre scale diffusion MRI measures with microscale influences. The\nother approach has been to represent diffusion as an anomalous transport\nprocess and infer microstructural information from the different anomalous\ndiffusion equation parameters. In this study, we investigated how parameters of\nvarious anomalous diffusion models vary with age in the human brain white\nmatter, particularly focusing on the corpus callosum. We first unified several\nestablished anomalous diffusion models (the super-diffusion, sub-diffusion,\nquasi-diffusion and fractional Bloch-Torrey models) under the continuous time\nrandom walk modelling framework. This unification allows a consistent parameter\nfitting strategy to be applied from which meaningful model parameter\ncomparisons can be made. We then provided a novel way to derive the diffusional\nkurtosis imaging (DKI) model, which is shown to be a degree two approximation\nof the sub-diffusion model. This link between the DKI and sub-diffusion models\nled to a new robust technique for generating maps of kurtosis and diffusivity\nusing the sub-diffusion parameters \\b{eta}_SUB and D_SUB. Superior tissue\ncontrast is achieved in kurtosis maps based on the sub-diffusion model. 7T\ndiffusion weighted MRI data for 65 healthy participants in the age range 19-78\nyears was used in this study. Results revealed that anomalous diffusion model\nparameters {\\alpha} and \\b{eta} have shown consistent positive correlation with\nage in the corpus callosum, indicating {\\alpha} and \\b{eta} are sensitive to\ntissue microstructural changes in aging.",
+                    "authors": "Qianqian Yang, David C. Reutens, Viktor Vegh",
+                    "published": "2021-04-28",
+                    "updated": "2022-01-17",
+                    "primary_cat": "physics.med-ph",
+                    "cats": [
+                        "physics.med-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2209.05557v3",
+                    "title": "Blurring Diffusion Models",
+                    "abstract": "Recently, Rissanen et al., (2022) have presented a new type of diffusion\nprocess for generative modeling based on heat dissipation, or blurring, as an\nalternative to isotropic Gaussian diffusion. Here, we show that blurring can\nequivalently be defined through a Gaussian diffusion process with non-isotropic\nnoise. In making this connection, we bridge the gap between inverse heat\ndissipation and denoising diffusion, and we shed light on the inductive bias\nthat results from this modeling choice. Finally, we propose a generalized class\nof diffusion models that offers the best of both standard Gaussian denoising\ndiffusion and inverse heat dissipation, which we call Blurring Diffusion\nModels.",
+                    "authors": "Emiel Hoogeboom, Tim Salimans",
+                    "published": "2022-09-12",
+                    "updated": "2024-05-01",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.CV",
+                        "stat.ML"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1404.3573v1",
+                    "title": "\"Diffusing diffusivity\": A model for anomalous and \"anomalous yet Brownian\" diffusion",
+                    "abstract": "Wang et al. [PNAS 106 (2009) 15160] have found that in several systems the\nlinear time dependence of the mean-square displacement (MSD) of diffusing\ncolloidal particles, typical of normal diffusion, is accompanied by a\nnon-Gaussian displacement distribution (DisD), with roughly exponential tails\nat short times, a situation they termed \"anomalous yet Brownian\" diffusion. The\ndiversity of systems in which this is observed calls for a generic model. We\npresent such a model where there is \"diffusivity memory\" but no \"direction\nmemory\" in the particle trajectory, and we show that it leads to both a linear\nMSD and a non-Gaussian DisD at short times. In our model, the diffusivity is\nundergoing a (perhaps biased) random walk, hence the expression \"diffusing\ndiffusivity\". The DisD is predicted to be exactly exponential at short times if\nthe distribution of diffusivities is itself exponential, but an exponential\nremains a good fit to the DisD for a variety of diffusivity distributions.\nMoreover, our generic model can be modified to produce subdiffusion.",
+                    "authors": "Mykyta V. Chubynsky, Gary W. Slater",
+                    "published": "2014-04-14",
+                    "updated": "2014-04-14",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech",
+                        "cond-mat.soft"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2010.02514v1",
+                    "title": "Diffusion model and analysis of diffusion process at lagrangian method",
+                    "abstract": "Based on Fick's 2nd law the development of moving particle semi-implicit\nmethod for predicting diffusion process is proposed in this study",
+                    "authors": "Ziqi Zhou",
+                    "published": "2020-10-06",
+                    "updated": "2020-10-06",
+                    "primary_cat": "physics.flu-dyn",
+                    "cats": [
+                        "physics.flu-dyn"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/0912.3770v1",
+                    "title": "SLE(6) and the geometry of diffusion fronts",
+                    "abstract": "We study the diffusion front for a natural two-dimensional model where many\nparticles starting at the origin diffuse independently. It turns out that this\nmodel can be described using properties of near-critical percolation, and\nprovides a natural example where critical fractal geometries spontaneously\narise.",
+                    "authors": "Pierre Nolin",
+                    "published": "2009-12-18",
+                    "updated": "2009-12-18",
+                    "primary_cat": "math.PR",
+                    "cats": [
+                        "math.PR"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/0910.2253v1",
+                    "title": "Linearized Kompaneetz equation as a relativistic diffusion",
+                    "abstract": "We show that Kompaneetz equation describing photon diffusion in an\nenvironment of an electron gas, when linearized around its equilibrium\ndistribution, coincides with the relativistic diffusion discussed in recent\npublications. The model of the relativistic diffusion is related to soluble\nmodels of imaginary time quantum mechanics. We suggest some non-linear\ngeneralizations of the relativistic diffusion equation and their astrophysical\napplications (in particular to the Sunyaev-Zeldovich effect).",
+                    "authors": "Z. Haba",
+                    "published": "2009-10-12",
+                    "updated": "2009-10-12",
+                    "primary_cat": "astro-ph.CO",
+                    "cats": [
+                        "astro-ph.CO"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2202.05830v1",
+                    "title": "Learning Fast Samplers for Diffusion Models by Differentiating Through Sample Quality",
+                    "abstract": "Diffusion models have emerged as an expressive family of generative models\nrivaling GANs in sample quality and autoregressive models in likelihood scores.\nStandard diffusion models typically require hundreds of forward passes through\nthe model to generate a single high-fidelity sample. We introduce\nDifferentiable Diffusion Sampler Search (DDSS): a method that optimizes fast\nsamplers for any pre-trained diffusion model by differentiating through sample\nquality scores. We also present Generalized Gaussian Diffusion Models (GGDM), a\nfamily of flexible non-Markovian samplers for diffusion models. We show that\noptimizing the degrees of freedom of GGDM samplers by maximizing sample quality\nscores via gradient descent leads to improved sample quality. Our optimization\nprocedure backpropagates through the sampling process using the\nreparametrization trick and gradient rematerialization. DDSS achieves strong\nresults on unconditional image generation across various datasets (e.g., FID\nscores on LSUN church 128x128 of 11.6 with only 10 inference steps, and 4.82\nwith 20 steps, compared to 51.1 and 14.9 with strongest DDPM/DDIM baselines).\nOur method is compatible with any pre-trained diffusion model without\nfine-tuning or re-training required.",
+                    "authors": "Daniel Watson, William Chan, Jonathan Ho, Mohammad Norouzi",
+                    "published": "2022-02-11",
+                    "updated": "2022-02-11",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2302.05737v2",
+                    "title": "A Reparameterized Discrete Diffusion Model for Text Generation",
+                    "abstract": "This work studies discrete diffusion probabilistic models with applications\nto natural language generation. We derive an alternative yet equivalent\nformulation of the sampling from discrete diffusion processes and leverage this\ninsight to develop a family of reparameterized discrete diffusion models. The\nderived generic framework is highly flexible, offers a fresh perspective of the\ngeneration process in discrete diffusion models, and features more effective\ntraining and decoding techniques. We conduct extensive experiments to evaluate\nthe text generation capability of our model, demonstrating significant\nimprovements over existing diffusion models.",
+                    "authors": "Lin Zheng, Jianbo Yuan, Lei Yu, Lingpeng Kong",
+                    "published": "2023-02-11",
+                    "updated": "2024-02-03",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL",
+                        "cs.LG"
+                    ],
+                    "category": "Diffusion AND Model"
+                }
+            ],
+            [
+                {
+                    "url": "http://arxiv.org/abs/2404.13518v1",
+                    "title": "Reliable Model Watermarking: Defending Against Theft without Compromising on Evasion",
+                    "abstract": "With the rise of Machine Learning as a Service (MLaaS) platforms,safeguarding\nthe intellectual property of deep learning models is becoming paramount. Among\nvarious protective measures, trigger set watermarking has emerged as a flexible\nand effective strategy for preventing unauthorized model distribution. However,\nthis paper identifies an inherent flaw in the current paradigm of trigger set\nwatermarking: evasion adversaries can readily exploit the shortcuts created by\nmodels memorizing watermark samples that deviate from the main task\ndistribution, significantly impairing their generalization in adversarial\nsettings. To counteract this, we leverage diffusion models to synthesize\nunrestricted adversarial examples as trigger sets. By learning the model to\naccurately recognize them, unique watermark behaviors are promoted through\nknowledge injection rather than error memorization, thus avoiding exploitable\nshortcuts. Furthermore, we uncover that the resistance of current trigger set\nwatermarking against removal attacks primarily relies on significantly damaging\nthe decision boundaries during embedding, intertwining unremovability with\nadverse impacts. By optimizing the knowledge transfer properties of protected\nmodels, our approach conveys watermark behaviors to extraction surrogates\nwithout aggressively decision boundary perturbation. Experimental results on\nCIFAR-10/100 and Imagenette datasets demonstrate the effectiveness of our\nmethod, showing not only improved robustness against evasion adversaries but\nalso superior resistance to watermark removal attacks compared to\nstate-of-the-art solutions.",
+                    "authors": "Hongyu Zhu, Sichu Liang, Wentao Hu, Fangqi Li, Ju Jia, Shilin Wang",
+                    "published": "2024-04-21",
+                    "updated": "2024-04-21",
+                    "primary_cat": "cs.CR",
+                    "cats": [
+                        "cs.CR",
+                        "cs.AI"
+                    ],
+                    "label": "Original Paper",
+                    "paper_cat": "Diffusion AND Model",
+                    "gt": "2.1 Model Stealing and Watermarking With the widespread application of deep learning, associated models have increasingly become targets for theft. Parameters Stealing directly acquiring models through cyberattacks and social engineering [65], or reversing model parameters through side channels [60, 83]. Functionality Stealing utilize unlabeled data to query the target API and leverage the soft labels to train a surrogate model via maximum likelihood estimation, approximating the functionality of the stolen victim on the target task [52, 56, 76, 85]. Based on the principles of knowledge distillation [26, 79], functionality stealing is scalable to large language models (LLMs) [35, 74], and is highly feasible in open world scenarios. To effectively counteract complex and varied thefts, embedding digital watermarks into protected models is a straightforward and effective strategy [32]. This allows the tracking of infringing actions by transferring watermarks to knockoffs obtained by adversaries. Parameter embedding watermarks [11, 77] directly implant secret patterns into model parameters, but the verification requires white-box access, which can be denied by the model owner. Furthermore, these patterns are often fragile [40, 54]. Hence, trigger set watermarks [1], which only require black-box access to the suspect model have become the most popular method. Poisoning-style watermarks embed a trigger set that deviates from the main task distribution, using unique behaviors on this set during verification to assert model copyright [1, 3, 31, 33, 46, 86]. Alternatively, watermark behaviors can be reflected by directly modifying the API\u2019s probability outputs [70, 80], though it may not be secure against parameter stealing. Notably, non-intrusive fingerprints that characterize decision boundaries are feasible [45], yet are easier to remove [33, 80, 84] and prone to false alarms [69]. 2.2 Watermark Removal and Countermeasures In the ongoing challenge for intellectual property protection, attackers strive to remove watermarks from stolen models while preserving their generalization performance. Model modification [44] involve slight alterations such as fine-tuning [43] or pruning [15] to make the model forget the trigger set. Input preprocessing [44] transforms input samples [23] to evade from watermark triggering, or employs anomaly detection [41] to filter out suspicious watermark inputs. Model extraction [44], primarily used for functionality stealing, also effectively removes watermarks since the trigger set usually does not appear in the extraction query set, complicating the transfer of watermark behaviors during the process of functionality approximating . To counteract watermark removal attacks, robust watermark embedding algorithms aim to fortify watermark behavior. Entangled Watermark Embedding (EWE) [31] tightly couples watermark samples with the main distribution through soft nearest neighbor loss regularization. Random smoothing (RS) in parameter space [3] provides certification of unremovability against minor parameter changes. Margin-based watermarking (MBW) [33] enhances the margin between watermark samples and the decision boundary via adversarial training on the trigger set, thereby increasing the likelihood of watermark retention during model extraction. MEADefender [46] employs mixed samples from two source classes as watermark samples, binding the watermark to the main task distribution by minimizing Kullback-Leibler divergence. Overall, robust watermarking algorithms embed the trigger set deeper within the original distribution, significantly altering the decision boundary to booster resilience of the watermarks.",
+                    "pre_questions": [],
+                    "main_content": "Introduction Over the past decade, significant advancements in deep learning have led to its widespread application in fields such as computer vision, natural language processing, and speech recognition [37]. Recent breakthroughs in Large Language Models (LLMs), such as ChatGPT, underscore the potential strides toward General Artificial Intelligence (AGI) [58]. These advancements have enabled companies such as OpenAI and Google to offer Machine Learning as a Service (MLaaS) via APIs, transforming sophisticated models into paid services accessible to the public. However, this also presents opportunities for adversaries to steal models [51], seeking to produce knockoffs and establish pirated API services for profit. The stolen victims involve significant investment including data annotation, expert knowledge and computational resources. For instance, training GPT-3 incurs a cost of approximately 12 million USD [4]. Therefore, model thefts severely damage the intellectual property and legitimate rights of the model owners. Model stealing typically occurs via two approachs. First, adversaries may directly steal the parameters, highlighted by the leak of Facebook\u2019s LLaMa model [25, 60]. Second, attackers might prepare unlabeled data to query the target API, employing the probability labels to distill knowledge into a surrogate model. Known as model extraction or functionality-stealing attacks [52], this strategy exploits legitimate black-box access, making it challenging for owners to distinguish between benign users and potential thieves. Preventing model theft at source is exceedingly difficult. Inspired by digital watermarking used to protect multimedia content [32], model watermarking is proposed as copyright identifiers to determine if a suspect model is a knockoff [77]. White-box watermarks [11] directly embed secret patterns into parameters, but require access to the suspect model parameters during verification, which may not be feasible in real-world scenarios. Thus, black-box watermarks [1] have emerged as the predominant approach, requiring only access to the model\u2019s outputs for the trigger sets. Typically, model owner generates a set of secret watermark samples with deliberately incorrect labels, using techniques like backdoor injection to ensure the model memorizes this trigger set. If a suspect model produces the predefined labels for the trigger set with a high probability, it is identified as a copy of the protected model. Memorizing a trigger set that deviates from the main task distribution will inevitably impair the generalization performance. However, due to benign overfitting [53], if the size of the trigger set is maintained within capacity limits [39], poisoning-style watermark embedding does not significantly degrade performance on standard testing benchmarks [1]. Consequently, the adverse effects of trigger set watermarks are often underestimated [3, 31, 33, 46, 86]. In this work, we identify that all poisoning-style watermarks, even those crafted with random label noise trigger sets, embed shortcuts into the protected model [20]. Evasion adversaries can arXiv:2404.13518v1  [cs.CR]  21 Apr 2024 Preprint Under Review, 2024, Hongyu Zhu, Sichu Liang, Wentao Hu, Fangqi Li, Ju Jia, and Shilin Wang readily exploit these shortcuts, employing efficient optimization frameworks to achieve significantly higher attack success rates than unwatermarked models. Hence, while designed to protect intellectual property from theft, poisoning-style watermarking inadvertently introduces severe vulnerabilities to evasion attacks. Furthermore, we identify a robustness pitfall phenomenon: current watermarks aggressively disrupt the decision boundary, generating misclassifications around watermark samples to achieve resistance against removal attacks. This trivial mechanism inadvertently entangles watermark unremovability with its adverse effects. To ensure effective watermark verification, representational capacity of the model must be sacrificed to focus on watermark behavior, laying severe risks for generalization in adversarial scenarios. In response to the vulnerabilities identified in this paper, we revisit the pipeline of trigger set watermarks, proposing a reliable algorithm that resists removal attacks without increasing evasion risks. Instead of error memorization, knowledge injection is utilized to foster unique watermark behaviors. Specifically, we leverage diffusion models to generate Unrestricted Adversarial Examples (UAEs) from random noise, ensuring diversity, hardness, and fidelity in creating a versatile trigger set. Building on this foundation, we identify optimization difficulties in replicating the protected model as the primary reason for watermarks failing to survive extraction. Thus, we enhance the knowledge transfer properties of the watermarked model during embedding, learning it as a \"friendly teacher\" to effectively guide the surrogate model in acquiring watermark behavior from a limited query set, without relying on any robustness pitfall phenomenon. The whole pipeline is shown in Figure 1. Our contributions are summarized as follows: (1) We reveal that all poisoning-style watermarks embed exploitable shortcuts into the model and provide a detailed assessment of the evasion vulnerabilities introduced. (2) We propose utilizing diffusion models to synthesize UAEs as assessment of the evasion vulnerabilities introduced. (2) We propose utilizing diffusion models to synthesize UAEs as the trigger set, devising effective generation algorithms that enable harmless watermarking via knowledge injection. (3) We identify the robustness pitfall that brings contradictions enable harmless watermarking via knowledge injection. (3) We identify the robustness pitfall that brings contradictions between generalization and watermark unremovability. We reconceptualize the embedding process by focusing on knowledge transfer properties of the protected model. (4) Integrating analyses and designs above, we propose the edge transfer properties of the protected model. (4) Integrating analyses and designs above, we propose the first reliable watermarking algorithm that demonstrates improved evasion robustness and surpasses current state-ofthe-art methods in watermark unremovability. Reliable Model Watermarking: Defending Against Theft without Compromising on Evasion Preprint Under Review, 2024, Figure 1: Comparison of Watermark Embedding Pipeline in this work and previous Works. excel in controlled test environments, their performance deteriorates in the real world characterized by distribution shifts or adversarial attacks, stemming from the reliance on domain-specific or non-robust features [19, 29]. Shortcuts often arise from dataset biases or learning dynamics of ERM optimizers [75]. Yet, we reveal that poisoning-style watermarking deliberately introduces shortcuts into models, creating hidden pathways adversaries can exploit, significantly amplifying vulnerabilities under evasion attacks. First, we formally define the process of trigger set watermark embedding to expose why shortcuts exist. 3.1 Formulation of trigger set watermarking In a \ud835\udc3e-class classification problem, a model \ud835\udc53parameterized by \ud835\udf03, maps inputs \ud835\udc4b\u2208{0, 1, ..., 255}\ud835\udc36\u00d7\ud835\udc4a\u00d7\ud835\udc3bto labels \ud835\udc4c\u2208{1, . . ., \ud835\udc3e}. Model owner generates a training dataset D\ud835\udc61\ud835\udc5f= {(\ud835\udc65\ud835\udc56,\ud835\udc66\ud835\udc56)} from the underlying distribution \ud835\udc4b\u00d7\ud835\udc4c, minimizing L(\ud835\udc53(\ud835\udc65),\ud835\udc66) over D\ud835\udc61\ud835\udc5f to learn the mapping. Performance is evaluated on a validation set \ud835\udc37\ud835\udc63\ud835\udc4e\ud835\udc59with accuracy score(\ud835\udf11\ud835\udc4e\ud835\udc50\ud835\udc50(\ud835\udc53, D\ud835\udc63\ud835\udc4e\ud835\udc59) = 1 | D\ud835\udc63\ud835\udc4e\ud835\udc59| \u00cd I(\ud835\udc53(\ud835\udc65) = \ud835\udc66)). For trigger set watermark, a secret dataset D\ud835\udc64\ud835\udc5awith unique mappings \ud835\udc65\ud835\udc64\ud835\udc5a\u2192\ud835\udc66\ud835\udc64\ud835\udc5anot present in \ud835\udc4b\u00d7 \ud835\udc4cis selected by the owner. Training on D\ud835\udc64\ud835\udc5aendows the watermarked model \ud835\udc53\ud835\udc64\ud835\udc5a with the capability to generate predetermined outputs on \ud835\udc65\ud835\udc64\ud835\udc5a. Watermark accuracy \ud835\udf11\ud835\udc64\ud835\udc5a(\ud835\udc53\ud835\udc64\ud835\udc5a, D\ud835\udc64\ud835\udc5a) = 1 | D\ud835\udc64\ud835\udc5a| \u00cd I(\ud835\udc53\u2032(\ud835\udc65\ud835\udc64\ud835\udc5a) = \ud835\udc66\ud835\udc64\ud835\udc5a) measures \ud835\udc53\ud835\udc64\ud835\udc5a\u2019s adherence to D\ud835\udc64\ud835\udc5a. The selection of triggers set can be categorized into two types: Pattern-based watermark. This backdoor style[81] approach[1, 3, 31, 61, 86] enables the model to map samples with a specific trigger pattern to a predetermined target class. Watermark samples are created by overlaying the trigger pattern \ud835\udeff\u2208{0, 1, ..., 255}\ud835\udc36\u00d7\ud835\udc4a\u00d7\ud835\udc3b with mask \ud835\udc5a\u2208[0, 1]\ud835\udc36\u00d7\ud835\udc4a\u00d7\ud835\udc3bonto samples \ud835\udc65\ud835\udc60from the source class \ud835\udc60, resulting in \ud835\udc65\ud835\udc64\ud835\udc5a= \ud835\udc65\ud835\udc60\u2299(1 \u2212\ud835\udc5a) + \ud835\udeff\u2299\ud835\udc5a. For watermark embedding, the model \ud835\udc53\ud835\udc64\ud835\udc5ais adjusted to classify any sample with the trigger pattern into target class \ud835\udc61through optimization min\ud835\udf03\ud835\udc64\ud835\udc5aL(\ud835\udc53\ud835\udc64\ud835\udc5a(\ud835\udc65\ud835\udc64\ud835\udc5a) = \ud835\udc66\ud835\udc61). Given the secrecy of \ud835\udeff, \ud835\udc5a, \ud835\udc60, and \ud835\udc61, knowledge of this backdoor serves as the proof of ownership. Pattern-free watermark. Pattern-based watermark is challenged by the continuous evolution of backdoor defenses [21]. Recent strategies suggest decoupling the embedding process, advocating for the use of any sample deviates from the main distribution \ud835\udc4b\u00d7 \ud835\udc4cas the trigger set D\ud835\udc64\ud835\udc5a, eliminating the reliance on a fixed trigger pattern. Trigger set in pattern-free watermark could be mixed samples from two classes [46] or purely label noises [33]. Trigger set watermarking hinges on overfitting to a unique set distinct from the main distribution \ud835\udc4b\u00d7\ud835\udc4c, leading to shortcuts from \ud835\udc65\ud835\udc64\ud835\udc5ato \ud835\udc66\ud835\udc64\ud835\udc5a. Although the potential harm of these shortcuts is often overlooked in literature, we introduce straightforward optimization frameworks demonstrating how evasion adversaries can effortlessly exploit these shortcuts, significantly compromising the model\u2019s performance in adversarial settings. In evasion attacks, adversaries craft a distortion \ud835\udeffwithin an \ud835\udc59\ud835\udc5d norm boundary, changing prediction of \ud835\udc53\ud835\udc64\ud835\udc5awhen added to an original sample \ud835\udc65(\ud835\udc53\ud835\udc64\ud835\udc5a(\ud835\udc65+\ud835\udeff) \u2260\ud835\udc53\ud835\udc64\ud835\udc5a(\ud835\udc65)). Equation 1 aims to find a perturbation \ud835\udeffthat leads \ud835\udc53\ud835\udc64\ud835\udc5ato incorrectly classify instances from class \ud835\udc60to \ud835\udc61, analog to the standard trigger inversion framework [75, 78]. Though trigger inversion has been evaluated in watermarking to neutralize suspicious inputs [31, 46, 78], it is dismissed as ineffective due to mismatches between recovered and actual patterns. Nonetheless, minimal modifications can activate backdoors [55], indicating exact pattern matching is unnecessary for evasion. By blindly optimizing \ud835\udeff, we demonstrate the feasibility of deceiving \ud835\udc53\ud835\udc64\ud835\udc5a. Additionally, with source and target classes hidden, a bruteforce search across class pairs is computationally challenging [78]. Thus, we investigate a universal attack as shown in Equation 2, aiming to maximize classification errors with a fixed \ud835\udeff. \ud835\udeff\u2217= arg min \u2225\ud835\udeff\u2225\ud835\udc5d\u2a7d\ud835\udf00L (\ud835\udc53\ud835\udc64\ud835\udc5a(\ud835\udc65\ud835\udc60+ \ud835\udeff) ,\ud835\udc66\ud835\udc61) , \u2200\ud835\udc65\u2208{\ud835\udc65| D\ud835\udc61\ud835\udc5f,\ud835\udc66= \ud835\udc60}. (1) \ud835\udeff\u2217= arg min \u2225\ud835\udeff\u2225\ud835\udc5d\u2a7d\ud835\udf00\u2212L (\ud835\udc53\ud835\udc64\ud835\udc5a(\ud835\udc65+ \ud835\udeff),\ud835\udc66) , \u2200(\ud835\udc65,\ud835\udc66) \u2208D\ud835\udc61\ud835\udc5f. (2) Solving Equations 1 and 2 reveals that while watermarked models maintain high accuracy on natural samples, the embedded watermark shortcuts greatly increase their susceptibility to evasion attacks. Moreover, the secrecy of the trigger pattern in pattern-based watermarks does not safeguard against adversarial exploitation. The question arises: can forgoing patterns in watermarking prevent associated vulnerabilities? Theory indicates that memorizing any noisy data undermines robustness to adversarial attacks [53]. Notably, risk from purely random label noise can rival that of the Preprint Under Review, 2024, Hongyu Zhu, Sichu Liang, Wentao Hu, Fangqi Li, Ju Jia, and Shilin Wang most sophisticated poisoning attacks [53]. To illustrate this empirically, we conduct adversarial attacks on \ud835\udc53\ud835\udc64\ud835\udc5aguided by an optimization goal akin to Equation 2. Here, \ud835\udeffis customized for specific samples rather than a universal pattern, showing higher flexibility. For noise label style watermarks, beyond empirically exploring the increased adversarial risk, we aim to delve into model vulnerability, explicitly linking decreased robustness to shortcut exploitation. Recent studies illustrate that backdoors can be implanted by merely altering labels [30]. Exploring the reverse scenario, we investigate whether a trigger pattern can be extracted from arbitrarily mislabeled samples to deceive the model. Algorithm 1 establishes a stochastic gradient approach Noise Label Trigger Inversion (NLTI) to solve this problem. It operates on the noise set D\ud835\udc5b\ud835\udc5c\ud835\udc56\ud835\udc60\ud835\udc52(\ud835\udc4b,\ud835\udc4c,\ud835\udc4c\u2032), where \ud835\udc4brepresents original samples, \ud835\udc4cthe correct labels, and \ud835\udc4c\u2032 the mislabels learned by the model. The intuition is to assume a pattern \ud835\udeffhas already been added to all \ud835\udc65\u2208\ud835\udc4b, causing the model to learn the corresponding incorrect labels in a backdoor injection manner. The algorithm aims to find this pattern such that all \ud835\udc65\u2212\ud835\udeff can be correctly classified: \ud835\udeff\u2217= arg min \u2225\ud835\udeff\u2225\ud835\udc5d L (\ud835\udc53\ud835\udc64\ud835\udc5a(\ud835\udc65\u2212\ud835\udeff),\ud835\udc66) , \u2200(\ud835\udc65,\ud835\udc66) \u2208D\ud835\udc5b\ud835\udc5c\ud835\udc56\ud835\udc60\ud835\udc52. (3) The pattern \ud835\udeffrepresents the cause of misclassifications in the noise set, reflecting the shortcut created by memorization the noise. Thus, applying \ud835\udeffto new samples is likely to confuse the model (\ud835\udc53\ud835\udc64\ud835\udc5a(\ud835\udc65+ \ud835\udeff) \u2260\ud835\udc53(\ud835\udc65)). During optimization, the logits loss [5, 9] shown in Equation 4 is applied to enhances the correct class logits \ud835\udc67\ud835\udc66while pushing outputs away from the noise labels. Additionally, the learning rate is updated according to a schedule to balancie exploration and exploitation [9]. L(\ud835\udc65+ \ud835\udeff,\ud835\udc66,\ud835\udc66\u2032) = \u2212\ud835\udc67\ud835\udc66+ \ud835\udc67\ud835\udc66\u2032. (4) NLTI mirrors the approach of universal adversarial perturbations (UAP) [64]. However, a key difference is that NLTI focuses on correcting the model\u2019s responses to de-noised samples while inducing errors in new samples with added \ud835\udeff. This distinction lies in NLTI\u2019s intent to uncover the trigger pattern absorbed through noise memorization. Ultimately, the optimization strategies offer an optimistic upper bound on the robustness against evasion. With persistent shortcuts, the exploitation capabilities of evasion adversaries will escalate with advancing attack techniques, progressively undermining watermarked model\u2019s generalization. Algorithm 1 Noise Label Trigger Inversion. 1: Input: noisy set {(\ud835\udc4b,\ud835\udc4c,\ud835\udc4c\u2032)}, watermark model \ud835\udc40, learning rate \ud835\udefc, schedule \ud835\udc46, perturbation bound \ud835\udf00. 2: Output: trigger pattern \ud835\udeff. 3: for epoch = 1 . . . \ud835\udc41do 4: for all (\ud835\udc65,\ud835\udc66,\ud835\udc66\u2032) \u2208{(\ud835\udc4b,\ud835\udc4c,\ud835\udc4c\u2032)} do 5: \ud835\udeff\u2190\ud835\udeff\u2212\ud835\udefc\u00b7 \u2207\ud835\udeffL(\ud835\udc65+ \ud835\udeff,\ud835\udc66,\ud835\udc66\u2032). 6: Project \ud835\udeffto the \ud835\udc59\ud835\udc5dball with bound \ud835\udf00. 7: end for 8: Update \ud835\udeffwith learning rate schedule \ud835\udc46. 9: end for 4 Towards Harmless Watermarking Even memorizing random label noise in poison-style watermarks inevitably introduces exploitable shortcuts to the model [53]. Thus, methods relying on misclassification of specific samples for ownership verification are fundamentally flawed. Safe trigger-set watermarking is possible only by ensuring unique correct responses to specific samples. Building on this principle, we propose a harmless watermarking scheme focusing on trigger-set generation, watermark embedding and watermark verification. 4.1 Trigger-set Generation 4.1.1 Motivation. While the optimization in modern deep networks produces diverse solutions [28], predictions by various models on in-distribution samples often converge. The challenge lies in identifying a set of samples that prompts models to exhibit uniquely correct behavior. First, we summarize the conditions that samples used to construct a harmless trigger set should satisfy: (1) Clarity: Possess clear semantics with a definite correct label; (2) Challenging: Sufficiently difficult to ensure that correct predictions highlight the model\u2019s distinct capabilities; (3) Stealth: Closely resemble the original data distribution to bypass anomaly detection; (4) Resilience: Maintain uniqueness against adaptive attacks. Straightforward choices such as out-of-distribution (OOD) and adversarial examples are challenging enough but either detectable [41] or highly fragile [8, 23]. In this paper, we introduce Unrestricted Adversarial Examples (UAEs) [66] as the trigger set. Free from \ud835\udc59\ud835\udc5dnorms constraints, UAEs provide superior flexibility in fooling classifiers and higher resistance to defenses [67]. We further design a pipeline for synthesizing UAEs via diffusion models [27], with powerful distribution prior [38] ensuring UAEs to be stealth [6, 82]. Moreover, diffusion models can synthesize infinitely realistic and diverse samples from random noise, producing elusive trigger sets. 4.1.2 UAE Generation. Diffusion models introduce Gaussian noise to samples in the forward process, leading to an isotropic Gaussian distribution. Conversely, the reverse process reconstruct samples from Gaussian noise [27]. This is achieved by training a denoising model \ud835\udc45\u03a6(\ud835\udc65\ud835\udf0f,\ud835\udf0f) progressively removes noise during the \ud835\udc47-step schedule, ultimately recovering sample \ud835\udc650 as shown in Equation 5: \ud835\udc5d(\ud835\udc650 : \ud835\udc47) = \ud835\udc5d(\ud835\udc65\ud835\udc47) \ud835\udc47 \u00d6 \ud835\udf0f=1 \ud835\udc5d\u03a6 (\ud835\udc65\ud835\udf0f\u22121 | \ud835\udc65\ud835\udf0f) . (5) Here, \ud835\udc65\ud835\udc47is the initial Gaussian seed for the reverse process, guided by the denoising model \ud835\udc45\u03a6(\ud835\udc65\ud835\udf0f,\ud835\udf0f) as \ud835\udc5d\u03a6(\ud835\udc65\ud835\udf0f\u22121 | \ud835\udc65\ud835\udf0f). Introducing a conditioning variable \ud835\udc50allows for a conditional diffusion model \ud835\udc45\u03a6(\ud835\udc65\ud835\udf0f,\ud835\udf0f,\ud835\udc50) [13]. Class-conditioned diffusion provides distribution priors to align generated samples with class semantics, guaranteeing UAEs bear unambiguous labels. Synthesizing UAEs involves steering the generation process to fool classifiers while preserving class semantics. Starting with a Gaussian seed \ud835\udc65\ud835\udc47, the process iteratively employs \ud835\udc45\u03a6(\ud835\udc65\ud835\udf0f,\ud835\udf0f,\ud835\udc50) for denoising to achieve a class-aligned sample \ud835\udc650. The adversarial nature emerges in three stages: seed selection, denoising trajectory, and final adjustment. We develop efficient methods for crafting UAEs at each stage: Adversarial Warm-up. The objective is to subtly modify the seed \ud835\udc65\ud835\udc47such that its denoised result can deceive the classifier (\ud835\udc53(\ud835\udc650) \u2260\ud835\udc50). EvoSeed [34] uses a genetic algorithm to add adversarial perturbations to \ud835\udc65\ud835\udc47, yet it demands thousands of iterations Reliable Model Watermarking: Defending Against Theft without Compromising on Evasion Preprint Under Review, 2024, Figure 2: The Generation Process for UAE trigger set. to converge. Therefore, we propose directly maximizing the loss of the classifier \ud835\udc53mapping \ud835\udc650 to class \ud835\udc50through Equation 6: \ud835\udc65\ud835\udefc+1 \ud835\udc47 = \ud835\udc43\ud835\udc35\ud835\udc5d(\ud835\udc65\ud835\udc47,\ud835\udf00) \u0010 \ud835\udc65\ud835\udefc \ud835\udc47+ \ud835\udf02\u2207\ud835\udc65\ud835\udefc \ud835\udc47L \u0000\ud835\udc53\u0000\ud835\udc65\ud835\udefc 0 \u0001 ,\ud835\udc50\u0001\u0011 . (6) Here, \ud835\udc43\ud835\udc35\ud835\udc5dprojects the updated seed onto the \ud835\udc59\ud835\udc5dball of radius \ud835\udf00 around \ud835\udc65\ud835\udc47, with \ud835\udf02and \ud835\udefcrepresenting the learning rate and iteration. However, the gradient of L(\ud835\udc53(\ud835\udc65\ud835\udefc 0 ),\ud835\udc50) relative to \ud835\udc65\ud835\udefc \ud835\udc47through the \ud835\udc47-step diffusion process is computationally infeasible. Therefore, we employ the acceleration technique [7, 82], treating the gradient through the diffusion model as constant, as shown in Equation7: \ud835\udf15\ud835\udc65\ud835\udefc 0 \ud835\udf15\ud835\udc65\ud835\udc47 \ud835\udc47 = \ud835\udf15\ud835\udc65\ud835\udefc \ud835\udc47\u22121 \ud835\udf15\ud835\udc65\ud835\udefc \ud835\udc47   \ud835\udf15\ud835\udc65\ud835\udefc \ud835\udc47\u22122 \ud835\udf15\ud835\udc65\ud835\udefc \ud835\udc47\u22121 \u00b7 \ud835\udf15\ud835\udc65\ud835\udefc \ud835\udc47\u22123 \ud835\udf15\ud835\udc65\ud835\udefc \ud835\udc47\u22122 \u00b7 \u00b7 \u00b7 \u00b7 \ud835\udf15\ud835\udc65\ud835\udefc 0 \ud835\udf15\ud835\udc65\ud835\udefc \ud835\udefc ! \u2248\ud835\udc58. (7) With this approximation, the back-propagation path can be simplified with only the classifier gradient: \ud835\udf15L \u0010 \ud835\udc53 \u0010 \ud835\udc65\ud835\udefc 0 ,\ud835\udc50 \u0011 \ud835\udf15\ud835\udc65\ud835\udefc \ud835\udc47 = \ud835\udc58\u00b7 \ud835\udf15L \u0010 \ud835\udc53 \u0010 \ud835\udc65\ud835\udefc 0 ,\ud835\udc50 \u0011 \ud835\udf15\ud835\udc65\ud835\udefc 0 . (8) In practice, gradient updates like PGD [47] are applied to the denoised \ud835\udc650, transferring the perturbation back to the seed \ud835\udc65\ud835\udc47. This approach achieves effects similar to EvoSeed with just a few updates. Since perturbations occur at the diffusion seed, they inherently modify high-level features of the denoised results, such as composition and shape. However, as \ud835\udc65\ud835\udc47undergoes the whole denoising purification process, perturbing the seed alone may not ensure the desired level of adversarial impact. Adversarial Guidance. Continuous adversarial guidance can be applied throughout generation [6, 10], introducing adversarial perturbations at each denoising step as shown in Equation 9: \ud835\udc65\ud835\udf0f= \ud835\udc65\ud835\udf0f+ \ud835\udf09\u00b7 \u2207\ud835\udc65\ud835\udf0fL (\ud835\udc53(\ud835\udc65\ud835\udf0f) ,\ud835\udc50) . (9) Here, \ud835\udf09determines the scale of perturbations,tailored to the sampling schedule [27]. As adversarial guidance spans from coarse to fine steps, it impacts both high-level and detailed texture features. Adversarial Edition Further optimization can be performed on the generation result. Integrating a denoising step after each gradient update in PGD can enhance fidelity and transferrability [82]. This is akin to the continuation of adversarial guidance, fine-tuning low-level features until achieving desired adversarial effect. We sequentially apply three methods, adding adversarial control at various feature granularities, as shown in Figure 2. In practice, flexible combinations can be chosen to balance effectiveness and cost. Furthermore, UAEs are selected based on quality and transferability, with details provided in the Supplementary Material. 4.2 Watermark Embedding Unremovability the robustness against removal attacks [1] ensures that adversaries, even when aware of the underlying watermarking algorithm, should struggle to remove or overwrite the watermark. Model extraction, particularly practical and effective among removal attempts [31, 44], has become a key focus in developing robust watermarking strategies[31, 33, 46]. 4.2.1 The Robustness Pitfall. Evaluating watermarking algorithms typically involves two aspects: Functionality Preservation and Unremovability. Successful embedding must maintain task performance, as measured by global accuracy metrics, and withstand removal attempts, ensuring that watermark accuracy \ud835\udf11\ud835\udc64\ud835\udc5aexceeds a threshold on the derived surrogate model. Fulfilling both criteria marks the success of a embedding algorithm [3, 31, 33, 46]. 1 5 10 20 50 Frequency 20 30 40 50 60 70 80 90 Accuracy test Acc WM Acc after extraction Train Acc (class s) T est Acc (class s) Figure 3: Generalization and \ud835\udf11\ud835\udc64\ud835\udc5a (WM Acc) under Various Frequencies. t-SNE Component 1 t-SNE Component 2 Class 0 Class 1 Class 0 predicted as 1 WM Samples Figure 4: Feature Space Visualization with t-SNE. In this paper, we expose a robustness pitfall in traditional evaluations of embedding algorithms. We present a simplistic algorithm trivial WM, which constructs a trigger set by relabeling unmodified samples from a source class \ud835\udc60to a target class \ud835\udc61and integrates it into the training process at high frequency. Surprisingly, trivial WM achieves high watermark accuracy on extraction surrogates while preserving competitive main task performance. Figure 3 illustrates how trivial WM performs on CIFAR-100 with varying updating frequencies. After training on watermark samples following each standard batch, trivial WM sets the state-of-the-art watermark accuracy on extraction surrogates but significantly undermines generalization in class \ud835\udc60. Lowering the frequency improves performance on class \ud835\udc60but causes a swift decline in watermark accuracy. Figure 4 delves into this phenomenon by analyzing feature distributions of the watermarked model. High-frequency updates with the trigger set shifts the decision boundary to map the surrounding region of watermark samples as the target class. Although no watermark samples are presented in the query set for extraction, samples close to them in the feature space are misclassified as the target class, smoothly transmitting watermark behavior. In extreme cases, the model learns to label all source class samples as the target class, achieving near-perfect surrogate watermark accuracy, at the cost of a minor 1% decline in overall task performance on CIFAR-100. Thus, sacrificing local decision boundaries for watermark behavior leads to exceptional unremovability. Yet, this is an undesirable outcome, harboring significant risks and acting as a misleading pitfall. In Section 3, we explored how poisoning-style watermarking introduces evasion-prone shortcuts. The robustness pitfall reveals a deeper issue: watermark persistence necessitates decision boundary perturbation driven by misclassifications, creating a conflict between evasion and watermark robustness. The unremovability of current watermarks cannot be decoupled from adverse effects. 4.2.2 Learning a Friendly Teacher. UAE watermark is naturally entangled with the task distribution, conceptually easy to survive Preprint Under Review, 2024, Hongyu Zhu, Sichu Liang, Wentao Hu, Fangqi Li, Ju Jia, and Shilin Wang in extraction. However, adversaries face optimization challenges in transferring knowledge via ERM [68]. Although the surrogate exhibit even better generalization performance, it does not faithfully mimic all behaviors of the watermarked model [18, 48, 50, 68]. Since the trigger set is absent from extraction queries [1], transferring watermark behavior is challenging [31, 52]. Poisoning-style watermarks compensate by exploiting the robustness pitfall phenomenon, but inevitably introduces evasion vulnerabilities. Therefore, we propose a novel embedding strategy: learning the watermarked model as a \"friendly teacher\" adept at sharing knowledge, guiding the surrogate to learn watermark behavior from limited queries. Training a better teacher is an underexplored direction, with current methods focusing on collaborative training between teacher and student networks [57, 63]. However, model owners lack control over the surrogates\u2019 training process. Thus, we attempt to learn a surrogate-agnostic friendly teacher from the perspectives of function mapping and output distribution properties. Function Mapping Properties. Recent studies theoretically indicate that teacher models should exhibit Lipschitz continuity and transformation equivariance, making them easier to emulate [14]. Lipschitz continuity implies the model \ud835\udc53reacts minimally to slight input changes, i.e., ||\ud835\udc53(\ud835\udc65) \u2212\ud835\udc53(\ud835\udc65\u2032)|| \u2264\ud835\udc3f||\ud835\udc65\u2212\ud835\udc65\u2032||, with || \u00b7 || representing a distance metric. However, exact computation of the Lipschitz constant \ud835\udc3fis notoriously difficult [2]. Yet, adversarial robustness ties closely to the Lipschitz constant [16, 89]. Employing UAEs as the trigger set naturally promotes local Lipschitz smoothness around watermark samples. We enhance this by varying data augmentation strategies for watermark samples per batch [49]. For transformation equivariance, we leverage consistency regularization [71], and choose random erasing as a highly controllable transformation [88]. It replaces small patches from the original image with random colors. The model \ud835\udc53is encouraged to produce similar outputs for the transformed and original samples: L\ud835\udc50\ud835\udc5f= \ud835\udc3e\ud835\udc3f(\ud835\udc53(\ud835\udc65)||\ud835\udc53(\ud835\udc5f\ud835\udc52(\ud835\udc65))). (10) Here, \ud835\udc5f\ud835\udc52(\u00b7) is the random erasing operator, and \ud835\udc3e\ud835\udc3f(\u00b7||\u00b7) calculates the Kullback-Leibler divergence. In practice, L\ud835\udc50\ud835\udc5fserves as a regularization term, jointly optimized with the classification loss. Output Distribution Properties. Extraction utilize soft labels from query responses, leveraging their rich information for efficient mimic [52]. However, modern networks often exhibit overconfidence [22, 50], which obstructs knowledge transfer. To mitigate this, temperature scaling is employed in knowledge distillation \u0393 to soften softmax layer outputs for both teacher and student, with \ud835\udc5d\ud835\udc56= \ud835\udf0e(\ud835\udc67\ud835\udc56/\u0393), where \ud835\udc67\ud835\udc56represents logits and \ud835\udf0ethe softmax function. However, model owners lack control over the evasion adversary, and temperature is often ignored in extraction (\u0393 = 1) [3, 31, 33, 52, 76]. We propose to apply temperature scaling to protected model, regardless of the extraction settings. As a result, the loss function of black-box extraction becomes Equation 11: L\ud835\udc38\ud835\udc4b\ud835\udc47= \u2212\u03932 \ud835\udc3e \u2211\ufe01 \ud835\udc56=1 \ud835\udf0e\ud835\udc56 \u0012 \ud835\udc67\ud835\udc63 \u0393 \u00b7 \u0393\ud835\udc63 \u0013 log\ud835\udf0e\ud835\udc56 \u0010\ud835\udc67\ud835\udc62 \u0393 \u0011 . (11) Where \ud835\udc67\ud835\udc63and \ud835\udc67\ud835\udc62are the output logits of the protected model and extraction surrogate, respectively. \u0393 is the adversary\u2019s chosen distillation temperature, while \u0393\ud835\udc63, set by the model owner, adjusts the output distribution. The adversary, limited to black-box API output access, remains unaware of \u0393\ud835\udc63. Incorporating \u0393\ud835\udc63modifies the extraction gradient for the \ud835\udc57th class as detailed in Equation 12: \u2207\ud835\udc67\ud835\udc60\ud835\udc57L\ud835\udc38\ud835\udc4b\ud835\udc47= \u2212\u03932 \ud835\udc3e \u2211\ufe01 \ud835\udc56=1 \u0014 \ud835\udf0e\ud835\udc56 \u0012 \ud835\udc67\ud835\udc63 \u0393 \u00b7 \u0393\ud835\udc63 \u0013 \u0010 \ud835\udeff\ud835\udc56\ud835\udc57\u2212\ud835\udf0e\ud835\udc57 \u0010\ud835\udc67\ud835\udc62 \u0393 \u0011\u0011\u0015 . (12) Where \ud835\udeff\ud835\udc56\ud835\udc57is the Kronecker delta function (1 for \ud835\udc56= \ud835\udc57, 0 otherwise), \u0393\ud835\udc63reduces class discrepancies of the protected model\u2019s output distribution, guiding gradient updates to align logits beyond focusing solely on the single correct class. To preserve watermark accuracy despite minor parameter adjustments, we further seek local optima with parameter neighbourhood continuing to exhibit the watermark behavior. This is achieved by bi-level optimization, minimizing watermark loss under the worstcase conditions within the parameter vicinity: min \ud835\udf03 max \u2225\ud835\udeff\u2225\ud835\udc5d\u2264\ud835\udf00L(\ud835\udc53\ud835\udf03+\ud835\udeff(\ud835\udc65),\ud835\udc66). (13) The inner optimization seeks the worst weight perturbation \ud835\udeff within the \ud835\udc5d-norm bound to remove the watermark, while the outer optimization adjusts the parameters to preserve watermark memorization. We employ an approximation in the form of sharpnessaware minimization [17] to efficiently solve the inner problem: \u02c6 \ud835\udeff\u2248\ud835\udf00\u00b7 \u2207\ud835\udf03L(\ud835\udc53\ud835\udf03(\ud835\udc65),\ud835\udc66) \u2225\u2207\ud835\udf03L(\ud835\udc53\ud835\udf03(\ud835\udc65),\ud835\udc66)\u2225. (14) Intuitively, sharpness-aware minimization aims for solutions with flatter loss landscapes to prevent adversaries from easily shifting parameters that support watermark behavior. Unlike traditional watermarking [3, 31, 33, 46], our training strategies apply to the entire training set, not just the trigger set. Our objective is to learn the protected model with desirable properties for watermarking, rather than sacrificing the main task to focus on the watermark. 4.2.3 Watermark Verification. Our verification approach is similar to traditional trigger-set watermarks, assessing ownership by evaluating watermark accuracy\ud835\udf11\ud835\udc64\ud835\udc5a. Yet,\ud835\udf11\ud835\udc64\ud835\udc5aoverlooks how thirdparty models perform on the watermark samples, potentially causing false alarms. Therefore, we introduce a self-calibration method: select control samples from the generated UAE set, matching the trigger set in size, which can mislead the model post-watermarking. The watermark samples and the control samples represent the \ud835\udc5d\ud835\udc5f\ud835\udc5c\ud835\udc60 and \ud835\udc50\ud835\udc5c\ud835\udc5b\ud835\udc60of the watermarked model. We use the difference in accuracy (\ud835\udf11\ud835\udc5d\ud835\udc5f\ud835\udc5c\ud835\udc60\u2212\ud835\udf11\ud835\udc50\ud835\udc5c\ud835\udc5b\ud835\udc60) as a similarity metric between the suspect and protected models, akin to \ud835\udf11\ud835\udc64\ud835\udc5a. Hypothesis testing based on the model\u2019s responses to both UAE sets can be further explored for more nuanced verification [31, 72]. 5 Experiments In this section, we evaluate the performance of UAE watermarking against leading methods in terms of evasion and watermark robustness. Comparative methods include the pattern-based approaches EWE from USENIX Security 21\u2019[31] and RS from ICML 22\u2019 [3], as well as pattern-free approaches MBW from ICML 23\u2019 [33] and MEA from S&P 24\u2019[46]. Experiments are conducted on the CIFAR-10/100 datasets [3, 31, 33, 36, 46], standard benchmarks for Reliable Model Watermarking: Defending Against Theft without Compromising on Evasion Preprint Under Review, 2024, model watermarking, and the more challenging high-resolution Imagenette dataset, a 10-class subset of Imagenet [12]. We use ResNet18 [24], the largest-scale model employed by comparative methods [3, 31, 46], for consistent performance evaluation. Exploration of more advanced structures is discussed in Section 5.2.2. Code and detailed settings are available in the supplementary material. 5.1 Robustness against Evasion Adversaries Evaluations of evasion robustness are conducted on the Imagenette dataset to better mirror real-world conditions. We instantiate Equation 1 with the Pixel Backdoor [75] and implement its untargeted universal attack form as described in Equation 2. Instance-specific adversarial attacks employ the \ud835\udc3f0 constraint AutoAttack [9, 87]. The perturbation pixel limits for Pixel backdoor and AutoAttack are set at 200 and 50, respectively, accounting for less than 0.5% and 0.1% of the original image pixels. 5.1.1 Overall Evaluation. We conduct a coarse-grained assessment through untargeted attack against all watermarking algorithms and normal models without watermark, as shown in Table 1. Table 1: Evasion Robustness Against Untargeted Attacks (Realtive means relative ASR compare with normal models). Method Clean(ACC)\u2191 PixelBackdoor(ASR)\u2193 SparseAuto(ASR)\u2193 avg&std avg&std relative avg&std relative Normal 98.32\u00b10.54 2.44\u00b10.80 32.36\u00b11.76 EWE 95.92\u00b10.64 83.20\u00b14.55 80.76 84.76\u00b15.04 52.40 RS 97.24\u00b10.17 71.04\u00b111.24 68.60 72.48\u00b112.76 40.12 MBW 89.80\u00b11.07 12.28\u00b11.37 9.84 38.88\u00b10.66 6.52 MEA 87.92\u00b11.66 67.08\u00b111.63 64.64 80.08\u00b13.88 47.72 UAE 98.00\u00b10.20 2.52\u00b10.36 0.08 21.20\u00b10.93 -11.16 Evasions achieve only modest attack success rate (ASR) on models without watermark due to the lack of shortcuts. Pattern-based watermarking slightly decreases generalization by about 2%, but the shortcuts introduced significantly amplify vulnerabilities. Under the same budget, ASR of Pixel Backdoor increases by about 30 times, and that of AutoAttack by over 40%. In contrast, pattern-free watermarking induces a 10% drop in generalization performance. Even without trigger patterns, vulnerability of MEA to evasion is comparable to pattern-based watermarking. Trigger inversion can exploit shortcuts without matching the exact pattern, and abandoning patterns does not lessen the risks. Among traditional watermarks, only MBW exhibits a relatively minor decrease in robustness. However, this does not imply the harm is negligible, with further details in Section 5.1.3. Finally, UAE watermarking matches the generalization performance of unwatermarked models, further reducing ASR of AutoAttack by 11.16%. The knowledge injection of UAE watermarking teaches models to recognize hard samples, avoiding the creation of shortcuts while patching inherent vulnerabilities, thereby enhancing their adaptability to challenging scenarios. 5.1.2 Class-wise Evaluation of Backdoor Watermarking. We explore the link between decrease in robustness and shortcuts in patternbased watermarking, which uses patterns to flip source class \ud835\udc60 samples to target classes \ud835\udc61. Therefore, we utilize Pixel Backdoor to solve Equation 1 and compare the targeted ASR from \ud835\udc60to target class \ud835\udc61for EWE, RS and unwatermarked models in Table 2. In this scenario, trigger inversion directly attempts to reconstruct the patterns, resulting in significantly higher ASRs compared to unwatermarked models. Furthermore, Figure 5 visualizes the target class distribution for samples successfully attacked with untargeted Pixel Backdoor on EWE models. Although the attack indiscriminately targets all classes, the target classes used for watermark become vulnerable entry points. Samples from various classes are easily perturbed to be classified as the target class, posing substantial risks in security-related scenarios. Method PixelBackdoor(ASR) avg&std relative Normal 8.40\u00b13.58 EWE 80.80\u00b15.76 71.67 RS 75.20\u00b17.43 66.07 Table 2: Attack Success Rate from Source Class \ud835\udc60to Target Class \ud835\udc61. 0 1 2 3 4 5 6 7 8 9 Category 10 2 10 1 100 Log-Scale Probability 0.961 0.011 0.003 0.004 0.005 0.008 0.004 0.002 0.002 Figure 5: Distribution of Target Classes for Attacked Samples. 5.1.3 In-depth Analysis of Noise Label Watermarking. MBW employs adversarial training (AT) on its label noise trigger set to increase margin. In Figure 6, we visualize the robust accuracy under a 5-step \ud835\udc3f\u221ePGD attack for MBW, MBW without margin, MBW with AT on the training set, and an unwatermarked model with AT. AT on the trigger set enhances the robustness of MBW, influencing fair comparison in Section 5.1.1. When both the MBW and normal models undergo AT, there consistently exists a gap in adversarial robustness. AT cannot fully compensate for the vulnerability introduced by watermark embedding. In Figure 7, we compare the attack effects of patterns derived from MBW using noise label trigger inversion with those of Gaussian noise. Effectiveness of the recovered pattern far surpasses that of Gaussian noise, explicitly demonstrating the existence of shortcuts. As attacks evolve, these shortcuts will continue to be exploited. 0 20 40 60 80 Epochs 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Robust Accuracy Adv. Train w/o Watermark MBW MBW with AT on Train MBW w/o Margin Figure 6: Robustness Accuracy in Different Epoches. 8/255 16/255 24/255 32/255 40/255 Perturbation Strength  40 50 60 70 80 90 Accuracy MBW Model NLTI Gaussian Noise No Attack Figure 7: Robustness Accuracy under Different Perturbations. 5.2 Robustness against Stealing Adversaries This section evaluates watermarks in resisting removal attacks. For model modification, we iteratively prune and fine-tune the model [43] on 20% of the training set until validation accuracy drops more than 5% or pruning rate exceeds 75%. For model extraction, we employ Knockoff Nets [52], using the training set as queries [31, 33, 46]. For input preprocessing, we employ CLIP [59] to extract features and then use 10% of the training set to create isolation forests [42] for each class, filtering out potential watermark samples. To reduce overhead, we employ only the first 2 blocks of the feature extractor for CIFAR-10/100 and the first 3 blocks for Imagenette. Table 3 presents the generalization performance and watermark accuracy of all methods. UAE watermarking achieves the highest main task accuracy across all datasets. We calculate watermark accuracy (\ud835\udf11\ud835\udc64\ud835\udc5a= \ud835\udf11\ud835\udc5d\ud835\udc5f\ud835\udc5c\ud835\udc60\u2212\ud835\udf11\ud835\udc50\ud835\udc5c\ud835\udc5b\ud835\udc60) as the difference between accuracy of trigger set and the UAE control group. This method yields \ud835\udf11\ud835\udc64\ud835\udc5avalues of -1%, 0.2% and 0% for unwatermarked models on three datasets, confirming the effectiveness of self-calibration. For removal attacks, UAE watermarking exhibits the best average robustness. Notably, Preprint Under Review, 2024, Hongyu Zhu, Sichu Liang, Wentao Hu, Fangqi Li, Ju Jia, and Shilin Wang Table 3: Comparative Analysis of Generalization and Watermark Accuracy Across CIFAR-10/100 and Imagenette on Watermark Model and Removal Attacks. Dataset Method Victim Fine-pruning Extraction Anomaly Detection Avg Acc on Main Task Acc Trigger Set Acc Main Task Acc Trigger Set Acc Main Task Acc Trigger Set Acc Main Task Acc Trigger Set Acc Trigger Set CIFAR10 EWE 93.26\u00b10.34 99.80\u00b10.45 89.62\u00b10.20 81.40\u00b14.67 93.91\u00b10.24 40.80\u00b122.07 88.22\u00b10.32 78.80\u00b17.01 67.00 RS 93.95\u00b10.22 100.00\u00b10.00 90.62\u00b10.73 75.80\u00b112.77 94.64\u00b10.20 2.40\u00b10.55 88.59\u00b10.23 73.80\u00b11.79 50.67 MBW 85.73\u00b12.38 99.80\u00b10.45 87.19\u00b10.28 10.40\u00b11.82 89.00\u00b12.17 78.60\u00b15.27 80.85\u00b12.52 75.20\u00b12.49 54.73 MEA 85.03\u00b11.51 99.00\u00b10.71 81.22\u00b10.97 79.40\u00b17.09 89.38\u00b10.82 87.80\u00b14.21 80.23\u00b11.59 34.20\u00b12.49 67.13 UAE 94.04\u00b10.11 100.00\u00b10.00 90.13\u00b10.38 87.40\u00b14.28 94.59\u00b10.15 88.00\u00b13.16 88.82\u00b10.22 91.80\u00b11.48 89.07 CIFAR100 EWE 72.75\u00b10.06 100.00\u00b10.00 68.63\u00b10.87 91.80\u00b13.03 75.29\u00b10.22 16.00\u00b12.74 65.36\u00b10.39 17.40\u00b18.93 41.73 RS 78.84\u00b10.52 100.00\u00b10.00 75.43\u00b11.06 64.40\u00b123.64 77.48\u00b10.67 3.20\u00b10.84 71.25\u00b10.57 47.60\u00b112.16 38.40 MBW 69.22\u00b11.40 100.00\u00b10.00 66.24\u00b11.49 91.00\u00b15.34 75.36\u00b11.00 52.40\u00b18.20 62.64\u00b11.17 62.80\u00b15.72 68.73 MEA 59.11\u00b13.77 99.60\u00b10.55 56.28\u00b12.20 99.20\u00b10.84 64.34\u00b13.47 71.80\u00b116.71 52.58\u00b13.62 37.80\u00b16.10 69.60 UAE 79.60\u00b10.95 100.00\u00b10.00 75.14\u00b10.61 96.60\u00b12.07 79.05\u00b10.83 83.00\u00b12.45 71.64\u00b11.08 94.00\u00b11.22 91.20 IMAGENETTE EWE 95.92\u00b10.64 100.00\u00b10.00 93.12\u00b10.78 35.40\u00b18.85 96.44\u00b10.26 15.80\u00b15.07 90.76\u00b10.55 61.40\u00b13.85 37.53 RS 97.24\u00b10.17 100.00\u00b10.00 94.04\u00b10.38 60.20\u00b123.31 96.40\u00b10.40 5.80\u00b15.36 91.66\u00b10.55 52.80\u00b15.40 39.60 MBW 89.80\u00b11.07 100.00\u00b10.00 85.72\u00b10.66 53.20\u00b121.21 91.84\u00b10.71 33.20\u00b15.40 85.84\u00b11.34 36.00\u00b14.00 40.80 MEA 87.92\u00b11.66 100.00\u00b10.00 83.28\u00b11.80 97.40\u00b11.52 92.08\u00b11.40 49.28\u00b128.40 84.68\u00b11.55 1.20\u00b11.79 49.29 UAE 98.00\u00b10.20 100.00\u00b10.00 94.32\u00b10.50 92.20\u00b16.10 97.56\u00b10.22 68.00\u00b110.84 93.24\u00b11.09 93.40\u00b12.30 84.53 without relying on robustness pitfalls, UAE watermarking achieves the highest \ud835\udf11\ud835\udc64\ud835\udc5aon extraction surrogates, illustrating the advantages of its \"friendly teacher\" learning approach. Furthermore, since UAEs adhere to the original distribution, they are difficult to identify in anomaly detection. Although UAE watermarking is not always the most robust against fine-pruning, modifications have never reduced \ud835\udf11\ud835\udc64\ud835\udc5abelow 85% without significantly impacting generalization. In cases of the same validation accuracy drop, both MBW and MEA tolerate higher pruning rates, with MBW even showing improved generalization on CIFAR-10, cause they adapt to watermarks by significantly sacrificing representation capacity. 5.2.1 Analysis of the Robustness Pitfall. Pattern-free watermarking exhibit competitiveness in extraction. However, their unremovability mainly stems from the robustness pitfall. On CIFAR-10, MBW and MEA achieve only 88.46% and 95.31% training accuracy, respectively, while a normally trained Resnet-18 approaches perfect accuracy. As the extraction queries reuse the training set, we filter out all misclassified samples and repeat experiments, resulting in \ud835\udf11\ud835\udc64\ud835\udc5aon extraction surrogates of MBW and MEA dropping to 53.4% and 30.4%. Figure 8 visualizes the feature distribution for the source and target classes of MEA and an unwatermarked model. Similar to Trivial WM, MEA induces misclassifications on the queries, easily transferring watermark behavior. In contrast, UAE watermarking achieves 100% training accuracy on CIFAR-10, without relying on any robustness pitfall phenomenon. PCA Feature 1 PCA Feature 2 Class 0 Class 1 Class 2 Class 0/1 predicted as 2 WM Samples (a) MEA PCA Feature 1 PCA Feature 2 Class 0 Class 1 Class 2 Class 0 or 1 predicted as 2 WM Samples (b) Normal Figure 8: Feature Space Visualization for MEA and normal models. The robustness pitfall connects poisoning-style watermarking to its adverse effects: the stronger the watermark, the more pronounced the vulnerabilities. Patterns recovered using the MEA extraction surrogate yield a 47.88% transfer ASR on MEA watermarked model, while those from a normal model achieve only a 15.88% transfer ASR. Adversaries targeting evasion rather than stealing even expect the extraction surrogates learn the watermark behavior better, facilitating successful evasions. 5.2.2 Advanced Extraction Scenario. In this section, we explore complex extraction scenarios. Table 4 shows watermark performance using out-of-distribution (OOD) samples as queries: CIFAR10 watermarked model use CIFAR-100 as queries, and vice versa. \ud835\udf11\ud835\udc64\ud835\udc5aon UAE watermarking surrogates is even higher than indistribution sample extraction, as separating the queries from training set facilitates knowledge transfer. Poisoning-style watermarks often struggle with large-scale networks [31, 46]. We conduct experiments on CIFAR-10 using EfficientNetV2 [73], with both samearchitecture models and Resnet-18 serving as extraction surrogates, as shown in Table 5. UAE watermarking retains satisfactory unremovability in modern networks and cross-architecture extraction. Table 4: Performance Comparison of Watermarking Methods Using OOD Samples as Query Sets for Model Extraction. Method CIFAR 10 CIFAR 100 Main Task Acc Trigger Set Acc Main Task Acc Trigger Set Acc MEA 83.20\u00b11.16 90.67\u00b11.53 50.18\u00b16.89 64.00\u00b122.34 MBW 82.98\u00b10.87 76.00\u00b17.00 58.42\u00b13.00 65.33\u00b11.53 UAE 93.06\u00b10.10 97.00\u00b11.00 74.05\u00b10.19 94.67\u00b11.15 Table 5: Comparison of Extraction Results Using Different Models. Surrogate Victim Extraction Main Task Acc Trigger Set Acc Main Task Acc Trigger Set Acc efficientnet v2 95.10\u00b10.14 100.00\u00b10.00 95.41\u00b10.09 81.00\u00b11.00 resnet18 94.91\u00b10.05 80.00\u00b13.61 5.2.3 Adaptive Removal Attack. We further investigated if adversarial defense methods hinder UAE watermark verification. Table 6 shows the impact of adversarial fine-tuning. While \ud835\udf11\ud835\udc64\ud835\udc5aof UAE decreases, it still outperforms MBA and MEA, indicating adversarial fine-tuning does not expose specific vulnerabilities of UAE. Figure 9 depicts the results of randomized smoothing [3], which affects UAE far less than regular adversarial samples. The flexibility of unbounded adversarial samples to circumvent defenses makes them particularly effective for constructing trigger sets, adapting to the diverse adversaries in the open world. Reliable Model Watermarking: Defending Against Theft without Compromising on Evasion Preprint Under Review, 2024, 0.01 0.05 0.1 0.2 scale of perturbations  20 40 60 80 100 Accuracy UAE main test UAE trigger set PGD trigger set Figure 9: Impact of Randomized Smoothing. Method Adv. finetuning Main Task Acc Trigger Set Acc MBW 82.29\u00b10.62 25.00\u00b12.65 MEA 80.43\u00b10.60 32.00\u00b12.00 UAE 88.93\u00b10.95 55.67\u00b19.71 Table 6: Impact of Adversial Finetuning. 6 Conclusion In this paper, we identify the dilemma that poisoning-style model watermarks increase susceptibility to evasion while protecting against theft. To tackle this issue, we introduced a novel, reliable watermarking algorithm utilizing knowledge injection as unique identifiers and optimizing knowledge transfer to enhance watermark behaviors. Experimental results demonstrate that our UAE watermarking not only outperforms SOTA methods in unremovability but also avoids evasion exploition. This dual effectiveness underscores its potential as a comprehensive solution to protect deep learning models from a spectrum of complex threats."
+                },
+                {
+                    "url": "http://arxiv.org/abs/2009.08697v2",
+                    "title": "Fine-tuning Is Not Enough: A Simple yet Effective Watermark Removal Attack for DNN Models",
+                    "abstract": "Watermarking has become the tendency in protecting the intellectual property\nof DNN models. Recent works, from the adversary's perspective, attempted to\nsubvert watermarking mechanisms by designing watermark removal attacks.\nHowever, these attacks mainly adopted sophisticated fine-tuning techniques,\nwhich have certain fatal drawbacks or unrealistic assumptions. In this paper,\nwe propose a novel watermark removal attack from a different perspective.\nInstead of just fine-tuning the watermarked models, we design a simple yet\npowerful transformation algorithm by combining imperceptible pattern embedding\nand spatial-level transformations, which can effectively and blindly destroy\nthe memorization of watermarked models to the watermark samples. We also\nintroduce a lightweight fine-tuning strategy to preserve the model performance.\nOur solution requires much less resource or knowledge about the watermarking\nscheme than prior works. Extensive experimental results indicate that our\nattack can bypass state-of-the-art watermarking solutions with very high\nsuccess rates. Based on our attack, we propose watermark augmentation\ntechniques to enhance the robustness of existing watermarks.",
+                    "authors": "Shangwei Guo, Tianwei Zhang, Han Qiu, Yi Zeng, Tao Xiang, Yang Liu",
+                    "published": "2020-09-18",
+                    "updated": "2021-05-17",
+                    "primary_cat": "cs.CR",
+                    "cats": [
+                        "cs.CR",
+                        "cs.LG",
+                        "stat.ML"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2111.04625v1",
+                    "title": "DeepSteal: Advanced Model Extractions Leveraging Efficient Weight Stealing in Memories",
+                    "abstract": "Recent advancements of Deep Neural Networks (DNNs) have seen widespread\ndeployment in multiple security-sensitive domains. The need of\nresource-intensive training and use of valuable domain-specific training data\nhave made these models a top intellectual property (IP) for model owners. One\nof the major threats to the DNN privacy is model extraction attacks where\nadversaries attempt to steal sensitive information in DNN models. Recent\nstudies show hardware-based side channel attacks can reveal internal knowledge\nabout DNN models (e.g., model architectures) However, to date, existing attacks\ncannot extract detailed model parameters (e.g., weights/biases). In this work,\nfor the first time, we propose an advanced model extraction attack framework\nDeepSteal that effectively steals DNN weights with the aid of memory\nside-channel attack. Our proposed DeepSteal comprises two key stages. Firstly,\nwe develop a new weight bit information extraction method, called HammerLeak,\nthrough adopting the rowhammer based hardware fault technique as the\ninformation leakage vector. HammerLeak leverages several novel system-level\ntechniques tailed for DNN applications to enable fast and efficient weight\nstealing. Secondly, we propose a novel substitute model training algorithm with\nMean Clustering weight penalty, which leverages the partial leaked bit\ninformation effectively and generates a substitute prototype of the target\nvictim model. We evaluate this substitute model extraction method on three\npopular image datasets (e.g., CIFAR-10/100/GTSRB) and four DNN architectures\n(e.g., ResNet-18/34/Wide-ResNet/VGG-11). The extracted substitute model has\nsuccessfully achieved more than 90 % test accuracy on deep residual networks\nfor the CIFAR-10 dataset. Moreover, our extracted substitute model could also\ngenerate effective adversarial input samples to fool the victim model.",
+                    "authors": "Adnan Siraj Rakin, Md Hafizul Islam Chowdhuryy, Fan Yao, Deliang Fan",
+                    "published": "2021-11-08",
+                    "updated": "2021-11-08",
+                    "primary_cat": "cs.CR",
+                    "cats": [
+                        "cs.CR",
+                        "cs.AI",
+                        "cs.CV",
+                        "cs.LG"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2306.06629v1",
+                    "title": "GKD: A General Knowledge Distillation Framework for Large-scale Pre-trained Language Model",
+                    "abstract": "Currently, the reduction in the parameter scale of large-scale pre-trained\nlanguage models (PLMs) through knowledge distillation has greatly facilitated\ntheir widespread deployment on various devices. However, the deployment of\nknowledge distillation systems faces great challenges in real-world\nindustrial-strength applications, which require the use of complex distillation\nmethods on even larger-scale PLMs (over 10B), limited by memory on GPUs and the\nswitching of methods. To overcome these challenges, we propose GKD, a general\nknowledge distillation framework that supports distillation on larger-scale\nPLMs using various distillation methods. With GKD, developers can build larger\ndistillation models on memory-limited GPUs and easily switch and combine\ndifferent distillation methods within a single framework. Experimental results\nshow that GKD can support the distillation of at least 100B-scale PLMs and 25\nmainstream methods on 8 NVIDIA A100 (40GB) GPUs.",
+                    "authors": "Shicheng Tan, Weng Lam Tam, Yuanchun Wang, Wenwen Gong, Yang Yang, Hongyin Tang, Keqing He, Jiahao Liu, Jingang Wang, Shu Zhao, Peng Zhang, Jie Tang",
+                    "published": "2023-06-11",
+                    "updated": "2023-06-11",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL",
+                        "cs.AI"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2207.01991v3",
+                    "title": "Conflicting Interactions Among Protection Mechanisms for Machine Learning Models",
+                    "abstract": "Nowadays, systems based on machine learning (ML) are widely used in different\ndomains. Given their popularity, ML models have become targets for various\nattacks. As a result, research at the intersection of security/privacy and ML\nhas flourished. Typically such work has focused on individual types of\nsecurity/privacy concerns and mitigations thereof. However, in real-life\ndeployments, an ML model will need to be protected against several concerns\nsimultaneously. A protection mechanism optimal for one security or privacy\nconcern may interact negatively with mechanisms intended to address other\nconcerns. Despite its practical relevance, the potential for such conflicts has\nnot been studied adequately. We first provide a framework for analyzing such\n\"conflicting interactions\". We then focus on systematically analyzing pairwise\ninteractions between protection mechanisms for one concern, model and data\nownership verification, with two other classes of ML protection mechanisms:\ndifferentially private training, and robustness against model evasion. We find\nthat several pairwise interactions result in conflicts. We explore potential\napproaches for avoiding such conflicts. First, we study the effect of\nhyperparameter relaxations, finding that there is no sweet spot balancing the\nperformance of both protection mechanisms. Second, we explore if modifying one\ntype of protection mechanism (ownership verification) so as to decouple it from\nfactors that may be impacted by a conflicting mechanism (differentially private\ntraining or robustness to model evasion) can avoid conflict. We show that this\napproach can avoid the conflict between ownership verification mechanisms when\ncombined with differentially private training, but has no effect on robustness\nto model evasion. Finally, we identify the gaps in the landscape of studying\ninteractions between other types of ML protection mechanisms.",
+                    "authors": "Sebastian Szyller, N. Asokan",
+                    "published": "2022-07-05",
+                    "updated": "2022-11-21",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.CR"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1912.00888v4",
+                    "title": "Deep Neural Network Fingerprinting by Conferrable Adversarial Examples",
+                    "abstract": "In Machine Learning as a Service, a provider trains a deep neural network and\ngives many users access. The hosted (source) model is susceptible to model\nstealing attacks, where an adversary derives a surrogate model from API access\nto the source model. For post hoc detection of such attacks, the provider needs\na robust method to determine whether a suspect model is a surrogate of their\nmodel. We propose a fingerprinting method for deep neural network classifiers\nthat extracts a set of inputs from the source model so that only surrogates\nagree with the source model on the classification of such inputs. These inputs\nare a subclass of transferable adversarial examples which we call conferrable\nadversarial examples that exclusively transfer with a target label from a\nsource model to its surrogates. We propose a new method to generate these\nconferrable adversarial examples. We present an extensive study on the\nirremovability of our fingerprint against fine-tuning, weight pruning,\nretraining, retraining with different architectures, three model extraction\nattacks from related work, transfer learning, adversarial training, and two new\nadaptive attacks. Our fingerprint is robust against distillation, related model\nextraction attacks, and even transfer learning when the attacker has no access\nto the model provider's dataset. Our fingerprint is the first method that\nreaches a ROC AUC of 1.0 in verifying surrogates, compared to a ROC AUC of 0.63\nby previous fingerprints.",
+                    "authors": "Nils Lukas, Yuxuan Zhang, Florian Kerschbaum",
+                    "published": "2019-12-02",
+                    "updated": "2021-01-20",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.CR",
+                        "stat.ML"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2401.15239v1",
+                    "title": "MEA-Defender: A Robust Watermark against Model Extraction Attack",
+                    "abstract": "Recently, numerous highly-valuable Deep Neural Networks (DNNs) have been\ntrained using deep learning algorithms. To protect the Intellectual Property\n(IP) of the original owners over such DNN models, backdoor-based watermarks\nhave been extensively studied. However, most of such watermarks fail upon model\nextraction attack, which utilizes input samples to query the target model and\nobtains the corresponding outputs, thus training a substitute model using such\ninput-output pairs. In this paper, we propose a novel watermark to protect IP\nof DNN models against model extraction, named MEA-Defender. In particular, we\nobtain the watermark by combining two samples from two source classes in the\ninput domain and design a watermark loss function that makes the output domain\nof the watermark within that of the main task samples. Since both the input\ndomain and the output domain of our watermark are indispensable parts of those\nof the main task samples, the watermark will be extracted into the stolen model\nalong with the main task during model extraction. We conduct extensive\nexperiments on four model extraction attacks, using five datasets and six\nmodels trained based on supervised learning and self-supervised learning\nalgorithms. The experimental results demonstrate that MEA-Defender is highly\nrobust against different model extraction attacks, and various watermark\nremoval/detection approaches.",
+                    "authors": "Peizhuo Lv, Hualong Ma, Kai Chen, Jiachen Zhou, Shengzhi Zhang, Ruigang Liang, Shenchen Zhu, Pan Li, Yingjun Zhang",
+                    "published": "2024-01-26",
+                    "updated": "2024-01-26",
+                    "primary_cat": "cs.CR",
+                    "cats": [
+                        "cs.CR",
+                        "cs.LG"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2309.01786v2",
+                    "title": "Safe and Robust Watermark Injection with a Single OoD Image",
+                    "abstract": "Training a high-performance deep neural network requires large amounts of\ndata and computational resources. Protecting the intellectual property (IP) and\ncommercial ownership of a deep model is challenging yet increasingly crucial. A\nmajor stream of watermarking strategies implants verifiable backdoor triggers\nby poisoning training samples, but these are often unrealistic due to data\nprivacy and safety concerns and are vulnerable to minor model changes such as\nfine-tuning. To overcome these challenges, we propose a safe and robust\nbackdoor-based watermark injection technique that leverages the diverse\nknowledge from a single out-of-distribution (OoD) image, which serves as a\nsecret key for IP verification. The independence of training data makes it\nagnostic to third-party promises of IP security. We induce robustness via\nrandom perturbation of model parameters during watermark injection to defend\nagainst common watermark removal attacks, including fine-tuning, pruning, and\nmodel extraction. Our experimental results demonstrate that the proposed\nwatermarking approach is not only time- and sample-efficient without training\ndata, but also robust against the watermark removal attacks above.",
+                    "authors": "Shuyang Yu, Junyuan Hong, Haobo Zhang, Haotao Wang, Zhangyang Wang, Jiayu Zhou",
+                    "published": "2023-09-04",
+                    "updated": "2024-03-11",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1812.02766v1",
+                    "title": "Knockoff Nets: Stealing Functionality of Black-Box Models",
+                    "abstract": "Machine Learning (ML) models are increasingly deployed in the wild to perform\na wide range of tasks. In this work, we ask to what extent can an adversary\nsteal functionality of such \"victim\" models based solely on blackbox\ninteractions: image in, predictions out. In contrast to prior work, we present\nan adversary lacking knowledge of train/test data used by the model, its\ninternals, and semantics over model outputs. We formulate model functionality\nstealing as a two-step approach: (i) querying a set of input images to the\nblackbox model to obtain predictions; and (ii) training a \"knockoff\" with\nqueried image-prediction pairs. We make multiple remarkable observations: (a)\nquerying random images from a different distribution than that of the blackbox\ntraining data results in a well-performing knockoff; (b) this is possible even\nwhen the knockoff is represented using a different architecture; and (c) our\nreinforcement learning approach additionally improves query sample efficiency\nin certain settings and provides performance gains. We validate model\nfunctionality stealing on a range of datasets and tasks, as well as on a\npopular image analysis API where we create a reasonable knockoff for as little\nas $30.",
+                    "authors": "Tribhuvanesh Orekondy, Bernt Schiele, Mario Fritz",
+                    "published": "2018-12-06",
+                    "updated": "2018-12-06",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.CR",
+                        "cs.LG"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2011.14779v2",
+                    "title": "Data-Free Model Extraction",
+                    "abstract": "Current model extraction attacks assume that the adversary has access to a\nsurrogate dataset with characteristics similar to the proprietary data used to\ntrain the victim model. This requirement precludes the use of existing model\nextraction techniques on valuable models, such as those trained on rare or hard\nto acquire datasets. In contrast, we propose data-free model extraction methods\nthat do not require a surrogate dataset. Our approach adapts techniques from\nthe area of data-free knowledge transfer for model extraction. As part of our\nstudy, we identify that the choice of loss is critical to ensuring that the\nextracted model is an accurate replica of the victim model. Furthermore, we\naddress difficulties arising from the adversary's limited access to the victim\nmodel in a black-box setting. For example, we recover the model's logits from\nits probability predictions to approximate gradients. We find that the proposed\ndata-free model extraction approach achieves high-accuracy with reasonable\nquery complexity -- 0.99x and 0.92x the victim model accuracy on SVHN and\nCIFAR-10 datasets given 2M and 20M queries respectively.",
+                    "authors": "Jean-Baptiste Truong, Pratyush Maini, Robert J. Walls, Nicolas Papernot",
+                    "published": "2020-11-30",
+                    "updated": "2021-03-31",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1805.12185v1",
+                    "title": "Fine-Pruning: Defending Against Backdooring Attacks on Deep Neural Networks",
+                    "abstract": "Deep neural networks (DNNs) provide excellent performance across a wide range\nof classification tasks, but their training requires high computational\nresources and is often outsourced to third parties. Recent work has shown that\noutsourced training introduces the risk that a malicious trainer will return a\nbackdoored DNN that behaves normally on most inputs but causes targeted\nmisclassifications or degrades the accuracy of the network when a trigger known\nonly to the attacker is present. In this paper, we provide the first effective\ndefenses against backdoor attacks on DNNs. We implement three backdoor attacks\nfrom prior work and use them to investigate two promising defenses, pruning and\nfine-tuning. We show that neither, by itself, is sufficient to defend against\nsophisticated attackers. We then evaluate fine-pruning, a combination of\npruning and fine-tuning, and show that it successfully weakens or even\neliminates the backdoors, i.e., in some cases reducing the attack success rate\nto 0% with only a 0.4% drop in accuracy for clean (non-triggering) inputs. Our\nwork provides the first step toward defenses against backdoor attacks in deep\nneural networks.",
+                    "authors": "Kang Liu, Brendan Dolan-Gavitt, Siddharth Garg",
+                    "published": "2018-05-30",
+                    "updated": "2018-05-30",
+                    "primary_cat": "cs.CR",
+                    "cats": [
+                        "cs.CR",
+                        "cs.LG"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2210.07809v2",
+                    "title": "Free Fine-tuning: A Plug-and-Play Watermarking Scheme for Deep Neural Networks",
+                    "abstract": "Watermarking has been widely adopted for protecting the intellectual property\n(IP) of Deep Neural Networks (DNN) to defend the unauthorized distribution.\nUnfortunately, the popular data-poisoning DNN watermarking scheme relies on\ntarget model fine-tuning to embed watermarks, which limits its practical\napplications in tackling real-world tasks. Specifically, the learning of\nwatermarks via tedious model fine-tuning on a poisoned dataset\n(carefully-crafted sample-label pairs) is not efficient in tackling the tasks\non challenging datasets and production-level DNN model protection. To address\nthe aforementioned limitations, in this paper, we propose a plug-and-play\nwatermarking scheme for DNN models by injecting an independent proprietary\nmodel into the target model to serve the watermark embedding and ownership\nverification. In contrast to the prior studies, our proposed method by\nincorporating a proprietary model is free of target model fine-tuning without\ninvolving any parameters update of the target model, thus the fidelity is well\npreserved. Our research findings reveal that model fine-tuning with poisoned\ndata is not prepared for the IP protection of DNN models deployed in real-world\ntasks and poses a new research direction toward a more thorough understanding\nand investigation of adopting the proprietary model for DNN watermarking. The\nsource code and models are available at\nhttps://github.com/AntigoneRandy/PTYNet.",
+                    "authors": "Run Wang, Jixing Ren, Boheng Li, Tianyi She, Chenhao Lin, Liming Fang, Jing Chen, Chao Shen, Lina Wang",
+                    "published": "2022-10-14",
+                    "updated": "2022-10-17",
+                    "primary_cat": "cs.CR",
+                    "cats": [
+                        "cs.CR"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2308.12319v3",
+                    "title": "RemovalNet: DNN Fingerprint Removal Attacks",
+                    "abstract": "With the performance of deep neural networks (DNNs) remarkably improving,\nDNNs have been widely used in many areas. Consequently, the DNN model has\nbecome a valuable asset, and its intellectual property is safeguarded by\nownership verification techniques (e.g., DNN fingerprinting). However, the\nfeasibility of the DNN fingerprint removal attack and its potential influence\nremains an open problem. In this paper, we perform the first comprehensive\ninvestigation of DNN fingerprint removal attacks. Generally, the knowledge\ncontained in a DNN model can be categorized into general semantic and\nfingerprint-specific knowledge. To this end, we propose a min-max bilevel\noptimization-based DNN fingerprint removal attack named RemovalNet, to evade\nmodel ownership verification. The lower-level optimization is designed to\nremove fingerprint-specific knowledge. While in the upper-level optimization,\nwe distill the victim model's general semantic knowledge to maintain the\nsurrogate model's performance. We conduct extensive experiments to evaluate the\nfidelity, effectiveness, and efficiency of the RemovalNet against four advanced\ndefense methods on six metrics. The empirical results demonstrate that (1) the\nRemovalNet is effective. After our DNN fingerprint removal attack, the model\ndistance between the target and surrogate models is x100 times higher than that\nof the baseline attacks, (2) the RemovalNet is efficient. It uses only 0.2%\n(400 samples) of the substitute dataset and 1,000 iterations to conduct our\nattack. Besides, compared with advanced model stealing attacks, the RemovalNet\nsaves nearly 85% of computational resources at most, (3) the RemovalNet\nachieves high fidelity that the created surrogate model maintains high accuracy\nafter the DNN fingerprint removal process. Our code is available at:\nhttps://github.com/grasses/RemovalNet.",
+                    "authors": "Hongwei Yao, Zheng Li, Kunzhe Huang, Jian Lou, Zhan Qin, Kui Ren",
+                    "published": "2023-08-23",
+                    "updated": "2023-11-22",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.AI"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2004.05937v7",
+                    "title": "Knowledge Distillation and Student-Teacher Learning for Visual Intelligence: A Review and New Outlooks",
+                    "abstract": "Deep neural models in recent years have been successful in almost every\nfield, including extremely complex problem statements. However, these models\nare huge in size, with millions (and even billions) of parameters, thus\ndemanding more heavy computation power and failing to be deployed on edge\ndevices. Besides, the performance boost is highly dependent on redundant\nlabeled data. To achieve faster speeds and to handle the problems caused by the\nlack of data, knowledge distillation (KD) has been proposed to transfer\ninformation learned from one model to another. KD is often characterized by the\nso-called `Student-Teacher' (S-T) learning framework and has been broadly\napplied in model compression and knowledge transfer. This paper is about KD and\nS-T learning, which are being actively studied in recent years. First, we aim\nto provide explanations of what KD is and how/why it works. Then, we provide a\ncomprehensive survey on the recent progress of KD methods together with S-T\nframeworks typically for vision tasks. In general, we consider some fundamental\nquestions that have been driving this research area and thoroughly generalize\nthe research progress and technical details. Additionally, we systematically\nanalyze the research status of KD in vision applications. Finally, we discuss\nthe potentials and open challenges of existing methods and prospect the future\ndirections of KD and S-T learning.",
+                    "authors": "Lin Wang, Kuk-Jin Yoon",
+                    "published": "2020-04-13",
+                    "updated": "2021-06-17",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.AI",
+                        "cs.LG"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2301.12900v2",
+                    "title": "DepGraph: Towards Any Structural Pruning",
+                    "abstract": "Structural pruning enables model acceleration by removing\nstructurally-grouped parameters from neural networks. However, the\nparameter-grouping patterns vary widely across different models, making\narchitecture-specific pruners, which rely on manually-designed grouping\nschemes, non-generalizable to new architectures. In this work, we study a\nhighly-challenging yet barely-explored task, any structural pruning, to tackle\ngeneral structural pruning of arbitrary architecture like CNNs, RNNs, GNNs and\nTransformers. The most prominent obstacle towards this goal lies in the\nstructural coupling, which not only forces different layers to be pruned\nsimultaneously, but also expects all removed parameters to be consistently\nunimportant, thereby avoiding structural issues and significant performance\ndegradation after pruning. To address this problem, we propose a general and\n{fully automatic} method, \\emph{Dependency Graph} (DepGraph), to explicitly\nmodel the dependency between layers and comprehensively group coupled\nparameters for pruning. In this work, we extensively evaluate our method on\nseveral architectures and tasks, including ResNe(X)t, DenseNet, MobileNet and\nVision transformer for images, GAT for graph, DGCNN for 3D point cloud,\nalongside LSTM for language, and demonstrate that, even with a simple\nnorm-based criterion, the proposed method consistently yields gratifying\nperformances.",
+                    "authors": "Gongfan Fang, Xinyin Ma, Mingli Song, Michael Bi Mi, Xinchao Wang",
+                    "published": "2023-01-30",
+                    "updated": "2023-03-23",
+                    "primary_cat": "cs.AI",
+                    "cats": [
+                        "cs.AI",
+                        "cs.CV"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1906.00830v5",
+                    "title": "DAWN: Dynamic Adversarial Watermarking of Neural Networks",
+                    "abstract": "Training machine learning (ML) models is expensive in terms of computational\npower, amounts of labeled data and human expertise. Thus, ML models constitute\nintellectual property (IP) and business value for their owners. Embedding\ndigital watermarks during model training allows a model owner to later identify\ntheir models in case of theft or misuse. However, model functionality can also\nbe stolen via model extraction, where an adversary trains a surrogate model\nusing results returned from a prediction API of the original model. Recent work\nhas shown that model extraction is a realistic threat. Existing watermarking\nschemes are ineffective against IP theft via model extraction since it is the\nadversary who trains the surrogate model. In this paper, we introduce DAWN\n(Dynamic Adversarial Watermarking of Neural Networks), the first approach to\nuse watermarking to deter model extraction IP theft. Unlike prior watermarking\nschemes, DAWN does not impose changes to the training process but it operates\nat the prediction API of the protected model, by dynamically changing the\nresponses for a small subset of queries (e.g., <0.5%) from API clients. This\nset is a watermark that will be embedded in case a client uses its queries to\ntrain a surrogate model. We show that DAWN is resilient against two\nstate-of-the-art model extraction attacks, effectively watermarking all\nextracted surrogate models, allowing model owners to reliably demonstrate\nownership (with confidence $>1- 2^{-64}$), incurring negligible loss of\nprediction accuracy (0.03-0.5%).",
+                    "authors": "Sebastian Szyller, Buse Gul Atli, Samuel Marchal, N. Asokan",
+                    "published": "2019-06-03",
+                    "updated": "2021-07-16",
+                    "primary_cat": "cs.CR",
+                    "cats": [
+                        "cs.CR",
+                        "stat.ML"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1701.04082v2",
+                    "title": "Embedding Watermarks into Deep Neural Networks",
+                    "abstract": "Deep neural networks have recently achieved significant progress. Sharing\ntrained models of these deep neural networks is very important in the rapid\nprogress of researching or developing deep neural network systems. At the same\ntime, it is necessary to protect the rights of shared trained models. To this\nend, we propose to use a digital watermarking technology to protect\nintellectual property or detect intellectual property infringement of trained\nmodels. Firstly, we formulate a new problem: embedding watermarks into deep\nneural networks. We also define requirements, embedding situations, and attack\ntypes for watermarking to deep neural networks. Secondly, we propose a general\nframework to embed a watermark into model parameters using a parameter\nregularizer. Our approach does not hurt the performance of networks into which\na watermark is embedded. Finally, we perform comprehensive experiments to\nreveal the potential of watermarking to deep neural networks as a basis of this\nnew problem. We show that our framework can embed a watermark in the situations\nof training a network from scratch, fine-tuning, and distilling without hurting\nthe performance of a deep neural network. The embedded watermark does not\ndisappear even after fine-tuning or parameter pruning; the watermark completely\nremains even after removing 65% of parameters were pruned. The implementation\nof this research is: https://github.com/yu4u/dnn-watermark",
+                    "authors": "Yusuke Uchida, Yuki Nagai, Shigeyuki Sakazawa, Shin'ichi Satoh",
+                    "published": "2017-01-15",
+                    "updated": "2017-04-20",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2002.12200v2",
+                    "title": "Entangled Watermarks as a Defense against Model Extraction",
+                    "abstract": "Machine learning involves expensive data collection and training procedures.\nModel owners may be concerned that valuable intellectual property can be leaked\nif adversaries mount model extraction attacks. As it is difficult to defend\nagainst model extraction without sacrificing significant prediction accuracy,\nwatermarking instead leverages unused model capacity to have the model overfit\nto outlier input-output pairs. Such pairs are watermarks, which are not sampled\nfrom the task distribution and are only known to the defender. The defender\nthen demonstrates knowledge of the input-output pairs to claim ownership of the\nmodel at inference. The effectiveness of watermarks remains limited because\nthey are distinct from the task distribution and can thus be easily removed\nthrough compression or other forms of knowledge transfer.\n  We introduce Entangled Watermarking Embeddings (EWE). Our approach encourages\nthe model to learn features for classifying data that is sampled from the task\ndistribution and data that encodes watermarks. An adversary attempting to\nremove watermarks that are entangled with legitimate data is also forced to\nsacrifice performance on legitimate data. Experiments on MNIST, Fashion-MNIST,\nCIFAR-10, and Speech Commands validate that the defender can claim model\nownership with 95\\% confidence with less than 100 queries to the stolen copy,\nat a modest cost below 0.81 percentage points on average in the defended\nmodel's performance.",
+                    "authors": "Hengrui Jia, Christopher A. Choquette-Choo, Varun Chandrasekaran, Nicolas Papernot",
+                    "published": "2020-02-27",
+                    "updated": "2021-02-19",
+                    "primary_cat": "cs.CR",
+                    "cats": [
+                        "cs.CR",
+                        "stat.ML"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1802.04633v3",
+                    "title": "Turning Your Weakness Into a Strength: Watermarking Deep Neural Networks by Backdooring",
+                    "abstract": "Deep Neural Networks have recently gained lots of success after enabling\nseveral breakthroughs in notoriously challenging problems. Training these\nnetworks is computationally expensive and requires vast amounts of training\ndata. Selling such pre-trained models can, therefore, be a lucrative business\nmodel. Unfortunately, once the models are sold they can be easily copied and\nredistributed. To avoid this, a tracking mechanism to identify models as the\nintellectual property of a particular vendor is necessary.\n  In this work, we present an approach for watermarking Deep Neural Networks in\na black-box way. Our scheme works for general classification tasks and can\neasily be combined with current learning algorithms. We show experimentally\nthat such a watermark has no noticeable impact on the primary task that the\nmodel is designed for and evaluate the robustness of our proposal against a\nmultitude of practical attacks. Moreover, we provide a theoretical analysis,\nrelating our approach to previous work on backdooring.",
+                    "authors": "Yossi Adi, Carsten Baum, Moustapha Cisse, Benny Pinkas, Joseph Keshet",
+                    "published": "2018-02-13",
+                    "updated": "2018-06-11",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2205.00199v2",
+                    "title": "Cracking White-box DNN Watermarks via Invariant Neuron Transforms",
+                    "abstract": "Recently, how to protect the Intellectual Property (IP) of deep neural\nnetworks (DNN) becomes a major concern for the AI industry. To combat potential\nmodel piracy, recent works explore various watermarking strategies to embed\nsecret identity messages into the prediction behaviors or the internals (e.g.,\nweights and neuron activation) of the target model. Sacrificing less\nfunctionality and involving more knowledge about the target model, the latter\nbranch of watermarking schemes (i.e., white-box model watermarking) is claimed\nto be accurate, credible and secure against most known watermark removal\nattacks, with emerging research efforts and applications in the industry.\n  In this paper, we present the first effective removal attack which cracks\nalmost all the existing white-box watermarking schemes with provably no\nperformance overhead and no required prior knowledge. By analyzing these IP\nprotection mechanisms at the granularity of neurons, we for the first time\ndiscover their common dependence on a set of fragile features of a local neuron\ngroup, all of which can be arbitrarily tampered by our proposed chain of\ninvariant neuron transforms. On $9$ state-of-the-art white-box watermarking\nschemes and a broad set of industry-level DNN architectures, our attack for the\nfirst time reduces the embedded identity message in the protected models to be\nalmost random. Meanwhile, unlike known removal attacks, our attack requires no\nprior knowledge on the training data distribution or the adopted watermark\nalgorithms, and leaves model functionality intact.",
+                    "authors": "Yifan Yan, Xudong Pan, Yining Wang, Mi Zhang, Min Yang",
+                    "published": "2022-04-30",
+                    "updated": "2022-05-19",
+                    "primary_cat": "cs.CR",
+                    "cats": [
+                        "cs.CR",
+                        "cs.CV",
+                        "cs.LG"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2207.07972v1",
+                    "title": "Certified Neural Network Watermarks with Randomized Smoothing",
+                    "abstract": "Watermarking is a commonly used strategy to protect creators' rights to\ndigital images, videos and audio. Recently, watermarking methods have been\nextended to deep learning models -- in principle, the watermark should be\npreserved when an adversary tries to copy the model. However, in practice,\nwatermarks can often be removed by an intelligent adversary. Several papers\nhave proposed watermarking methods that claim to be empirically resistant to\ndifferent types of removal attacks, but these new techniques often fail in the\nface of new or better-tuned adversaries. In this paper, we propose a\ncertifiable watermarking method. Using the randomized smoothing technique\nproposed in Chiang et al., we show that our watermark is guaranteed to be\nunremovable unless the model parameters are changed by more than a certain l2\nthreshold. In addition to being certifiable, our watermark is also empirically\nmore robust compared to previous watermarking methods. Our experiments can be\nreproduced with code at https://github.com/arpitbansal297/Certified_Watermarks",
+                    "authors": "Arpit Bansal, Ping-yeh Chiang, Michael Curry, Rajiv Jain, Curtis Wigington, Varun Manjunatha, John P Dickerson, Tom Goldstein",
+                    "published": "2022-07-16",
+                    "updated": "2022-07-16",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.CR"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1602.02697v4",
+                    "title": "Practical Black-Box Attacks against Machine Learning",
+                    "abstract": "Machine learning (ML) models, e.g., deep neural networks (DNNs), are\nvulnerable to adversarial examples: malicious inputs modified to yield\nerroneous model outputs, while appearing unmodified to human observers.\nPotential attacks include having malicious content like malware identified as\nlegitimate or controlling vehicle behavior. Yet, all existing adversarial\nexample attacks require knowledge of either the model internals or its training\ndata. We introduce the first practical demonstration of an attacker controlling\na remotely hosted DNN with no such knowledge. Indeed, the only capability of\nour black-box adversary is to observe labels given by the DNN to chosen inputs.\nOur attack strategy consists in training a local model to substitute for the\ntarget DNN, using inputs synthetically generated by an adversary and labeled by\nthe target DNN. We use the local substitute to craft adversarial examples, and\nfind that they are misclassified by the targeted DNN. To perform a real-world\nand properly-blinded evaluation, we attack a DNN hosted by MetaMind, an online\ndeep learning API. We find that their DNN misclassifies 84.24% of the\nadversarial examples crafted with our substitute. We demonstrate the general\napplicability of our strategy to many ML techniques by conducting the same\nattack against models hosted by Amazon and Google, using logistic regression\nsubstitutes. They yield adversarial examples misclassified by Amazon and Google\nat rates of 96.19% and 88.94%. We also find that this black-box attack strategy\nis capable of evading defense strategies previously found to make adversarial\nexample crafting harder.",
+                    "authors": "Nicolas Papernot, Patrick McDaniel, Ian Goodfellow, Somesh Jha, Z. Berkay Celik, Ananthram Swami",
+                    "published": "2016-02-08",
+                    "updated": "2017-03-19",
+                    "primary_cat": "cs.CR",
+                    "cats": [
+                        "cs.CR",
+                        "cs.LG"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2211.07804v3",
+                    "title": "Diffusion Models for Medical Image Analysis: A Comprehensive Survey",
+                    "abstract": "Denoising diffusion models, a class of generative models, have garnered\nimmense interest lately in various deep-learning problems. A diffusion\nprobabilistic model defines a forward diffusion stage where the input data is\ngradually perturbed over several steps by adding Gaussian noise and then learns\nto reverse the diffusion process to retrieve the desired noise-free data from\nnoisy data samples. Diffusion models are widely appreciated for their strong\nmode coverage and quality of the generated samples despite their known\ncomputational burdens. Capitalizing on the advances in computer vision, the\nfield of medical imaging has also observed a growing interest in diffusion\nmodels. To help the researcher navigate this profusion, this survey intends to\nprovide a comprehensive overview of diffusion models in the discipline of\nmedical image analysis. Specifically, we introduce the solid theoretical\nfoundation and fundamental concepts behind diffusion models and the three\ngeneric diffusion modelling frameworks: diffusion probabilistic models,\nnoise-conditioned score networks, and stochastic differential equations. Then,\nwe provide a systematic taxonomy of diffusion models in the medical domain and\npropose a multi-perspective categorization based on their application, imaging\nmodality, organ of interest, and algorithms. To this end, we cover extensive\napplications of diffusion models in the medical domain. Furthermore, we\nemphasize the practical use case of some selected approaches, and then we\ndiscuss the limitations of the diffusion models in the medical domain and\npropose several directions to fulfill the demands of this field. Finally, we\ngather the overviewed studies with their available open-source implementations\nat\nhttps://github.com/amirhossein-kz/Awesome-Diffusion-Models-in-Medical-Imaging.",
+                    "authors": "Amirhossein Kazerouni, Ehsan Khodapanah Aghdam, Moein Heidari, Reza Azad, Mohsen Fayyaz, Ilker Hacihaliloglu, Dorit Merhof",
+                    "published": "2022-11-14",
+                    "updated": "2023-06-03",
+                    "primary_cat": "eess.IV",
+                    "cats": [
+                        "eess.IV",
+                        "cs.CV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2304.01565v1",
+                    "title": "A Survey on Graph Diffusion Models: Generative AI in Science for Molecule, Protein and Material",
+                    "abstract": "Diffusion models have become a new SOTA generative modeling method in various\nfields, for which there are multiple survey works that provide an overall\nsurvey. With the number of articles on diffusion models increasing\nexponentially in the past few years, there is an increasing need for surveys of\ndiffusion models on specific fields. In this work, we are committed to\nconducting a survey on the graph diffusion models. Even though our focus is to\ncover the progress of diffusion models in graphs, we first briefly summarize\nhow other generative modeling methods are used for graphs. After that, we\nintroduce the mechanism of diffusion models in various forms, which facilitates\nthe discussion on the graph diffusion models. The applications of graph\ndiffusion models mainly fall into the category of AI-generated content (AIGC)\nin science, for which we mainly focus on how graph diffusion models are\nutilized for generating molecules and proteins but also cover other cases,\nincluding materials design. Moreover, we discuss the issue of evaluating\ndiffusion models in the graph domain and the existing challenges.",
+                    "authors": "Mengchun Zhang, Maryam Qamar, Taegoo Kang, Yuna Jung, Chenshuang Zhang, Sung-Ho Bae, Chaoning Zhang",
+                    "published": "2023-04-04",
+                    "updated": "2023-04-04",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.CV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/nlin/0212039v2",
+                    "title": "Front dynamics in reaction-diffusion systems with Levy flights: a fractional diffusion approach",
+                    "abstract": "The use of reaction-diffusion models rests on the key assumption that the\nunderlying diffusive process is Gaussian. However, a growing number of studies\nhave pointed out the prevalence of anomalous diffusion, and there is a need to\nunderstand the dynamics of reactive systems in the presence of this type of\nnon-Gaussian diffusion. Here we present a study of front dynamics in\nreaction-diffusion systems where anomalous diffusion is due to the presence of\nasymmetric Levy flights. Our approach consists of replacing the Laplacian\ndiffusion operator by a fractional diffusion operator, whose fundamental\nsolutions are Levy $\\alpha$-stable distributions. Numerical simulation of the\nfractional Fisher-Kolmogorov equation, and analytical arguments show that\nanomalous diffusion leads to the exponential acceleration of fronts and a\nuniversal power law decay, $x^{-\\alpha}$, of the tail, where $\\alpha$, the\nindex of the Levy distribution, is the order of the fractional derivative.",
+                    "authors": "D. del-Castillo-Negrete, B. A. Carreras, V. E. Lynch",
+                    "published": "2002-12-17",
+                    "updated": "2003-06-30",
+                    "primary_cat": "nlin.PS",
+                    "cats": [
+                        "nlin.PS",
+                        "nlin.CD"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2308.06342v2",
+                    "title": "Mirror Diffusion Models",
+                    "abstract": "Diffusion models have successfully been applied to generative tasks in\nvarious continuous domains. However, applying diffusion to discrete categorical\ndata remains a non-trivial task. Moreover, generation in continuous domains\noften requires clipping in practice, which motivates the need for a theoretical\nframework for adapting diffusion to constrained domains. Inspired by the mirror\nLangevin algorithm for the constrained sampling problem, in this theoretical\nreport we propose Mirror Diffusion Models (MDMs). We demonstrate MDMs in the\ncontext of simplex diffusion and propose natural extensions to popular domains\nsuch as image and text generation.",
+                    "authors": "Jaesung Tae",
+                    "published": "2023-08-11",
+                    "updated": "2023-08-18",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1212.2829v1",
+                    "title": "Spin diffusion in one-dimensional classical Heisenberg mode",
+                    "abstract": "The problem of spin diffusion is studied numerically in one-dimensional\nclassical Heisenberg model using a deterministic odd even spin precession\ndynamics. We demonstrate that spin diffusion in this model, like energy\ndiffusion, is normal and one obtains a long time diffusive tail in the decay of\nautocorrelation function (ACF). Some variations of the model with different\ncoupling schemes and with anisotropy are also studied and we find normal\ndiffusion in all of them. A systematic finite size analysis of the Heisenberg\nmodel also suggests diffusive spreading of fluctuation, contrary to previous\nclaims of anomalous diffusion.",
+                    "authors": "Debarshee Bagchi",
+                    "published": "2012-12-12",
+                    "updated": "2012-12-12",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/physics/0403039v1",
+                    "title": "Non-diffusive transport in plasma turbulence: a fractional diffusion approach",
+                    "abstract": "Numerical evidence of non-diffusive transport in three-dimensional, resistive\npressure-gradient-driven plasma turbulence is presented. It is shown that the\nprobability density function (pdf) of test particles' radial displacements is\nstrongly non-Gaussian and exhibits algebraic decaying tails. To model these\nresults we propose a macroscopic transport model for the pdf based on the use\nof fractional derivatives in space and time, that incorporate in a unified way\nspace-time non-locality (non-Fickian transport), non-Gaussianity, and\nnon-diffusive scaling. The fractional diffusion model reproduces the shape, and\nspace-time scaling of the non-Gaussian pdf of turbulent transport calculations.\nThe model also reproduces the observed super-diffusive scaling.",
+                    "authors": "D. del-Castillo-Negrete, B. A. Carreras, V. E. Lynch",
+                    "published": "2004-03-04",
+                    "updated": "2004-03-04",
+                    "primary_cat": "physics.plasm-ph",
+                    "cats": [
+                        "physics.plasm-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2207.09786v1",
+                    "title": "Non-Uniform Diffusion Models",
+                    "abstract": "Diffusion models have emerged as one of the most promising frameworks for\ndeep generative modeling. In this work, we explore the potential of non-uniform\ndiffusion models. We show that non-uniform diffusion leads to multi-scale\ndiffusion models which have similar structure to this of multi-scale\nnormalizing flows. We experimentally find that in the same or less training\ntime, the multi-scale diffusion model achieves better FID score than the\nstandard uniform diffusion model. More importantly, it generates samples $4.4$\ntimes faster in $128\\times 128$ resolution. The speed-up is expected to be\nhigher in higher resolutions where more scales are used. Moreover, we show that\nnon-uniform diffusion leads to a novel estimator for the conditional score\nfunction which achieves on par performance with the state-of-the-art\nconditional denoising estimator. Our theoretical and experimental findings are\naccompanied by an open source library MSDiff which can facilitate further\nresearch of non-uniform diffusion models.",
+                    "authors": "Georgios Batzolis, Jan Stanczuk, Carola-Bibiane Sch\u00f6nlieb, Christian Etmann",
+                    "published": "2022-07-20",
+                    "updated": "2022-07-20",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2310.05264v3",
+                    "title": "The Emergence of Reproducibility and Consistency in Diffusion Models",
+                    "abstract": "In this work, we investigate an intriguing and prevalent phenomenon of\ndiffusion models which we term as \"consistent model reproducibility\": given the\nsame starting noise input and a deterministic sampler, different diffusion\nmodels often yield remarkably similar outputs. We confirm this phenomenon\nthrough comprehensive experiments, implying that different diffusion models\nconsistently reach the same data distribution and scoring function regardless\nof diffusion model frameworks, model architectures, or training procedures.\nMore strikingly, our further investigation implies that diffusion models are\nlearning distinct distributions affected by the training data size. This is\nsupported by the fact that the model reproducibility manifests in two distinct\ntraining regimes: (i) \"memorization regime\", where the diffusion model overfits\nto the training data distribution, and (ii) \"generalization regime\", where the\nmodel learns the underlying data distribution. Our study also finds that this\nvaluable property generalizes to many variants of diffusion models, including\nthose for conditional use, solving inverse problems, and model fine-tuning.\nFinally, our work raises numerous intriguing theoretical questions for future\ninvestigation and highlights practical implications regarding training\nefficiency, model privacy, and the controlled generation of diffusion models.",
+                    "authors": "Huijie Zhang, Jinfan Zhou, Yifu Lu, Minzhe Guo, Peng Wang, Liyue Shen, Qing Qu",
+                    "published": "2023-10-08",
+                    "updated": "2024-02-21",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.CV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2306.03436v2",
+                    "title": "Intellectual Property Protection of Diffusion Models via the Watermark Diffusion Process",
+                    "abstract": "Diffusion models have rapidly become a vital part of deep generative\narchitectures, given today's increasing demands. Obtaining large,\nhigh-performance diffusion models demands significant resources, highlighting\ntheir importance as intellectual property worth protecting. However, existing\nwatermarking techniques for ownership verification are insufficient when\napplied to diffusion models. Very recent research in watermarking diffusion\nmodels either exposes watermarks during task generation, which harms the\nimperceptibility, or is developed for conditional diffusion models that require\nprompts to trigger the watermark. This paper introduces WDM, a novel\nwatermarking solution for diffusion models without imprinting the watermark\nduring task generation. It involves training a model to concurrently learn a\nWatermark Diffusion Process (WDP) for embedding watermarks alongside the\nstandard diffusion process for task generation. We provide a detailed\ntheoretical analysis of WDP training and sampling, relating it to a shifted\nGaussian diffusion process via the same reverse noise. Extensive experiments\nare conducted to validate the effectiveness and robustness of our approach in\nvarious trigger and watermark data configurations.",
+                    "authors": "Sen Peng, Yufei Chen, Cong Wang, Xiaohua Jia",
+                    "published": "2023-06-06",
+                    "updated": "2023-11-29",
+                    "primary_cat": "cs.CR",
+                    "cats": [
+                        "cs.CR",
+                        "cs.LG"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2404.07771v1",
+                    "title": "An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimization",
+                    "abstract": "Diffusion models, a powerful and universal generative AI technology, have\nachieved tremendous success in computer vision, audio, reinforcement learning,\nand computational biology. In these applications, diffusion models provide\nflexible high-dimensional data modeling, and act as a sampler for generating\nnew samples under active guidance towards task-desired properties. Despite the\nsignificant empirical success, theory of diffusion models is very limited,\npotentially slowing down principled methodological innovations for further\nharnessing and improving diffusion models. In this paper, we review emerging\napplications of diffusion models, understanding their sample generation under\nvarious controls. Next, we overview the existing theories of diffusion models,\ncovering their statistical properties and sampling capabilities. We adopt a\nprogressive routine, beginning with unconditional diffusion models and\nconnecting to conditional counterparts. Further, we review a new avenue in\nhigh-dimensional structured optimization through conditional diffusion models,\nwhere searching for solutions is reformulated as a conditional sampling problem\nand solved by diffusion models. Lastly, we discuss future directions about\ndiffusion models. The purpose of this paper is to provide a well-rounded\ntheoretical exposure for stimulating forward-looking theories and methods of\ndiffusion models.",
+                    "authors": "Minshuo Chen, Song Mei, Jianqing Fan, Mengdi Wang",
+                    "published": "2024-04-11",
+                    "updated": "2024-04-11",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "math.ST",
+                        "stat.ML",
+                        "stat.TH"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1705.01542v2",
+                    "title": "A Spatial Structural Derivative Model for Ultraslow Diffusion",
+                    "abstract": "This study investigates the ultraslow diffusion by a spatial structural\nderivative, in which the exponential function exp(x)is selected as the\nstructural function to construct the local structural derivative diffusion\nequation model. The analytical solution of the diffusion equation is a form of\nBiexponential distribution. Its corresponding mean squared displacement is\nnumerically calculated, and increases more slowly than the logarithmic function\nof time. The local structural derivative diffusion equation with the structural\nfunction exp(x)in space is an alternative physical and mathematical modeling\nmodel to characterize a kind of ultraslow diffusion.",
+                    "authors": "Wei Xu, Wen Chen, Yingjie Liang, Jose Weberszpil",
+                    "published": "2017-05-03",
+                    "updated": "2017-06-13",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2302.07261v2",
+                    "title": "Where to Diffuse, How to Diffuse, and How to Get Back: Automated Learning for Multivariate Diffusions",
+                    "abstract": "Diffusion-based generative models (DBGMs) perturb data to a target noise\ndistribution and reverse this process to generate samples. The choice of\nnoising process, or inference diffusion process, affects both likelihoods and\nsample quality. For example, extending the inference process with auxiliary\nvariables leads to improved sample quality. While there are many such\nmultivariate diffusions to explore, each new one requires significant\nmodel-specific analysis, hindering rapid prototyping and evaluation. In this\nwork, we study Multivariate Diffusion Models (MDMs). For any number of\nauxiliary variables, we provide a recipe for maximizing a lower-bound on the\nMDMs likelihood without requiring any model-specific analysis. We then\ndemonstrate how to parameterize the diffusion for a specified target noise\ndistribution; these two points together enable optimizing the inference\ndiffusion process. Optimizing the diffusion expands easy experimentation from\njust a few well-known processes to an automatic search over all linear\ndiffusions. To demonstrate these ideas, we introduce two new specific\ndiffusions as well as learn a diffusion process on the MNIST, CIFAR10, and\nImageNet32 datasets. We show learned MDMs match or surpass bits-per-dims (BPDs)\nrelative to fixed choices of diffusions for a given dataset and model\narchitecture.",
+                    "authors": "Raghav Singhal, Mark Goldstein, Rajesh Ranganath",
+                    "published": "2023-02-14",
+                    "updated": "2023-03-03",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "stat.ML"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2401.06046v2",
+                    "title": "Quantifying the contributions to diffusion in complex materials",
+                    "abstract": "Using machine learning with a variational formula for diffusivity, we recast\ndiffusion as a sum of individual contributions to diffusion--called\n\"kinosons\"--and compute their statistical distribution to model a complex\nmulticomponent alloy. Calculating kinosons is orders of magnitude more\nefficient than computing whole trajectories, and elucidates kinetic mechanisms\nfor diffusion. The distribution of kinosons with temperature leads to new\naccurate analytic models for macroscale diffusivity. This combination of\nmachine learning with diffusion theory promises insight into other complex\nmaterials.",
+                    "authors": "Soham Chattopadhyay, Dallas R. Trinkle",
+                    "published": "2024-01-11",
+                    "updated": "2024-03-14",
+                    "primary_cat": "cond-mat.mtrl-sci",
+                    "cats": [
+                        "cond-mat.mtrl-sci"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1611.06202v2",
+                    "title": "Brownian yet non-Gaussian diffusion: from superstatistics to subordination of diffusing diffusivities",
+                    "abstract": "A growing number of biological, soft, and active matter systems are observed\nto exhibit normal diffusive dynamics with a linear growth of the mean squared\ndisplacement, yet with a non-Gaussian distribution of increments. Based on the\nChubinsky-Slater idea of a diffusing diffusivity we here establish and analyze\na minimal model framework of diffusion processes with fluctuating diffusivity.\nIn particular, we demonstrate the equivalence of the diffusing diffusivity\nprocess with a superstatistical approach with a distribution of diffusivities,\nat times shorter than the diffusivity correlation time. At longer times a\ncrossover to a Gaussian distribution with an effective diffusivity emerges.\nSpecifically, we establish a subordination picture of Brownian but non-Gaussian\ndiffusion processes, that can be used for a wide class of diffusivity\nfluctuation statistics. Our results are shown to be in excellent agreement with\nsimulations and numerical evaluations.",
+                    "authors": "A. V. Chechkin, F. Seno, R. Metzler, I. M. Sokolov",
+                    "published": "2016-11-18",
+                    "updated": "2017-03-30",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech",
+                        "physics.bio-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2010.02514v1",
+                    "title": "Diffusion model and analysis of diffusion process at lagrangian method",
+                    "abstract": "Based on Fick's 2nd law the development of moving particle semi-implicit\nmethod for predicting diffusion process is proposed in this study",
+                    "authors": "Ziqi Zhou",
+                    "published": "2020-10-06",
+                    "updated": "2020-10-06",
+                    "primary_cat": "physics.flu-dyn",
+                    "cats": [
+                        "physics.flu-dyn"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1801.09352v1",
+                    "title": "Distributed order Hausdorff derivative diffusion model to characterize non-Fickian diffusion in porous media",
+                    "abstract": "Many theoretical and experimental results show that solute transport in\nheterogeneous porous media exhibits multi-scaling behaviors. To describe such\nnon-Fickian diffusions, this work provides a distributed order Hausdorff\ndiffusion model to describe the tracer transport in porous media. This model is\nproved to be equivalent with the diffusion equation model with a nonlinear time\ndependent diffusion coefficient. In conjunction with the structural derivative,\nits mean squared displacement (MSD) of the tracer particles is explicitly\nderived as a dilogarithm function when the weight function of the order\ndistribution is a linear function of the time derivative order. This model can\ncapture both accelerating and decelerating anomalous and ultraslow diffusions\nby varying the weight parameter c. In this study, the tracer transport in\nwater-filled pore spaces of two-dimensional Euclidean is demonstrated as a\ndecelerating sub-diffusion, and can well be described by the distributed order\nHausdorff diffusion model with c = 1.73. While the Hausdorff diffusion model\ncan accurately fit the sub-diffusion experimental data of the tracer transport\nin the pore-solid prefractal porous media.",
+                    "authors": "Yingjie Liang, Wen Chen, Wei Xu, HongGuang Sun",
+                    "published": "2018-01-29",
+                    "updated": "2018-01-29",
+                    "primary_cat": "physics.flu-dyn",
+                    "cats": [
+                        "physics.flu-dyn"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2212.10777v4",
+                    "title": "Hierarchically branched diffusion models leverage dataset structure for class-conditional generation",
+                    "abstract": "Class-labeled datasets, particularly those common in scientific domains, are\nrife with internal structure, yet current class-conditional diffusion models\nignore these relationships and implicitly diffuse on all classes in a flat\nfashion. To leverage this structure, we propose hierarchically branched\ndiffusion models as a novel framework for class-conditional generation.\nBranched diffusion models rely on the same diffusion process as traditional\nmodels, but learn reverse diffusion separately for each branch of a hierarchy.\nWe highlight several advantages of branched diffusion models over the current\nstate-of-the-art methods for class-conditional diffusion, including extension\nto novel classes in a continual-learning setting, a more sophisticated form of\nanalogy-based conditional generation (i.e. transmutation), and a novel\ninterpretability into the generation process. We extensively evaluate branched\ndiffusion models on several benchmark and large real-world scientific datasets\nspanning many data modalities.",
+                    "authors": "Alex M. Tseng, Max Shen, Tommaso Biancalani, Gabriele Scalia",
+                    "published": "2022-12-21",
+                    "updated": "2024-02-01",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2002.02101v1",
+                    "title": "Trace of anomalous diffusion in a biased quenched trap model",
+                    "abstract": "Diffusion on a quenched heterogeneous environment in the presence of bias is\nconsidered analytically. The first-passage-time statistics can be applied to\nobtain the drift and the diffusion coefficient in periodic quenched\nenvironments. We show several transition points at which sample-to-sample\nfluctuations of the drift or the diffusion coefficient remain large even when\nthe system size becomes large, i.e., non-self-averaging. Moreover, we find that\nthe disorder average of the diffusion coefficient diverges or becomes zero when\nthe corresponding annealed model generates superdiffusion or subdiffusion,\nrespectively. This result implies that anomalous diffusion in an annealed model\nis traced by anomaly of the diffusion coefficients in the corresponding\nquenched model.",
+                    "authors": "Takuma Akimoto, Keiji Saito",
+                    "published": "2020-02-06",
+                    "updated": "2020-02-06",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2211.08892v2",
+                    "title": "Fast Graph Generation via Spectral Diffusion",
+                    "abstract": "Generating graph-structured data is a challenging problem, which requires\nlearning the underlying distribution of graphs. Various models such as graph\nVAE, graph GANs, and graph diffusion models have been proposed to generate\nmeaningful and reliable graphs, among which the diffusion models have achieved\nstate-of-the-art performance. In this paper, we argue that running full-rank\ndiffusion SDEs on the whole graph adjacency matrix space hinders diffusion\nmodels from learning graph topology generation, and hence significantly\ndeteriorates the quality of generated graph data. To address this limitation,\nwe propose an efficient yet effective Graph Spectral Diffusion Model (GSDM),\nwhich is driven by low-rank diffusion SDEs on the graph spectrum space. Our\nspectral diffusion model is further proven to enjoy a substantially stronger\ntheoretical guarantee than standard diffusion models. Extensive experiments\nacross various datasets demonstrate that, our proposed GSDM turns out to be the\nSOTA model, by exhibiting both significantly higher generation quality and much\nless computational consumption than the baselines.",
+                    "authors": "Tianze Luo, Zhanfeng Mo, Sinno Jialin Pan",
+                    "published": "2022-11-16",
+                    "updated": "2022-11-19",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2305.14671v2",
+                    "title": "A Survey of Diffusion Models in Natural Language Processing",
+                    "abstract": "This survey paper provides a comprehensive review of the use of diffusion\nmodels in natural language processing (NLP). Diffusion models are a class of\nmathematical models that aim to capture the diffusion of information or signals\nacross a network or manifold. In NLP, diffusion models have been used in a\nvariety of applications, such as natural language generation, sentiment\nanalysis, topic modeling, and machine translation. This paper discusses the\ndifferent formulations of diffusion models used in NLP, their strengths and\nlimitations, and their applications. We also perform a thorough comparison\nbetween diffusion models and alternative generative models, specifically\nhighlighting the autoregressive (AR) models, while also examining how diverse\narchitectures incorporate the Transformer in conjunction with diffusion models.\nCompared to AR models, diffusion models have significant advantages for\nparallel generation, text interpolation, token-level controls such as syntactic\nstructures and semantic contents, and robustness. Exploring further\npermutations of integrating Transformers into diffusion models would be a\nvaluable pursuit. Also, the development of multimodal diffusion models and\nlarge-scale diffusion language models with notable capabilities for few-shot\nlearning would be important directions for the future advance of diffusion\nmodels in NLP.",
+                    "authors": "Hao Zou, Zae Myung Kim, Dongyeop Kang",
+                    "published": "2023-05-24",
+                    "updated": "2023-06-14",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2310.01221v2",
+                    "title": "Nonlocal diffusion model with maximum principle",
+                    "abstract": "In this paper, we propose nonlocal diffusion models with Dirichlet boundary.\nThese nonlocal diffusion models preserve the maximum principle and also have\ncorresponding variational form. With these good properties, It is relatively\neasy to prove the well-posedness and the vanishing nonlocality convergence.\nFurthermore, by specifically designed weight function, we can get a nonlocal\ndiffusion model with second order convergence which is optimal for nonlocal\ndiffusion models.",
+                    "authors": "Zuoqiang Shi",
+                    "published": "2023-10-02",
+                    "updated": "2023-10-12",
+                    "primary_cat": "math.AP",
+                    "cats": [
+                        "math.AP",
+                        "cs.NA",
+                        "math.NA"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2402.13144v1",
+                    "title": "Neural Network Diffusion",
+                    "abstract": "Diffusion models have achieved remarkable success in image and video\ngeneration. In this work, we demonstrate that diffusion models can also\n\\textit{generate high-performing neural network parameters}. Our approach is\nsimple, utilizing an autoencoder and a standard latent diffusion model. The\nautoencoder extracts latent representations of a subset of the trained network\nparameters. A diffusion model is then trained to synthesize these latent\nparameter representations from random noise. It then generates new\nrepresentations that are passed through the autoencoder's decoder, whose\noutputs are ready to use as new subsets of network parameters. Across various\narchitectures and datasets, our diffusion process consistently generates models\nof comparable or improved performance over trained networks, with minimal\nadditional cost. Notably, we empirically find that the generated models perform\ndifferently with the trained networks. Our results encourage more exploration\non the versatile use of diffusion models.",
+                    "authors": "Kai Wang, Zhaopan Xu, Yukun Zhou, Zelin Zang, Trevor Darrell, Zhuang Liu, Yang You",
+                    "published": "2024-02-20",
+                    "updated": "2024-02-20",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.CV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2307.13949v1",
+                    "title": "How Does Diffusion Influence Pretrained Language Models on Out-of-Distribution Data?",
+                    "abstract": "Transformer-based pretrained language models (PLMs) have achieved great\nsuccess in modern NLP. An important advantage of PLMs is good\nout-of-distribution (OOD) robustness. Recently, diffusion models have attracted\na lot of work to apply diffusion to PLMs. It remains under-explored how\ndiffusion influences PLMs on OOD data. The core of diffusion models is a\nforward diffusion process which gradually applies Gaussian noise to inputs, and\na reverse denoising process which removes noise. The noised input\nreconstruction is a fundamental ability of diffusion models. We directly\nanalyze OOD robustness by measuring the reconstruction loss, including testing\nthe abilities to reconstruct OOD data, and to detect OOD samples. Experiments\nare conducted by analyzing different training parameters and data statistical\nfeatures on eight datasets. It shows that finetuning PLMs with diffusion\ndegrades the reconstruction ability on OOD data. The comparison also shows that\ndiffusion models can effectively detect OOD samples, achieving state-of-the-art\nperformance in most of the datasets with an absolute accuracy improvement up to\n18%. These results indicate that diffusion reduces OOD robustness of PLMs.",
+                    "authors": "Huazheng Wang, Daixuan Cheng, Haifeng Sun, Jingyu Wang, Qi Qi, Jianxin Liao, Jing Wang, Cong Liu",
+                    "published": "2023-07-26",
+                    "updated": "2023-07-26",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL",
+                        "cs.AI"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1202.6521v1",
+                    "title": "Coherence transition in degenerate diffusion equations with mean field coupling",
+                    "abstract": "We introduce non-linear diffusion in a classical diffusion advection model\nwith non local aggregative coupling on the circle, that exhibits a transition\nfrom an uncoherent state to a coherent one when the coupling strength is\nincreased. We show first that all solutions of the equation converge to the set\nof equilibria, second that the set of equilibria undergoes a bifurcation\nrepresenting the transition to coherence when the coupling strength is\nincreased. These two properties are similar to the situation with linear\ndiffusion. Nevertheless nonlinear diffusion alters the transition scenari,\nwhich are different when the diffusion is sub-quadratic and when the diffusion\nis super-quadratic. When the diffusion is super-quadratic, it results in a\nmultistability region that preceeds the pitchfork bifurcation at which the\nuncoherent equilibrium looses stability. When the diffusion is quadratic the\npitchfork bifurcation at the onset of coherence is infinitely degenerate and a\ndisk of equilibria exist for the critical value of the coupling strength.\nAnother impact of nonlinear diffusion is that coherent equilibria become\nlocalized when advection is strong enough, a phenomenon that is preculded when\nthe diffusion is linear.",
+                    "authors": "Khashayar Pakdaman, Xavier Pellegrin",
+                    "published": "2012-02-29",
+                    "updated": "2012-02-29",
+                    "primary_cat": "nlin.AO",
+                    "cats": [
+                        "nlin.AO",
+                        "37N25, 92B25, 35Q35, 35K55, 37B25, 82C26"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/0912.3770v1",
+                    "title": "SLE(6) and the geometry of diffusion fronts",
+                    "abstract": "We study the diffusion front for a natural two-dimensional model where many\nparticles starting at the origin diffuse independently. It turns out that this\nmodel can be described using properties of near-critical percolation, and\nprovides a natural example where critical fractal geometries spontaneously\narise.",
+                    "authors": "Pierre Nolin",
+                    "published": "2009-12-18",
+                    "updated": "2009-12-18",
+                    "primary_cat": "math.PR",
+                    "cats": [
+                        "math.PR"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2402.01965v2",
+                    "title": "Analyzing Neural Network-Based Generative Diffusion Models through Convex Optimization",
+                    "abstract": "Diffusion models are becoming widely used in state-of-the-art image, video\nand audio generation. Score-based diffusion models stand out among these\nmethods, necessitating the estimation of score function of the input data\ndistribution. In this study, we present a theoretical framework to analyze\ntwo-layer neural network-based diffusion models by reframing score matching and\ndenoising score matching as convex optimization. Though existing diffusion\ntheory is mainly asymptotic, we characterize the exact predicted score function\nand establish the convergence result for neural network-based diffusion models\nwith finite data. This work contributes to understanding what neural\nnetwork-based diffusion model learns in non-asymptotic settings.",
+                    "authors": "Fangzhao Zhang, Mert Pilanci",
+                    "published": "2024-02-03",
+                    "updated": "2024-02-06",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "math.OC"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2202.05830v1",
+                    "title": "Learning Fast Samplers for Diffusion Models by Differentiating Through Sample Quality",
+                    "abstract": "Diffusion models have emerged as an expressive family of generative models\nrivaling GANs in sample quality and autoregressive models in likelihood scores.\nStandard diffusion models typically require hundreds of forward passes through\nthe model to generate a single high-fidelity sample. We introduce\nDifferentiable Diffusion Sampler Search (DDSS): a method that optimizes fast\nsamplers for any pre-trained diffusion model by differentiating through sample\nquality scores. We also present Generalized Gaussian Diffusion Models (GGDM), a\nfamily of flexible non-Markovian samplers for diffusion models. We show that\noptimizing the degrees of freedom of GGDM samplers by maximizing sample quality\nscores via gradient descent leads to improved sample quality. Our optimization\nprocedure backpropagates through the sampling process using the\nreparametrization trick and gradient rematerialization. DDSS achieves strong\nresults on unconditional image generation across various datasets (e.g., FID\nscores on LSUN church 128x128 of 11.6 with only 10 inference steps, and 4.82\nwith 20 steps, compared to 51.1 and 14.9 with strongest DDPM/DDIM baselines).\nOur method is compatible with any pre-trained diffusion model without\nfine-tuning or re-training required.",
+                    "authors": "Daniel Watson, William Chan, Jonathan Ho, Mohammad Norouzi",
+                    "published": "2022-02-11",
+                    "updated": "2022-02-11",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2301.00059v2",
+                    "title": "Describing NMR chemical exchange by effective phase diffusion approach",
+                    "abstract": "This paper proposes an effective phase diffusion method to analyze chemical\nexchange in nuclear magnetic resonance (NMR). The chemical exchange involves\nspin jumps around different sites where the spin angular frequencies vary,\nwhich leads to a random phase walk viewed from the rotating frame reference.\nTherefore, the random walk in phase space can be treated by the effective phase\ndiffusion method. Both the coupled and uncoupled phase diffusions are\nconsidered; additionally, it includes normal diffusion as well as fractional\ndiffusion. Based on these phase diffusion equations, the line shape of NMR\nexchange spectrum can be analyzed. By comparing these theoretical results with\nthe conventional theory, this phase diffusion approach works for fast exchange,\nranging from slightly faster than intermediate exchange to very fast exchange.\nFor normal diffusion models, the theoretically predicted curves agree with\nthose predicted from traditional models in the literature, and the\ncharacteristic exchange time obtained from phase diffusion with a fixed jump\ntime is the same as that obtained from the conventional model. However, the\nphase diffusion with a monoexponential time distribution gives a characteristic\nexchange time constant which is half of that obtained from the traditional\nmodel. Additionally, the fractional diffusion obtains a significantly different\nline shape than that predicted based on normal diffusion.",
+                    "authors": "Guoxing Lin",
+                    "published": "2022-12-30",
+                    "updated": "2023-05-17",
+                    "primary_cat": "physics.chem-ph",
+                    "cats": [
+                        "physics.chem-ph",
+                        "cond-mat.stat-mech"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/0801.3436v1",
+                    "title": "Model for Diffusion-Induced Ramsey Narrowing",
+                    "abstract": "Diffusion-induced Ramsey narrowing that appears when atoms can leave the\ninteraction region and repeatedly return without lost of coherence is\ninvestigated using strong collisions approximation. The effective diffusion\nequation is obtained and solved for low-dimensional model configurations and\nthree-dimensional real one.",
+                    "authors": "Alexander Romanenko, Leonid Yatsenko",
+                    "published": "2008-01-22",
+                    "updated": "2008-01-22",
+                    "primary_cat": "quant-ph",
+                    "cats": [
+                        "quant-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2403.15766v1",
+                    "title": "BEND: Bagging Deep Learning Training Based on Efficient Neural Network Diffusion",
+                    "abstract": "Bagging has achieved great success in the field of machine learning by\nintegrating multiple base classifiers to build a single strong classifier to\nreduce model variance. The performance improvement of bagging mainly relies on\nthe number and diversity of base classifiers. However, traditional deep\nlearning model training methods are expensive to train individually and\ndifficult to train multiple models with low similarity in a restricted dataset.\nRecently, diffusion models, which have been tremendously successful in the\nfields of imaging and vision, have been found to be effective in generating\nneural network model weights and biases with diversity. We creatively propose a\nBagging deep learning training algorithm based on Efficient Neural network\nDiffusion (BEND). The originality of BEND comes from the first use of a neural\nnetwork diffusion model to efficiently build base classifiers for bagging. Our\napproach is simple but effective, first using multiple trained model weights\nand biases as inputs to train autoencoder and latent diffusion model to realize\na diffusion model from noise to valid neural network parameters. Subsequently,\nwe generate several base classifiers using the trained diffusion model.\nFinally, we integrate these ba se classifiers for various inference tasks using\nthe Bagging method. Resulting experiments on multiple models and datasets show\nthat our proposed BEND algorithm can consistently outperform the mean and\nmedian accuracies of both the original trained model and the diffused model. At\nthe same time, new models diffused using the diffusion model have higher\ndiversity and lower cost than multiple models trained using traditional\nmethods. The BEND approach successfully introduces diffusion models into the\nnew deep learning training domain and provides a new paradigm for future deep\nlearning training and inference.",
+                    "authors": "Jia Wei, Xingjun Zhang, Witold Pedrycz",
+                    "published": "2024-03-23",
+                    "updated": "2024-03-23",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/cond-mat/0208120v1",
+                    "title": "Aging in a Chaotic System",
+                    "abstract": "We demonstrate aging behavior in a simple non-linear system. Our model is a\nchaotic map which generates deterministically sub-diffusion. Asymptotic\nbehaviors of the diffusion process are described using aging continuous time\nrandom walks, introduced previously to model diffusion in glasses.",
+                    "authors": "E. Barkai",
+                    "published": "2002-08-06",
+                    "updated": "2002-08-06",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech",
+                        "nlin.CD"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2302.05737v2",
+                    "title": "A Reparameterized Discrete Diffusion Model for Text Generation",
+                    "abstract": "This work studies discrete diffusion probabilistic models with applications\nto natural language generation. We derive an alternative yet equivalent\nformulation of the sampling from discrete diffusion processes and leverage this\ninsight to develop a family of reparameterized discrete diffusion models. The\nderived generic framework is highly flexible, offers a fresh perspective of the\ngeneration process in discrete diffusion models, and features more effective\ntraining and decoding techniques. We conduct extensive experiments to evaluate\nthe text generation capability of our model, demonstrating significant\nimprovements over existing diffusion models.",
+                    "authors": "Lin Zheng, Jianbo Yuan, Lei Yu, Lingpeng Kong",
+                    "published": "2023-02-11",
+                    "updated": "2024-02-03",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL",
+                        "cs.LG"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1906.02405v1",
+                    "title": "Indirect interactions influence contact network structure and diffusion dynamics",
+                    "abstract": "Interaction patterns at the individual level influence the behaviour of\ndiffusion over contact networks. Most of the current diffusion models only\nconsider direct interactions among individuals to build underlying infectious\nitems transmission networks. However, delayed indirect interactions, where a\nsusceptible individual interacts with infectious items after the infected\nindividual has left the interaction space, can also cause transmission events.\nWe define a diffusion model called the same place different time transmission\n(SPDT) based diffusion that considers transmission links for these indirect\ninteractions. Our SPDT model changes the network dynamics where the\nconnectivity among individuals varies with the decay rates of link infectivity.\nWe investigate SPDT diffusion behaviours by simulating airborne disease\nspreading on data-driven contact networks. The SPDT model significantly\nincreases diffusion dynamics (particularly for networks with low link densities\nwhere indirect interactions create new infection pathways) and is capable of\nproducing realistic disease reproduction number. Our results show that the SPDT\nmodel is significantly more likely to lead to outbreaks compared to current\ndiffusion models with direct interactions. We find that the diffusion dynamics\nwith including indirect links are not reproducible by the current models,\nhighlighting the importance of the indirect links for predicting outbreaks.",
+                    "authors": "Md Shahzamal, Raja Jurdak, Bernard Mans, Frank de Hoog",
+                    "published": "2019-06-06",
+                    "updated": "2019-06-06",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "physics.soc-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2307.06272v1",
+                    "title": "Exposing the Fake: Effective Diffusion-Generated Images Detection",
+                    "abstract": "Image synthesis has seen significant advancements with the advent of\ndiffusion-based generative models like Denoising Diffusion Probabilistic Models\n(DDPM) and text-to-image diffusion models. Despite their efficacy, there is a\ndearth of research dedicated to detecting diffusion-generated images, which\ncould pose potential security and privacy risks. This paper addresses this gap\nby proposing a novel detection method called Stepwise Error for\nDiffusion-generated Image Detection (SeDID). Comprising statistical-based\n$\\text{SeDID}_{\\text{Stat}}$ and neural network-based\n$\\text{SeDID}_{\\text{NNs}}$, SeDID exploits the unique attributes of diffusion\nmodels, namely deterministic reverse and deterministic denoising computation\nerrors. Our evaluations demonstrate SeDID's superior performance over existing\nmethods when applied to diffusion models. Thus, our work makes a pivotal\ncontribution to distinguishing diffusion model-generated images, marking a\nsignificant step in the domain of artificial intelligence security.",
+                    "authors": "Ruipeng Ma, Jinhao Duan, Fei Kong, Xiaoshuang Shi, Kaidi Xu",
+                    "published": "2023-07-12",
+                    "updated": "2023-07-12",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.CR",
+                        "cs.LG"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1708.06890v1",
+                    "title": "Collaborative Inference of Coexisting Information Diffusions",
+                    "abstract": "Recently, \\textit{diffusion history inference} has become an emerging\nresearch topic due to its great benefits for various applications, whose\npurpose is to reconstruct the missing histories of information diffusion traces\naccording to incomplete observations. The existing methods, however, often\nfocus only on single information diffusion trace, while in a real-world social\nnetwork, there often coexist multiple information diffusions over the same\nnetwork. In this paper, we propose a novel approach called Collaborative\nInference Model (CIM) for the problem of the inference of coexisting\ninformation diffusions. By exploiting the synergism between the coexisting\ninformation diffusions, CIM holistically models multiple information diffusions\nas a sparse 4th-order tensor called Coexisting Diffusions Tensor (CDT) without\nany prior assumption of diffusion models, and collaboratively infers the\nhistories of the coexisting information diffusions via a low-rank approximation\nof CDT with a fusion of heterogeneous constraints generated from additional\ndata sources. To improve the efficiency, we further propose an optimal\nalgorithm called Time Window based Parallel Decomposition Algorithm (TWPDA),\nwhich can speed up the inference without compromise on the accuracy by\nutilizing the temporal locality of information diffusions. The extensive\nexperiments conducted on real world datasets and synthetic datasets verify the\neffectiveness and efficiency of CIM and TWPDA.",
+                    "authors": "Yanchao Sun, Cong Qian, Ning Yang, Philip S. Yu",
+                    "published": "2017-08-23",
+                    "updated": "2017-08-23",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2303.09295v1",
+                    "title": "DIRE for Diffusion-Generated Image Detection",
+                    "abstract": "Diffusion models have shown remarkable success in visual synthesis, but have\nalso raised concerns about potential abuse for malicious purposes. In this\npaper, we seek to build a detector for telling apart real images from\ndiffusion-generated images. We find that existing detectors struggle to detect\nimages generated by diffusion models, even if we include generated images from\na specific diffusion model in their training data. To address this issue, we\npropose a novel image representation called DIffusion Reconstruction Error\n(DIRE), which measures the error between an input image and its reconstruction\ncounterpart by a pre-trained diffusion model. We observe that\ndiffusion-generated images can be approximately reconstructed by a diffusion\nmodel while real images cannot. It provides a hint that DIRE can serve as a\nbridge to distinguish generated and real images. DIRE provides an effective way\nto detect images generated by most diffusion models, and it is general for\ndetecting generated images from unseen diffusion models and robust to various\nperturbations. Furthermore, we establish a comprehensive diffusion-generated\nbenchmark including images generated by eight diffusion models to evaluate the\nperformance of diffusion-generated image detectors. Extensive experiments on\nour collected benchmark demonstrate that DIRE exhibits superiority over\nprevious generated-image detectors. The code and dataset are available at\nhttps://github.com/ZhendongWang6/DIRE.",
+                    "authors": "Zhendong Wang, Jianmin Bao, Wengang Zhou, Weilun Wang, Hezhen Hu, Hong Chen, Houqiang Li",
+                    "published": "2023-03-16",
+                    "updated": "2023-03-16",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1304.0925v1",
+                    "title": "A new approach to multi-modal diffusions with applications to protein folding",
+                    "abstract": "This article demonstrates that flexible and statistically tractable\nmulti-modal diffusion models can be attained by transformation of simple\nwell-known diffusion models such as the Ornstein-Uhlenbeck model, or more\ngenerally a Pearson diffusion. The transformed diffusion inherits many\nproperties of the underlying simple diffusion including its mixing rates and\ndistributions of first passage times. Likelihood inference and martingale\nestimating functions are considered in the case of a discretely observed\nbimodal diffusion. It is further demonstrated that model parameters can be\nidentified and estimated when the diffusion is observed with additional\nmeasurement error. The new approach is applied to molecular dynamics data in\nform of a reaction coordinate of the small Trp-zipper protein, for which the\nfolding and unfolding rates are estimated. The new models provide a better fit\nto this type of protein folding data than previous models because the diffusion\ncoefficient is state-dependent.",
+                    "authors": "Julie Forman, Michael S\u00f8rensen",
+                    "published": "2013-04-03",
+                    "updated": "2013-04-03",
+                    "primary_cat": "stat.ME",
+                    "cats": [
+                        "stat.ME"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2301.00527v1",
+                    "title": "Diffusion Probabilistic Models for Scene-Scale 3D Categorical Data",
+                    "abstract": "In this paper, we learn a diffusion model to generate 3D data on a\nscene-scale. Specifically, our model crafts a 3D scene consisting of multiple\nobjects, while recent diffusion research has focused on a single object. To\nrealize our goal, we represent a scene with discrete class labels, i.e.,\ncategorical distribution, to assign multiple objects into semantic categories.\nThus, we extend discrete diffusion models to learn scene-scale categorical\ndistributions. In addition, we validate that a latent diffusion model can\nreduce computation costs for training and deploying. To the best of our\nknowledge, our work is the first to apply discrete and latent diffusion for 3D\ncategorical data on a scene-scale. We further propose to perform semantic scene\ncompletion (SSC) by learning a conditional distribution using our diffusion\nmodel, where the condition is a partial observation in a sparse point cloud. In\nexperiments, we empirically show that our diffusion models not only generate\nreasonable scenes, but also perform the scene completion task better than a\ndiscriminative model. Our code and models are available at\nhttps://github.com/zoomin-lee/scene-scale-diffusion",
+                    "authors": "Jumin Lee, Woobin Im, Sebin Lee, Sung-Eui Yoon",
+                    "published": "2023-01-02",
+                    "updated": "2023-01-02",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1609.04658v1",
+                    "title": "Analyzing Signal Attenuation in PFG Anomalous Diffusion via a Modified Gaussian Phase Distribution Approximation Based on Fractal Derivative Model",
+                    "abstract": "Pulsed field gradient (PFG) has been increasingly employed to study anomalous\ndiffusions in Nuclear Magnetic Resonance (NMR) and Magnetic Resonance Imaging\n(MRI). However, the analysis of PFG anomalous diffusion is complicated. In this\npaper, a fractal derivative model based modified Gaussian phase distribution\nmethod is proposed to describe PFG anomalous diffusion. By using the phase\ndistribution obtained from the effective phase shift diffusion method based on\nfractal derivatives, and employing some of the traditional Gaussian phase\ndistribution approximation techniques, a general signal attenuation expression\nfor free fractional diffusion is derived. This expression describes a stretched\nexponential function based attenuation, which is distinct from both the\nexponential attenuation for normal diffusion obtained from conventional\nGaussian phase distribution approximation, and the Mittag-Leffler function\nbased attenuation for anomalous diffusion obtained from fractional derivative.\nThe obtained signal attenuation expression can analyze the finite gradient\npulse width (FGPW) effect. Additionally, it can generally be applied to all\nthree types of PFG fractional diffusions classified based on time derivative\norder alpha and space derivative order beta. These three types of fractional\ndiffusions include time-fractional diffusion, space-fractional diffusion, and\ngeneral fractional diffusion. The results in this paper are consistent with\nreported results based on effective phase shift diffusion equation method and\ninstantaneous signal attenuation method. This method provides a new, convenient\napproximation formalism for analyzing PFG anomalous diffusion experiments.",
+                    "authors": "Guoxing Lin",
+                    "published": "2016-09-15",
+                    "updated": "2016-09-15",
+                    "primary_cat": "physics.chem-ph",
+                    "cats": [
+                        "physics.chem-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1911.11645v1",
+                    "title": "Effects of different discretisations of the Laplacian upon stochastic simulations of reaction-diffusion systems on both static and growing domains",
+                    "abstract": "By discretising space into compartments and letting system dynamics be\ngoverned by the reaction-diffusion master equation, it is possible to derive\nand simulate a stochastic model of reaction and diffusion on an arbitrary\ndomain. However, there are many implementation choices involved in this\nprocess, such as the choice of discretisation and method of derivation of the\ndiffusive jump rates, and it is not clear a priori how these affect model\npredictions. To shed light on this issue, in this work we explore how a variety\nof discretisations and method for derivation of the diffusive jump rates affect\nthe outputs of stochastic simulations of reaction-diffusion models, in\nparticular using Turing's model of pattern formation as a key example. We\nconsider both static and uniformly growing domains and demonstrate that, while\nonly minor differences are observed for simple reaction-diffusion systems,\nthere can be vast differences in model predictions for systems that include\ncomplicated reaction kinetics, such as Turing's model of pattern formation. Our\nwork highlights that care must be taken in using the reaction-diffusion master\nequation to make predictions as to the dynamics of stochastic\nreaction-diffusion systems.",
+                    "authors": "Bartosz J. Bartmanski, Ruth E. Baker",
+                    "published": "2019-11-26",
+                    "updated": "2019-11-26",
+                    "primary_cat": "physics.comp-ph",
+                    "cats": [
+                        "physics.comp-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2006.00003v1",
+                    "title": "Coupling particle-based reaction-diffusion simulations with reservoirs mediated by reaction-diffusion PDEs",
+                    "abstract": "Open biochemical systems of interacting molecules are ubiquitous in\nlife-related processes. However, established computational methodologies, like\nmolecular dynamics, are still mostly constrained to closed systems and\ntimescales too small to be relevant for life processes. Alternatively,\nparticle-based reaction-diffusion models are currently the most accurate and\ncomputationally feasible approach at these scales. Their efficiency lies in\nmodeling entire molecules as particles that can diffuse and interact with each\nother. In this work, we develop modeling and numerical schemes for\nparticle-based reaction-diffusion in an open setting, where the reservoirs are\nmediated by reaction-diffusion PDEs. We derive two important theoretical\nresults. The first one is the mean-field for open systems of diffusing\nparticles; the second one is the mean-field for a particle-based\nreaction-diffusion system with second-order reactions. We employ these two\nresults to develop a numerical scheme that consistently couples particle-based\nreaction-diffusion processes with reaction-diffusion PDEs. This allows modeling\nopen biochemical systems in contact with reservoirs that are time-dependent and\nspatially inhomogeneous, as in many relevant real-world applications.",
+                    "authors": "Margarita Kostr\u00e9, Christof Sch\u00fctte, Frank No\u00e9, Mauricio J. del Razo",
+                    "published": "2020-05-29",
+                    "updated": "2020-05-29",
+                    "primary_cat": "q-bio.QM",
+                    "cats": [
+                        "q-bio.QM",
+                        "physics.chem-ph",
+                        "physics.comp-ph",
+                        "92C40, 92C45, 60J70, 60Gxx, 70Lxx"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1404.3573v1",
+                    "title": "\"Diffusing diffusivity\": A model for anomalous and \"anomalous yet Brownian\" diffusion",
+                    "abstract": "Wang et al. [PNAS 106 (2009) 15160] have found that in several systems the\nlinear time dependence of the mean-square displacement (MSD) of diffusing\ncolloidal particles, typical of normal diffusion, is accompanied by a\nnon-Gaussian displacement distribution (DisD), with roughly exponential tails\nat short times, a situation they termed \"anomalous yet Brownian\" diffusion. The\ndiversity of systems in which this is observed calls for a generic model. We\npresent such a model where there is \"diffusivity memory\" but no \"direction\nmemory\" in the particle trajectory, and we show that it leads to both a linear\nMSD and a non-Gaussian DisD at short times. In our model, the diffusivity is\nundergoing a (perhaps biased) random walk, hence the expression \"diffusing\ndiffusivity\". The DisD is predicted to be exactly exponential at short times if\nthe distribution of diffusivities is itself exponential, but an exponential\nremains a good fit to the DisD for a variety of diffusivity distributions.\nMoreover, our generic model can be modified to produce subdiffusion.",
+                    "authors": "Mykyta V. Chubynsky, Gary W. Slater",
+                    "published": "2014-04-14",
+                    "updated": "2014-04-14",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech",
+                        "cond-mat.soft"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1807.03744v2",
+                    "title": "Enhanced Diffusivity in Perturbed Senile Reinforced Random Walk Models",
+                    "abstract": "We consider diffusivity of random walks with transition probabilities\ndepending on the number of consecutive traversals of the last traversed edge,\nthe so called senile reinforced random walk (SeRW). In one dimension, the walk\nis known to be sub-diffusive with identity reinforcement function. We perturb\nthe model by introducing a small probability $\\delta$ of escaping the last\ntraversed edge at each step. The perturbed SeRW model is diffusive for any\n$\\delta >0 $, with enhanced diffusivity ($\\gg O(\\delta^2)$) in the small\n$\\delta$ regime. We further study stochastically perturbed SeRW models by\nhaving the last edge escape probability of the form $\\delta\\, \\xi_n$ with\n$\\xi_n$'s being independent random variables. Enhanced diffusivity in such\nmodels are logarithmically close to the so called residual diffusivity\n(positive in the zero $\\delta$ limit), with diffusivity between\n$O\\left(\\frac{1}{|\\log\\delta |}\\right)$ and\n$O\\left(\\frac{1}{\\log|\\log\\delta|}\\right)$. Finally, we generalize our results\nto higher dimensions where the unperturbed model is already diffusive. The\nenhanced diffusivity can be as much as $O(\\log^{-2}\\delta)$.",
+                    "authors": "Thu Dinh, Jack Xin",
+                    "published": "2018-07-10",
+                    "updated": "2020-03-16",
+                    "primary_cat": "math.PR",
+                    "cats": [
+                        "math.PR",
+                        "60G50, 60H30, 58J37"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2305.13122v1",
+                    "title": "Policy Representation via Diffusion Probability Model for Reinforcement Learning",
+                    "abstract": "Popular reinforcement learning (RL) algorithms tend to produce a unimodal\npolicy distribution, which weakens the expressiveness of complicated policy and\ndecays the ability of exploration. The diffusion probability model is powerful\nto learn complicated multimodal distributions, which has shown promising and\npotential applications to RL. In this paper, we formally build a theoretical\nfoundation of policy representation via the diffusion probability model and\nprovide practical implementations of diffusion policy for online model-free RL.\nConcretely, we character diffusion policy as a stochastic process, which is a\nnew approach to representing a policy. Then we present a convergence guarantee\nfor diffusion policy, which provides a theory to understand the multimodality\nof diffusion policy. Furthermore, we propose the DIPO which is an\nimplementation for model-free online RL with DIffusion POlicy. To the best of\nour knowledge, DIPO is the first algorithm to solve model-free online RL\nproblems with the diffusion model. Finally, extensive empirical results show\nthe effectiveness and superiority of DIPO on the standard continuous control\nMujoco benchmark.",
+                    "authors": "Long Yang, Zhixiong Huang, Fenghao Lei, Yucun Zhong, Yiming Yang, Cong Fang, Shiting Wen, Binbin Zhou, Zhouchen Lin",
+                    "published": "2023-05-22",
+                    "updated": "2023-05-22",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2210.05559v2",
+                    "title": "Unifying Diffusion Models' Latent Space, with Applications to CycleDiffusion and Guidance",
+                    "abstract": "Diffusion models have achieved unprecedented performance in generative\nmodeling. The commonly-adopted formulation of the latent code of diffusion\nmodels is a sequence of gradually denoised samples, as opposed to the simpler\n(e.g., Gaussian) latent space of GANs, VAEs, and normalizing flows. This paper\nprovides an alternative, Gaussian formulation of the latent space of various\ndiffusion models, as well as an invertible DPM-Encoder that maps images into\nthe latent space. While our formulation is purely based on the definition of\ndiffusion models, we demonstrate several intriguing consequences. (1)\nEmpirically, we observe that a common latent space emerges from two diffusion\nmodels trained independently on related domains. In light of this finding, we\npropose CycleDiffusion, which uses DPM-Encoder for unpaired image-to-image\ntranslation. Furthermore, applying CycleDiffusion to text-to-image diffusion\nmodels, we show that large-scale text-to-image diffusion models can be used as\nzero-shot image-to-image editors. (2) One can guide pre-trained diffusion\nmodels and GANs by controlling the latent codes in a unified, plug-and-play\nformulation based on energy-based models. Using the CLIP model and a face\nrecognition model as guidance, we demonstrate that diffusion models have better\ncoverage of low-density sub-populations and individuals than GANs. The code is\npublicly available at https://github.com/ChenWu98/cycle-diffusion.",
+                    "authors": "Chen Henry Wu, Fernando De la Torre",
+                    "published": "2022-10-11",
+                    "updated": "2022-12-07",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.GR",
+                        "cs.LG"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2303.06574v2",
+                    "title": "Diffusion Models for Non-autoregressive Text Generation: A Survey",
+                    "abstract": "Non-autoregressive (NAR) text generation has attracted much attention in the\nfield of natural language processing, which greatly reduces the inference\nlatency but has to sacrifice the generation accuracy. Recently, diffusion\nmodels, a class of latent variable generative models, have been introduced into\nNAR text generation, showing an improved text generation quality. In this\nsurvey, we review the recent progress in diffusion models for NAR text\ngeneration. As the background, we first present the general definition of\ndiffusion models and the text diffusion models, and then discuss their merits\nfor NAR generation. As the core content, we further introduce two mainstream\ndiffusion models in existing work of text diffusion, and review the key designs\nof the diffusion process. Moreover, we discuss the utilization of pre-trained\nlanguage models (PLMs) for text diffusion models and introduce optimization\ntechniques for text data. Finally, we discuss several promising directions and\nconclude this paper. Our survey aims to provide researchers with a systematic\nreference of related research on text diffusion models for NAR generation. We\npresent our collection of text diffusion models at\nhttps://github.com/RUCAIBox/Awesome-Text-Diffusion-Models.",
+                    "authors": "Yifan Li, Kun Zhou, Wayne Xin Zhao, Ji-Rong Wen",
+                    "published": "2023-03-12",
+                    "updated": "2023-05-13",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2104.13565v2",
+                    "title": "Generalisation of continuous time random walk to anomalous diffusion MRI models with an age-related evaluation of human corpus callosum",
+                    "abstract": "Diffusion MRI measures of the human brain provide key insight into\nmicrostructural variations across individuals and into the impact of central\nnervous system diseases and disorders. One approach to extract information from\ndiffusion signals has been to use biologically relevant analytical models to\nlink millimetre scale diffusion MRI measures with microscale influences. The\nother approach has been to represent diffusion as an anomalous transport\nprocess and infer microstructural information from the different anomalous\ndiffusion equation parameters. In this study, we investigated how parameters of\nvarious anomalous diffusion models vary with age in the human brain white\nmatter, particularly focusing on the corpus callosum. We first unified several\nestablished anomalous diffusion models (the super-diffusion, sub-diffusion,\nquasi-diffusion and fractional Bloch-Torrey models) under the continuous time\nrandom walk modelling framework. This unification allows a consistent parameter\nfitting strategy to be applied from which meaningful model parameter\ncomparisons can be made. We then provided a novel way to derive the diffusional\nkurtosis imaging (DKI) model, which is shown to be a degree two approximation\nof the sub-diffusion model. This link between the DKI and sub-diffusion models\nled to a new robust technique for generating maps of kurtosis and diffusivity\nusing the sub-diffusion parameters \\b{eta}_SUB and D_SUB. Superior tissue\ncontrast is achieved in kurtosis maps based on the sub-diffusion model. 7T\ndiffusion weighted MRI data for 65 healthy participants in the age range 19-78\nyears was used in this study. Results revealed that anomalous diffusion model\nparameters {\\alpha} and \\b{eta} have shown consistent positive correlation with\nage in the corpus callosum, indicating {\\alpha} and \\b{eta} are sensitive to\ntissue microstructural changes in aging.",
+                    "authors": "Qianqian Yang, David C. Reutens, Viktor Vegh",
+                    "published": "2021-04-28",
+                    "updated": "2022-01-17",
+                    "primary_cat": "physics.med-ph",
+                    "cats": [
+                        "physics.med-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2404.04629v1",
+                    "title": "DifFUSER: Diffusion Model for Robust Multi-Sensor Fusion in 3D Object Detection and BEV Segmentation",
+                    "abstract": "Diffusion models have recently gained prominence as powerful deep generative\nmodels, demonstrating unmatched performance across various domains. However,\ntheir potential in multi-sensor fusion remains largely unexplored. In this\nwork, we introduce DifFUSER, a novel approach that leverages diffusion models\nfor multi-modal fusion in 3D object detection and BEV map segmentation.\nBenefiting from the inherent denoising property of diffusion, DifFUSER is able\nto refine or even synthesize sensor features in case of sensor malfunction,\nthereby improving the quality of the fused output. In terms of architecture,\nour DifFUSER blocks are chained together in a hierarchical BiFPN fashion,\ntermed cMini-BiFPN, offering an alternative architecture for latent diffusion.\nWe further introduce a Gated Self-conditioned Modulated (GSM) latent diffusion\nmodule together with a Progressive Sensor Dropout Training (PSDT) paradigm,\ndesigned to add stronger conditioning to the diffusion process and robustness\nto sensor failures. Our extensive evaluations on the Nuscenes dataset reveal\nthat DifFUSER not only achieves state-of-the-art performance with a 69.1% mIOU\nin BEV map segmentation tasks but also competes effectively with leading\ntransformer-based fusion techniques in 3D object detection.",
+                    "authors": "Duy-Tho Le, Hengcan Shi, Jianfei Cai, Hamid Rezatofighi",
+                    "published": "2024-04-06",
+                    "updated": "2024-04-06",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/0805.0647v1",
+                    "title": "Scaling of Rough Surfaces: Effects of Surface Diffusion on Growth and Roughness Exponents",
+                    "abstract": "Random deposition model with surface diffusion over several next nearest\nneighbours is studied. The results agree with the results obtained by Family\nfor the case of nearest neighbour diffusion [F. Family, J. Phys. A 19(8), L441,\n1986]. However for larger diffusion steps, the growth exponent and the\nroughness exponent show interesting dependence on diffusion length.",
+                    "authors": "Baisakhi Mal, Subhankar Ray, J. Shamanna",
+                    "published": "2008-05-06",
+                    "updated": "2008-05-06",
+                    "primary_cat": "cond-mat.soft",
+                    "cats": [
+                        "cond-mat.soft",
+                        "cond-mat.stat-mech"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2111.03914v2",
+                    "title": "A systematic approach for modeling a nonlocal eddy diffusivity",
+                    "abstract": "This study considers advective and diffusive transport of passive scalar\nfields by spatially-varying incompressible flows. Prior studies have shown that\nthe eddy diffusivities governing the mean field transport in such systems can\ngenerally be nonlocal in space and time. While for many flows nonlocal eddy\ndiffusivities are more accurate than commonly-used Boussinesq eddy\ndiffusivities, nonlocal eddy diffusivities are often computationally\ncost-prohibitive to obtain and difficult to implement in practice. We develop a\nsystematic and more cost-effective approach for modeling nonlocal eddy\ndiffusivities using matched moment inverse (MMI) operators. These operators are\nconstructed using only a few leading-order moments of the exact nonlocal eddy\ndiffusivity kernel, which can be easily computed using the inverse macroscopic\nforcing method (IMFM) (Mani and Park (2021)). The resulting reduced-order\nmodels for the mean fields that incorporate the modeled eddy diffusivities\noften improve Boussinesq-limit models since they capture leading-order nonlocal\neffects. But more importantly, these models can be expressed as partial\ndifferential equations that are readily solvable using existing computational\nfluid dynamics capabilities rather than as integro-partial differential\nequations.",
+                    "authors": "Jessie Liu, Hannah Williams, Ali Mani",
+                    "published": "2021-11-06",
+                    "updated": "2023-06-28",
+                    "primary_cat": "physics.flu-dyn",
+                    "cats": [
+                        "physics.flu-dyn"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1701.00257v2",
+                    "title": "Analyzing PFG anisotropic anomalous diffusions by instantaneous signal attenuation method",
+                    "abstract": "Anomalous diffusion has been investigated in many systems. Pulsed field\ngradient (PFG) anomalous diffusion is much more complicated than PFG normal\ndiffusion. There have been many theoretical and experimental studies for PFG\nisotropic anomalous diffusion, but there are very few theoretical treatments\nreported for anisotropic anomalous diffusion. Currently, there is not a general\nPFG signal attenuation expression, which includes the finite gradient pulse\neffect and can treat all three types of anisotropic fractional diffusions:\ngeneral fractional diffusion, time fractional diffusion, and space-fractional\ndiffusion. In this paper, the recently developed instantaneous signal\nattenuation (ISA) method was applied to obtain PFG signal attenuation\nexpression for free and restricted anisotropic anomalous diffusion with two\nmodels: fractal derivative and fractional derivative models. The obtained PFG\nsignal attenuation expression for anisotropic anomalous diffusion can reduce to\nthe reported result for PFG anisotropic normal diffusion. The results can also\nreduce to reported PFG isotropic anomalous diffusion results obtained by\neffective phase shift diffusion equation method and instantaneous signal\nattenuation method. For anisotropic space-fractional diffusion, the obtained\nresult agrees with that obtained by the modified Bloch equation method.\nAdditionally, The PFG signal attenuation expressions for free and restricted\nanisotropic curvilinear diffusions were derived by the traditional method, the\nresults of which agree with the PFG anisotropic fractional diffusion results\nbased on the fractional derivative model. The powder pattern of PFG anisotropic\ndiffusion was also discussed. The results here improve our understanding of PFG\nanomalous diffusion, and provide new formalisms for PFG anisotropic anomalous\ndiffusion in NMR and MRI.",
+                    "authors": "Guoxing Lin",
+                    "published": "2017-01-01",
+                    "updated": "2017-01-05",
+                    "primary_cat": "physics.chem-ph",
+                    "cats": [
+                        "physics.chem-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1009.5965v1",
+                    "title": "Sensitivity of a Babcock-Leighton Flux-Transport Dynamo to Magnetic Diffusivity Profiles",
+                    "abstract": "We study the influence of various magnetic diffusivity profiles on the\nevolution of the poloidal and toroidal magnetic fields in a kinematic flux\ntransport dynamo model for the Sun. The diffusivity is a poorly understood\ningredient in solar dynamo models. We mathematically construct various\ntheoretical profiles of the depth-dependent diffusivity, based on constraints\nfrom mixing length theory and turbulence, and on comparisons of poloidal field\nevolution on the Sun with that from the flux-transport dynamo model.\n  We then study the effect of each diffusivity profile in the cyclic evolution\nof the magnetic fields in the Sun, by solving the mean-field dynamo equations.\nWe investigate effects on the solar cycle periods, the maximum tachocline field\nstrengths, and the evolution of the toroidal and poloidal field structures\ninside the convection zone, due to different diffusivity profiles.\n  We conduct three experiments: (I) comparing very different magnetic\ndiffusivity profiles; (II) comparing different locations of diffusivity\ngradient near the tachocline for the optimal profile; and (III) comparing\ndifferent slopes of diffusivity gradient for an optimal profile.\n  Based on these simulations, we discuss which aspects of depth-dependent\ndiffusivity profiles may be most relevant for magnetic flux evolution in the\nSun, and how certain observations could help improve knowledge of this dynamo\ningredient.",
+                    "authors": "E. J. Zita",
+                    "published": "2010-09-29",
+                    "updated": "2010-09-29",
+                    "primary_cat": "astro-ph.SR",
+                    "cats": [
+                        "astro-ph.SR",
+                        "physics.flu-dyn"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2303.16203v3",
+                    "title": "Your Diffusion Model is Secretly a Zero-Shot Classifier",
+                    "abstract": "The recent wave of large-scale text-to-image diffusion models has\ndramatically increased our text-based image generation abilities. These models\ncan generate realistic images for a staggering variety of prompts and exhibit\nimpressive compositional generalization abilities. Almost all use cases thus\nfar have solely focused on sampling; however, diffusion models can also provide\nconditional density estimates, which are useful for tasks beyond image\ngeneration. In this paper, we show that the density estimates from large-scale\ntext-to-image diffusion models like Stable Diffusion can be leveraged to\nperform zero-shot classification without any additional training. Our\ngenerative approach to classification, which we call Diffusion Classifier,\nattains strong results on a variety of benchmarks and outperforms alternative\nmethods of extracting knowledge from diffusion models. Although a gap remains\nbetween generative and discriminative approaches on zero-shot recognition\ntasks, our diffusion-based approach has significantly stronger multimodal\ncompositional reasoning ability than competing discriminative approaches.\nFinally, we use Diffusion Classifier to extract standard classifiers from\nclass-conditional diffusion models trained on ImageNet. Our models achieve\nstrong classification performance using only weak augmentations and exhibit\nqualitatively better \"effective robustness\" to distribution shift. Overall, our\nresults are a step toward using generative over discriminative models for\ndownstream tasks. Results and visualizations at\nhttps://diffusion-classifier.github.io/",
+                    "authors": "Alexander C. Li, Mihir Prabhudesai, Shivam Duggal, Ellis Brown, Deepak Pathak",
+                    "published": "2023-03-28",
+                    "updated": "2023-09-13",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI",
+                        "cs.CV",
+                        "cs.NE",
+                        "cs.RO"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2305.10028v1",
+                    "title": "Pyramid Diffusion Models For Low-light Image Enhancement",
+                    "abstract": "Recovering noise-covered details from low-light images is challenging, and\nthe results given by previous methods leave room for improvement. Recent\ndiffusion models show realistic and detailed image generation through a\nsequence of denoising refinements and motivate us to introduce them to\nlow-light image enhancement for recovering realistic details. However, we found\ntwo problems when doing this, i.e., 1) diffusion models keep constant\nresolution in one reverse process, which limits the speed; 2) diffusion models\nsometimes result in global degradation (e.g., RGB shift). To address the above\nproblems, this paper proposes a Pyramid Diffusion model (PyDiff) for low-light\nimage enhancement. PyDiff uses a novel pyramid diffusion method to perform\nsampling in a pyramid resolution style (i.e., progressively increasing\nresolution in one reverse process). Pyramid diffusion makes PyDiff much faster\nthan vanilla diffusion models and introduces no performance degradation.\nFurthermore, PyDiff uses a global corrector to alleviate the global degradation\nthat may occur in the reverse process, significantly improving the performance\nand making the training of diffusion models easier with little additional\ncomputational consumption. Extensive experiments on popular benchmarks show\nthat PyDiff achieves superior performance and efficiency. Moreover, PyDiff can\ngeneralize well to unseen noise and illumination distributions.",
+                    "authors": "Dewei Zhou, Zongxin Yang, Yi Yang",
+                    "published": "2023-05-17",
+                    "updated": "2023-05-17",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2206.12327v1",
+                    "title": "Source Localization of Graph Diffusion via Variational Autoencoders for Graph Inverse Problems",
+                    "abstract": "Graph diffusion problems such as the propagation of rumors, computer viruses,\nor smart grid failures are ubiquitous and societal. Hence it is usually crucial\nto identify diffusion sources according to the current graph diffusion\nobservations. Despite its tremendous necessity and significance in practice,\nsource localization, as the inverse problem of graph diffusion, is extremely\nchallenging as it is ill-posed: different sources may lead to the same graph\ndiffusion patterns. Different from most traditional source localization\nmethods, this paper focuses on a probabilistic manner to account for the\nuncertainty of different candidate sources. Such endeavors require overcoming\nchallenges including 1) the uncertainty in graph diffusion source localization\nis hard to be quantified; 2) the complex patterns of the graph diffusion\nsources are difficult to be probabilistically characterized; 3) the\ngeneralization under any underlying diffusion patterns is hard to be imposed.\nTo solve the above challenges, this paper presents a generic framework: Source\nLocalization Variational AutoEncoder (SL-VAE) for locating the diffusion\nsources under arbitrary diffusion patterns. Particularly, we propose a\nprobabilistic model that leverages the forward diffusion estimation model along\nwith deep generative models to approximate the diffusion source distribution\nfor quantifying the uncertainty. SL-VAE further utilizes prior knowledge of the\nsource-observation pairs to characterize the complex patterns of diffusion\nsources by a learned generative prior. Lastly, a unified objective that\nintegrates the forward diffusion estimation model is derived to enforce the\nmodel to generalize under arbitrary diffusion patterns. Extensive experiments\nare conducted on 7 real-world datasets to demonstrate the superiority of SL-VAE\nin reconstructing the diffusion sources by excelling other methods on average\n20% in AUC score.",
+                    "authors": "Chen Ling, Junji Jiang, Junxiang Wang, Liang Zhao",
+                    "published": "2022-06-24",
+                    "updated": "2022-06-24",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.IT",
+                        "math.IT"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2401.17181v1",
+                    "title": "Transfer Learning for Text Diffusion Models",
+                    "abstract": "In this report, we explore the potential for text diffusion to replace\nautoregressive (AR) decoding for the training and deployment of large language\nmodels (LLMs). We are particularly interested to see whether pretrained AR\nmodels can be transformed into text diffusion models through a lightweight\nadaptation procedure we call ``AR2Diff''. We begin by establishing a strong\nbaseline setup for training text diffusion models. Comparing across multiple\narchitectures and pretraining objectives, we find that training a decoder-only\nmodel with a prefix LM objective is best or near-best across several tasks.\nBuilding on this finding, we test various transfer learning setups for text\ndiffusion models. On machine translation, we find that text diffusion\nunderperforms the standard AR approach. However, on code synthesis and\nextractive QA, we find diffusion models trained from scratch outperform AR\nmodels in many cases. We also observe quality gains from AR2Diff -- adapting AR\nmodels to use diffusion decoding. These results are promising given that text\ndiffusion is relatively underexplored and can be significantly faster than AR\ndecoding for long text generation.",
+                    "authors": "Kehang Han, Kathleen Kenealy, Aditya Barua, Noah Fiedel, Noah Constant",
+                    "published": "2024-01-30",
+                    "updated": "2024-01-30",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2312.04410v1",
+                    "title": "Smooth Diffusion: Crafting Smooth Latent Spaces in Diffusion Models",
+                    "abstract": "Recently, diffusion models have made remarkable progress in text-to-image\n(T2I) generation, synthesizing images with high fidelity and diverse contents.\nDespite this advancement, latent space smoothness within diffusion models\nremains largely unexplored. Smooth latent spaces ensure that a perturbation on\nan input latent corresponds to a steady change in the output image. This\nproperty proves beneficial in downstream tasks, including image interpolation,\ninversion, and editing. In this work, we expose the non-smoothness of diffusion\nlatent spaces by observing noticeable visual fluctuations resulting from minor\nlatent variations. To tackle this issue, we propose Smooth Diffusion, a new\ncategory of diffusion models that can be simultaneously high-performing and\nsmooth. Specifically, we introduce Step-wise Variation Regularization to\nenforce the proportion between the variations of an arbitrary input latent and\nthat of the output image is a constant at any diffusion training step. In\naddition, we devise an interpolation standard deviation (ISTD) metric to\neffectively assess the latent space smoothness of a diffusion model. Extensive\nquantitative and qualitative experiments demonstrate that Smooth Diffusion\nstands out as a more desirable solution not only in T2I generation but also\nacross various downstream tasks. Smooth Diffusion is implemented as a\nplug-and-play Smooth-LoRA to work with various community models. Code is\navailable at https://github.com/SHI-Labs/Smooth-Diffusion.",
+                    "authors": "Jiayi Guo, Xingqian Xu, Yifan Pu, Zanlin Ni, Chaofei Wang, Manushree Vasu, Shiji Song, Gao Huang, Humphrey Shi",
+                    "published": "2023-12-07",
+                    "updated": "2023-12-07",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1905.04004v2",
+                    "title": "Well-posedness of a cross-diffusion population model with nonlocal diffusion",
+                    "abstract": "We prove the existence and uniqueness of solution of a nonlocal\ncross-diffusion competitive population model for two species. The model may be\nconsidered as a version, or even an approximation, of the paradigmatic\nShigesada-Kawasaki-Teramoto cross-diffusion model, in which the usual diffusion\ndifferential operator is replaced by an integral diffusion operator. The proof\nof existence of solutions is based on a compactness argument, while the\nuniqueness of solution is achieved through a duality technique.",
+                    "authors": "Gonzalo Galiano, Juli\u00e1n Velasco",
+                    "published": "2019-05-10",
+                    "updated": "2024-01-24",
+                    "primary_cat": "math.AP",
+                    "cats": [
+                        "math.AP"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2106.04745v2",
+                    "title": "Evaluation of diffuse mismatch model for phonon scattering at disordered interfaces",
+                    "abstract": "Diffuse phonon scattering strongly affects the phonon transport through a\ndisordered interface. The often-used diffuse mismatch model assumes that\nphonons lose memory of their origin after being scattered by the interface.\nUsing mode-resolved atomic Green's function simulation, we demonstrate that\ndiffuse phonon scattering by a single disordered interface cannot make a phonon\nlose its memory and thus the applicability of diffusive mismatch model is\nlimited. An analytical expression for diffuse scattering probability based on\nthe continuum approximation is also derived and shown to work reasonably well\nat low frequencies.",
+                    "authors": "Qichen Song, Gang Chen",
+                    "published": "2021-06-09",
+                    "updated": "2021-08-04",
+                    "primary_cat": "cond-mat.mes-hall",
+                    "cats": [
+                        "cond-mat.mes-hall"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1712.02290v2",
+                    "title": "Effects of nongaussian diffusion on \"isotropic diffusion measurements'': an ex-vivo microimaging and simulation study",
+                    "abstract": "Designing novel diffusion-weighted pulse sequences to probe tissue\nmicrostructure beyond the conventional Stejskal-Tanner family is currently of\nbroad interest. One such technique, multidimensional diffusion MRI, has been\nrecently proposed to afford model-free decomposition of diffusion signal\nkurtosis into terms originating from either ensemble variance of isotropic\ndiffusivity or microscopic diffusion anisotropy. This ability rests on the\nassumption that diffusion can be described as a sum of multiple Gaussian\ncompartments, but this is often not strictly fulfilled. The effects of\nnongaussian diffusion on single shot isotropic diffusion sequences were first\nconsidered in detail by de Swiet and Mitra in 1996. They showed theoretically\nthat anisotropic compartments lead to anisotropic time dependence of the\ndiffusion tensors, which causes the measured isotropic diffusivity to depend on\ngradient frame orientation. Here we show how such deviations from the multiple\nGaussian compartments assumption conflates orientation dispersion with ensemble\nvariance in isotropic diffusivity. Second, we consider additional contributions\nto the apparent variance in isotropic diffusivity arising due to\nintracompartmental kurtosis. These will likewise depend on gradient frame\norientation. We illustrate the potential importance of these confounds with\nanalytical expressions, numerical simulations in simple model geometries, and\nmicroimaging experiments in fixed spinal cord using isotropic diffusion\nencoding waveforms with 7.5 ms duration and 3000 mT/m maximum amplitude.",
+                    "authors": "Sune N\u00f8rh\u00f8j Jespersen, Jonas Lynge Olesen, Andrada Ianu\u015f, Noam Shemesh",
+                    "published": "2017-12-06",
+                    "updated": "2019-02-04",
+                    "primary_cat": "physics.bio-ph",
+                    "cats": [
+                        "physics.bio-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2304.05060v2",
+                    "title": "SPIRiT-Diffusion: Self-Consistency Driven Diffusion Model for Accelerated MRI",
+                    "abstract": "Diffusion models have emerged as a leading methodology for image generation\nand have proven successful in the realm of magnetic resonance imaging (MRI)\nreconstruction. However, existing reconstruction methods based on diffusion\nmodels are primarily formulated in the image domain, making the reconstruction\nquality susceptible to inaccuracies in coil sensitivity maps (CSMs). k-space\ninterpolation methods can effectively address this issue but conventional\ndiffusion models are not readily applicable in k-space interpolation. To\novercome this challenge, we introduce a novel approach called SPIRiT-Diffusion,\nwhich is a diffusion model for k-space interpolation inspired by the iterative\nself-consistent SPIRiT method. Specifically, we utilize the iterative solver of\nthe self-consistent term (i.e., k-space physical prior) in SPIRiT to formulate\na novel stochastic differential equation (SDE) governing the diffusion process.\nSubsequently, k-space data can be interpolated by executing the diffusion\nprocess. This innovative approach highlights the optimization model's role in\ndesigning the SDE in diffusion models, enabling the diffusion process to align\nclosely with the physics inherent in the optimization model, a concept referred\nto as model-driven diffusion. We evaluated the proposed SPIRiT-Diffusion method\nusing a 3D joint intracranial and carotid vessel wall imaging dataset. The\nresults convincingly demonstrate its superiority over image-domain\nreconstruction methods, achieving high reconstruction quality even at a\nsubstantial acceleration rate of 10.",
+                    "authors": "Zhuo-Xu Cui, Chentao Cao, Yue Wang, Sen Jia, Jing Cheng, Xin Liu, Hairong Zheng, Dong Liang, Yanjie Zhu",
+                    "published": "2023-04-11",
+                    "updated": "2024-04-20",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2404.08926v2",
+                    "title": "Diffusion Models Meet Remote Sensing: Principles, Methods, and Perspectives",
+                    "abstract": "As a newly emerging advance in deep generative models, diffusion models have\nachieved state-of-the-art results in many fields, including computer vision,\nnatural language processing, and molecule design. The remote sensing community\nhas also noticed the powerful ability of diffusion models and quickly applied\nthem to a variety of tasks for image processing. Given the rapid increase in\nresearch on diffusion models in the field of remote sensing, it is necessary to\nconduct a comprehensive review of existing diffusion model-based remote sensing\npapers, to help researchers recognize the potential of diffusion models and\nprovide some directions for further exploration. Specifically, this paper first\nintroduces the theoretical background of diffusion models, and then\nsystematically reviews the applications of diffusion models in remote sensing,\nincluding image generation, enhancement, and interpretation. Finally, the\nlimitations of existing remote sensing diffusion models and worthy research\ndirections for further exploration are discussed and summarized.",
+                    "authors": "Yidan Liu, Jun Yue, Shaobo Xia, Pedram Ghamisi, Weiying Xie, Leyuan Fang",
+                    "published": "2024-04-13",
+                    "updated": "2024-04-17",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2403.05794v2",
+                    "title": "Privacy-Preserving Diffusion Model Using Homomorphic Encryption",
+                    "abstract": "In this paper, we introduce a privacy-preserving stable diffusion framework\nleveraging homomorphic encryption, called HE-Diffusion, which primarily focuses\non protecting the denoising phase of the diffusion process. HE-Diffusion is a\ntailored encryption framework specifically designed to align with the unique\narchitecture of stable diffusion, ensuring both privacy and functionality. To\naddress the inherent computational challenges, we propose a novel\nmin-distortion method that enables efficient partial image encryption,\nsignificantly reducing the overhead without compromising the model's output\nquality. Furthermore, we adopt a sparse tensor representation to expedite\ncomputational operations, enhancing the overall efficiency of the\nprivacy-preserving diffusion process. We successfully implement HE-based\nprivacy-preserving stable diffusion inference. The experimental results show\nthat HE-Diffusion achieves 500 times speedup compared with the baseline method,\nand reduces time cost of the homomorphically encrypted inference to the minute\nlevel. Both the performance and accuracy of the HE-Diffusion are on par with\nthe plaintext counterpart. Our approach marks a significant step towards\nintegrating advanced cryptographic techniques with state-of-the-art generative\nmodels, paving the way for privacy-preserving and efficient image generation in\ncritical applications.",
+                    "authors": "Yaojian Chen, Qiben Yan",
+                    "published": "2024-03-09",
+                    "updated": "2024-05-02",
+                    "primary_cat": "cs.CR",
+                    "cats": [
+                        "cs.CR",
+                        "cs.AI"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1711.09967v2",
+                    "title": "CO diffusion and desorption kinetics in CO$_2$ ices",
+                    "abstract": "Diffusion of species in icy dust grain mantles is a fundamental process that\nshapes the chemistry of interstellar regions; yet measurements of diffusion in\ninterstellar ice analogs are scarce. Here we present measurements of CO\ndiffusion into CO$_2$ ice at low temperatures (T=11--23~K) using CO$_2$\nlongitudinal optical (LO) phonon modes to monitor the level of mixing of\ninitially layered ices. We model the diffusion kinetics using Fick's second law\nand find the temperature dependent diffusion coefficients are well fit by an\nArrhenius equation giving a diffusion barrier of 300 $\\pm$ 40 K. The low\nbarrier along with the diffusion kinetics through isotopically labeled layers\nsuggest that CO diffuses through CO$_2$ along pore surfaces rather than through\nbulk diffusion. In complementary experiments, we measure the desorption energy\nof CO from CO$_2$ ices deposited at 11-50 K by temperature-programmed\ndesorption (TPD) and find that the desorption barrier ranges from 1240 $\\pm$ 90\nK to 1410 $\\pm$ 70 K depending on the CO$_2$ deposition temperature and\nresultant ice porosity. The measured CO-CO$_2$ desorption barriers demonstrate\nthat CO binds equally well to CO$_2$ and H$_2$O ices when both are compact. The\nCO-CO$_2$ diffusion-desorption barrier ratio ranges from 0.21-0.24 dependent on\nthe binding environment during diffusion. The diffusion-desorption ratio is\nconsistent with the above hypothesis that the observed diffusion is a surface\nprocess and adds to previous experimental evidence on diffusion in water ice\nthat suggests surface diffusion is important to the mobility of molecules\nwithin interstellar ices.",
+                    "authors": "Ilsa R. Cooke, Karin I. \u00d6berg, Edith C. Fayolle, Zoe Peeler, Jennifer B. Bergner",
+                    "published": "2017-11-27",
+                    "updated": "2017-12-18",
+                    "primary_cat": "astro-ph.GA",
+                    "cats": [
+                        "astro-ph.GA"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2306.07491v2",
+                    "title": "Exact sharp-fronted solutions for nonlinear diffusion on evolving domains",
+                    "abstract": "Models of diffusive processes that occur on evolving domains are frequently\nemployed to describe biological and physical phenomena, such as diffusion\nwithin expanding tissues or substrates. Previous investigations into these\nmodels either report numerical solutions or require an assumption of linear\ndiffusion to determine exact solutions. Unfortunately, numerical solutions do\nnot reveal the relationship between the model parameters and the solution\nfeatures. Additionally, experimental observations typically report the presence\nof sharp fronts, which are not captured by linear diffusion. Here we address\nboth limitations by presenting exact sharp-fronted solutions to a model of\ndegenerate nonlinear diffusion on a growing domain. We obtain the solution by\nidentifying a series of transformations that converts the model of a nonlinear\ndiffusive process on an evolving domain to a nonlinear diffusion equation on a\nfixed domain, which admits known exact solutions for certain choices of\ndiffusivity functions. We determine expressions for critical time scales and\ndomain growth rates such that the diffusive population never reaches the domain\nboundaries and hence the solution remains valid.",
+                    "authors": "Stuart T. Johnston, Matthew J. Simpson",
+                    "published": "2023-06-13",
+                    "updated": "2023-10-06",
+                    "primary_cat": "q-bio.PE",
+                    "cats": [
+                        "q-bio.PE"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2312.14589v1",
+                    "title": "Non-Denoising Forward-Time Diffusions",
+                    "abstract": "The scope of this paper is generative modeling through diffusion processes.\nAn approach falling within this paradigm is the work of Song et al. (2021),\nwhich relies on a time-reversal argument to construct a diffusion process\ntargeting the desired data distribution. We show that the time-reversal\nargument, common to all denoising diffusion probabilistic modeling proposals,\nis not necessary. We obtain diffusion processes targeting the desired data\ndistribution by taking appropriate mixtures of diffusion bridges. The resulting\ntransport is exact by construction, allows for greater flexibility in choosing\nthe dynamics of the underlying diffusion, and can be approximated by means of a\nneural network via novel training objectives. We develop a unifying view of the\ndrift adjustments corresponding to our and to time-reversal approaches and make\nuse of this representation to inspect the inner workings of diffusion-based\ngenerative models. Finally, we leverage on scalable simulation and inference\ntechniques common in spatial statistics to move beyond fully factorial\ndistributions in the underlying diffusion dynamics. The methodological advances\ncontained in this work contribute toward establishing a general framework for\ngenerative modeling based on diffusion processes.",
+                    "authors": "Stefano Peluchetti",
+                    "published": "2023-12-22",
+                    "updated": "2023-12-22",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "stat.ML"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1908.03076v3",
+                    "title": "The strategy of survival for a competition between normal and anomalous diffusion",
+                    "abstract": "In this paper, we study the competition of two diffusion processes for\nachieving the maximum possible diffusion in an area. This competition, however,\ndoes not occur in the same circumstance; one of these processes is a normal\ndiffusion with a higher growth rate, and another one is an anomalous diffusion\nwith a lower growth rate. The trivial solution of the proposed model suggests\nthat the winner is the one with the higher growth rate. But, the question is:\nwhat characteristics and strategies should the second diffusion include to\nprolong the survival in such a competition? The studied diffusion equations\ncorrespond to the SI model such that the anomalous diffusion has memory\ndescribed by a fractional order derivative. The strategy promise that anomalous\ndiffusion reaches maximum survival in case of forgetting some parts of the\nmemory. This model can represent some of real phenomena, such as the contest of\ntwo companies in a market share, the spreading of two epidemic diseases, the\ndiffusion of two species, or any reaction-diffusion related to real-world\ncompetition.",
+                    "authors": "Moein Khalighi, Jamshid Ardalankia, Abbas Karimi Rizi, Haleh Ebadi, Gholamreza Jafari",
+                    "published": "2019-08-07",
+                    "updated": "2020-10-18",
+                    "primary_cat": "physics.soc-ph",
+                    "cats": [
+                        "physics.soc-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1409.3132v1",
+                    "title": "Front propagation in reaction-diffusion systems with anomalous diffusion",
+                    "abstract": "A numerical study of the role of anomalous diffusion in front propagation in\nreaction-diffusion systems is presented. Three models of anomalous diffusion\nare considered: fractional diffusion, tempered fractional diffusion, and a\nmodel that combines fractional diffusion and regular diffusion. The reaction\nkinetics corresponds to a Fisher-Kolmogorov nonlinearity. The numerical method\nis based on a finite-difference operator splitting algorithm with an explicit\nEuler step for the time advance of the reaction kinetics, and a Crank-Nicholson\nsemi-implicit time step for the transport operator. The anomalous diffusion\noperators are discretized using an upwind, flux-conserving, Grunwald-Letnikov\nfinite-difference scheme applied to the regularized fractional derivatives.\nWith fractional diffusion of order $\\alpha$, fronts exhibit exponential\nacceleration, $a_L(t) \\sim e^{\\gamma t/\\alpha}$, and develop algebraic decaying\ntails, $\\phi \\sim 1/x^{\\alpha}$. In the case of tempered fractional diffusion,\nthis phenomenology prevails in the intermediate asymptotic regime\n  $\\left(\\chi t \\right)^{1/\\alpha} \\ll x \\ll 1/\\lambda$, where $1/\\lambda$ is\nthe scale of the tempering. Outside this regime, i.e. for $x > 1/\\lambda$, the\ntail exhibits the tempered decay $\\phi \\sim e^{-\\lambda x}/x^{\\alpha+1}$, and\nthe front velocity approaches the terminal speed $v_*=\n\\left(\\gamma-\\lambda^\\alpha \\chi\\right)/ \\lambda$. Of particular interest is\nthe study of the interplay of regular and fractional diffusion. It is shown\nthat the main role of regular diffusion is to delay the onset of front\nacceleration. In particular, the crossover time, $t_c$, to transition to the\naccelerated fractional regime exhibits a logarithmic scaling of the form $t_c\n\\sim \\log \\left(\\chi_d/\\chi_f\\right)$ where $\\chi_d$ and $\\chi_f$ are the\nregular and fractional diffusivities.",
+                    "authors": "D. del-Castillo-Negrete",
+                    "published": "2014-09-10",
+                    "updated": "2014-09-10",
+                    "primary_cat": "nlin.PS",
+                    "cats": [
+                        "nlin.PS",
+                        "cond-mat.stat-mech"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2209.05557v3",
+                    "title": "Blurring Diffusion Models",
+                    "abstract": "Recently, Rissanen et al., (2022) have presented a new type of diffusion\nprocess for generative modeling based on heat dissipation, or blurring, as an\nalternative to isotropic Gaussian diffusion. Here, we show that blurring can\nequivalently be defined through a Gaussian diffusion process with non-isotropic\nnoise. In making this connection, we bridge the gap between inverse heat\ndissipation and denoising diffusion, and we shed light on the inductive bias\nthat results from this modeling choice. Finally, we propose a generalized class\nof diffusion models that offers the best of both standard Gaussian denoising\ndiffusion and inverse heat dissipation, which we call Blurring Diffusion\nModels.",
+                    "authors": "Emiel Hoogeboom, Tim Salimans",
+                    "published": "2022-09-12",
+                    "updated": "2024-05-01",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.CV",
+                        "stat.ML"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2005.00562v1",
+                    "title": "Unexpected crossovers in correlated random-diffusivity processes",
+                    "abstract": "The passive and active motion of micron-sized tracer particles in crowded\nliquids and inside living biological cells is ubiquitously characterised by\n\"viscoelastic\" anomalous diffusion, in which the increments of the motion\nfeature long-ranged negative and positive correlations. While viscoelastic\nanomalous diffusion is typically modelled by a Gaussian process with correlated\nincrements, so-called fractional Gaussian noise, an increasing number of\nsystems are reported, in which viscoelastic anomalous diffusion is paired with\nnon-Gaussian displacement distributions. Following recent advances in Brownian\nyet non-Gaussian diffusion we here introduce and discuss several possible\nversions of random-diffusivity models with long-ranged correlations. While all\nthese models show a crossover from non-Gaussian to Gaussian distributions\nbeyond some correlation time, their mean squared displacements exhibit\nstrikingly different behaviours: depending on the model crossovers from\nanomalous to normal diffusion are observed, as well as unexpected dependencies\nof the effective diffusion coefficient on the correlation exponent. Our\nobservations of the strong non-universality of random-diffusivity viscoelastic\nanomalous diffusion are important for the analysis of experiments and a better\nunderstanding of the physical origins of \"viscoelastic yet non-Gaussian\"\ndiffusion.",
+                    "authors": "Wei Wang, Flavio Seno, Igor M. Sokolov, Aleksei V. Chechkin, Ralf Metzler",
+                    "published": "2020-05-01",
+                    "updated": "2020-05-01",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech",
+                        "physics.bio-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1907.09989v1",
+                    "title": "Rogue Heat and Diffusion Waves",
+                    "abstract": "In this paper, we numerically show and discuss the existence and\ncharacteristics of rogue heat and diffusion waves. More specifically, we use\ntwo different nonlinear heat (diffusion) models and show that modulation\ninstability leads to the generation of unexpected and large fluctuations in the\nframe of these models. These fluctuations can be named as rogue heat\n(diffusion) waves. We discuss the properties and statistics of such rogue\nwaves. Our results can find many important applications in many branches such\nas the nonlinear heat transfer, turbulence, financial mathematics, chemical or\nbiological diffusion, nuclear reactions, subsurface water infiltration, and\npore water pressure diffusion modeled in the frame of nonlinear Terzaghi\nconsolidation models, just to name a few.",
+                    "authors": "Cihan Bayindir",
+                    "published": "2019-07-18",
+                    "updated": "2019-07-18",
+                    "primary_cat": "nlin.PS",
+                    "cats": [
+                        "nlin.PS",
+                        "physics.flu-dyn"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/astro-ph/0012545v1",
+                    "title": "Diffusion and the occurrence of hydrogen shell flashes in helium white dwarf stars",
+                    "abstract": "We investigate the effects of element diffusion on the structure and\nevolution of low-mass helium white dwarfs (WD). Attention is focused on the\noccurrence of hydrogen shell flashes induced by diffusion processes during\ncooling phases. Initial models from 0.406 to 0.161 solar masses are constructed\nby applying mass loss rates at different stages of the RGB evolution of a solar\nmodel. The multicomponent flow equations describing gravitational settling, and\nchemical and thermal diffusion are solved and the diffusion calculations are\ncoupled to an evolutionary code. In addition, the same sequences are computed\nbut neglecting diffusion. We find that element diffusion strongly affects the\nstructure and cooling history of helium WD. In particular, diffusion induces\nthe occurrence of hydrogen shell flashes in models with masses ranging from\n0.18 to 0.41 solar masses, which is in sharp contrast from the situation when\ndiffusion is neglected. In connection with the further evolution, these\ndiffusion-induced flashes lead to much thinner hydrogen envelopes, preventing\nstable nuclear burning from being an appreciable energy source at advanced\nstages of evolution. This implies much shorter cooling ages than in the case\nwhen diffusion is neglected. These new WD models are discussed in light of\nrecent observational data of some millisecond pulsar systems with WD\ncompanions. We find that age discrepancies between the predictions of standard\nevolutionary models and such observations appear to be the result of ignoring\nelement diffusion in such models. Indeed, such discrepancies vanish when\naccount is made of diffusion.",
+                    "authors": "L. G. Althaus, A. M. Serenelli, O. G. Benvenuto",
+                    "published": "2000-12-29",
+                    "updated": "2000-12-29",
+                    "primary_cat": "astro-ph",
+                    "cats": [
+                        "astro-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1210.5101v1",
+                    "title": "Global well-posedness and zero-diffusion limit of classical solutions to the 3D conservation laws arising in chemotaxis",
+                    "abstract": "In this paper, we study the relationship between a diffusive model and a\nnon-diffusive model which are both derived from the well-known Keller-Segel\nmodel, as a coefficient of diffusion $\\varepsilon$ goes to zero. First, we\nestablish the global well-posedness of classical solutions to the Cauchy\nproblem for the diffusive model with smooth initial data which is of small\n$L^2$ norm, together with some {\\it a priori} estimates uniform for $t$ and\n$\\varepsilon$. Then we investigate the zero-diffusion limit, and get the global\nwell-posedness of classical solutions to the Cauchy problem for the\nnon-diffusive model. Finally, we derive the convergence rate of the diffusive\nmodel toward the non-diffusive model. It is shown that the convergence rate in\n$L^\\infty$ norm is of the order $O(\\varepsilon^{1/2})$. It should be noted that\nthe initial data is small in $L^2$-norm but can be of large oscillations with\nconstant state at far field. As a byproduct, we improve the corresponding\nresult on the well-posedness of the non-difussive model which requires small\noscillations.",
+                    "authors": "Hongyun Peng, Huanyao Wen, Changjiang Zhu",
+                    "published": "2012-10-18",
+                    "updated": "2012-10-18",
+                    "primary_cat": "math.AP",
+                    "cats": [
+                        "math.AP"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/0910.2253v1",
+                    "title": "Linearized Kompaneetz equation as a relativistic diffusion",
+                    "abstract": "We show that Kompaneetz equation describing photon diffusion in an\nenvironment of an electron gas, when linearized around its equilibrium\ndistribution, coincides with the relativistic diffusion discussed in recent\npublications. The model of the relativistic diffusion is related to soluble\nmodels of imaginary time quantum mechanics. We suggest some non-linear\ngeneralizations of the relativistic diffusion equation and their astrophysical\napplications (in particular to the Sunyaev-Zeldovich effect).",
+                    "authors": "Z. Haba",
+                    "published": "2009-10-12",
+                    "updated": "2009-10-12",
+                    "primary_cat": "astro-ph.CO",
+                    "cats": [
+                        "astro-ph.CO"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2012.06816v1",
+                    "title": "Evaluation and Comparison of Diffusion Models with Motif Features",
+                    "abstract": "Diffusion models simulate the propagation of influence in networks. The\ndesign and evaluation of diffusion models has been subjective and empirical.\nWhen being applied to a network represented by a graph, the diffusion model\ngenerates a sequence of edges on which the influence flows, such sequence forms\na temporal network. In most scenarios, the statistical properties or the\ncharacteristics of a network are inferred by analyzing the temporal networks\ngenerated by diffusion models. To analyze real temporal networks, the motif has\nbeen proposed as a reliable feature. However, it is unclear how the network\ntopology and the diffusion model affect the motif feature of a generated\ntemporal network. In this paper, we adopt the motif feature to evaluate the\ntemporal graph generated by a diffusion model, thence the diffusion model\nitself. Two benchmarks for quantitively evaluating diffusion models with motif,\nstability and separability, are proposed and measured on numerous diffusion\nmodels. One motif-based metric is proposed to measure the similarity between\ndiffusion models. The experiments suggest that the motif of a generated\ntemporal network is dominated by the diffusion model, while the network\ntopology is almost ignored. This result indicates that more practical and\nreliable diffusion models have to be designed with delicacy in order to capture\nthe propagation patterns of real temporal networks.",
+                    "authors": "Fangqi Li",
+                    "published": "2020-12-12",
+                    "updated": "2020-12-12",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "cs.NI"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2305.12377v1",
+                    "title": "The vanishing diffusion limit for an Oldroyd-B model in $\\mathbb{R}^2_+$",
+                    "abstract": "We consider the initial-boundary value problem for an incompressible\nOldroyd-B model with stress diffusion in two-dimensional upper half plane which\ndescribes the motion of viscoelastic polymeric fluids. From the physical point\nof view, the diffusive coefficient is several orders of magnitude smaller than\nother parameters in the model, and is usually assumed to be zero. However, the\nlink between the diffusive model and the standard one (zero diffusion) via\nvanishing diffusion limit is still unknown from the mathematical point of view,\nin particular for the problem with boundary. Some numerical results [13]\nsuggest that this should be true. In this work, we provide a rigorous\njustification for the vanishing diffusion in $L^\\infty$-norm.",
+                    "authors": "Yinghui Wang, Huanyao Wen",
+                    "published": "2023-05-21",
+                    "updated": "2023-05-21",
+                    "primary_cat": "math.AP",
+                    "cats": [
+                        "math.AP",
+                        "35Q35, 76A10, 76D10"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/math/0204289v1",
+                    "title": "On diffusion approximation with discontinuous coefficients",
+                    "abstract": "Convergence of stochastic processes with jumps to diffusion processes is\ninvestigated in the case when the limit process has discontinuous coefficients.\n  An example is given in which the diffusion approximation of a queueing model\nyields a diffusion process with discontinuous diffusion and drift coefficients.",
+                    "authors": "N. V. Krylov, R. Liptser",
+                    "published": "2002-04-24",
+                    "updated": "2002-04-24",
+                    "primary_cat": "math.PR",
+                    "cats": [
+                        "math.PR",
+                        "math.SG",
+                        "60B10; 60K25}"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1709.05336v1",
+                    "title": "Cs diffusion in SiC high-energy grain boundaries",
+                    "abstract": "Cesium (Cs) is a radioactive fission product whose release is of concern for\nTristructural-Isotropic (TRISO) fuel particles. In this work, Cs diffusion\nthrough high energy grain boundaries (HEGBs) of cubic-SiC is studied using an\nab-initio based kinetic Monte Carlo (kMC) model. The HEGB environment was\nmodeled as an amorphous SiC (a-SiC), and Cs defect energies were calculated\nusing density functional theory (DFT). From defect energies, it was suggested\nthat the fastest diffusion mechanism as Cs interstitial in an amorphous SiC.\nThe diffusion of Cs interstitial was simulated using a kMC, based on the site\nand transition state energies sampled from the DFT. The Cs HEGB diffusion\nexhibited an Arrhenius type diffusion in the range of 1200-1600{\\deg}C. The\ncomparison between HEGB results and the other studies suggests not only that\nthe GB diffusion dominates the bulk diffusion, but also that the HEGB is one of\nthe fastest grain boundary paths for the Cs diffusion. The diffusion\ncoefficients in HEGB are clearly a few orders of magnitude lower than the\nreported diffusion coefficients from in- and out-of- pile samples, suggesting\nthat other contributions are responsible, such as a radiation enhanced\ndiffusion.",
+                    "authors": "Hyunseok Ko, Izabela Szlufarska, Dane Morgan",
+                    "published": "2017-09-11",
+                    "updated": "2017-09-11",
+                    "primary_cat": "cond-mat.mtrl-sci",
+                    "cats": [
+                        "cond-mat.mtrl-sci",
+                        "nucl-th"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2305.08379v2",
+                    "title": "TESS: Text-to-Text Self-Conditioned Simplex Diffusion",
+                    "abstract": "Diffusion models have emerged as a powerful paradigm for generation,\nobtaining strong performance in various continuous domains. However, applying\ncontinuous diffusion models to natural language remains challenging due to its\ndiscrete nature and the need for a large number of diffusion steps to generate\ntext, making diffusion-based generation expensive. In this work, we propose\nText-to-text Self-conditioned Simplex Diffusion (TESS), a text diffusion model\nthat is fully non-autoregressive, employs a new form of self-conditioning, and\napplies the diffusion process on the logit simplex space rather than the\nlearned embedding space. Through extensive experiments on natural language\nunderstanding and generation tasks including summarization, text\nsimplification, paraphrase generation, and question generation, we demonstrate\nthat TESS outperforms state-of-the-art non-autoregressive models, requires\nfewer diffusion steps with minimal drop in performance, and is competitive with\npretrained autoregressive sequence-to-sequence models. We publicly release our\ncodebase at https://github.com/allenai/tess-diffusion.",
+                    "authors": "Rabeeh Karimi Mahabadi, Hamish Ivison, Jaesung Tae, James Henderson, Iz Beltagy, Matthew E. Peters, Arman Cohan",
+                    "published": "2023-05-15",
+                    "updated": "2024-02-21",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL",
+                        "cs.LG"
+                    ],
+                    "category": "Diffusion AND Model"
+                }
+            ],
+            [
+                {
+                    "url": "http://arxiv.org/abs/2404.14700v3",
+                    "title": "FlashSpeech: Efficient Zero-Shot Speech Synthesis",
+                    "abstract": "Recent progress in large-scale zero-shot speech synthesis has been\nsignificantly advanced by language models and diffusion models. However, the\ngeneration process of both methods is slow and computationally intensive.\nEfficient speech synthesis using a lower computing budget to achieve quality on\npar with previous work remains a significant challenge. In this paper, we\npresent FlashSpeech, a large-scale zero-shot speech synthesis system with\napproximately 5\\% of the inference time compared with previous work.\nFlashSpeech is built on the latent consistency model and applies a novel\nadversarial consistency training approach that can train from scratch without\nthe need for a pre-trained diffusion model as the teacher. Furthermore, a new\nprosody generator module enhances the diversity of prosody, making the rhythm\nof the speech sound more natural. The generation processes of FlashSpeech can\nbe achieved efficiently with one or two sampling steps while maintaining high\naudio quality and high similarity to the audio prompt for zero-shot speech\ngeneration. Our experimental results demonstrate the superior performance of\nFlashSpeech. Notably, FlashSpeech can be about 20 times faster than other\nzero-shot speech synthesis systems while maintaining comparable performance in\nterms of voice quality and similarity. Furthermore, FlashSpeech demonstrates\nits versatility by efficiently performing tasks like voice conversion, speech\nediting, and diverse speech sampling. Audio samples can be found in\nhttps://flashspeech.github.io/.",
+                    "authors": "Zhen Ye, Zeqian Ju, Haohe Liu, Xu Tan, Jianyi Chen, Yiwen Lu, Peiwen Sun, Jiahao Pan, Weizhen Bian, Shulin He, Qifeng Liu, Yike Guo, Wei Xue",
+                    "published": "2024-04-23",
+                    "updated": "2024-04-25",
+                    "primary_cat": "eess.AS",
+                    "cats": [
+                        "eess.AS",
+                        "cs.AI",
+                        "cs.CL",
+                        "cs.LG",
+                        "cs.SD"
+                    ],
+                    "label": "Original Paper",
+                    "paper_cat": "Diffusion AND Model",
+                    "gt": "2.1 Large-Scale Speech Synthesis Motivated by the success of the large language model, the speech research community has recently shown increasing interest in scaling the sizes of model and training data to bolster generalization capabilities, producing natural speech with diverse speaker identities and prosody under zero-shot settings. The pioneering work is VALL-E Wang et al. (2023a), which adopts the Encodec D\u00e9fossez et al. (2022) to discretize the audio waveform into tokens. Therefore, a language model can be trained via in-context learning that can generate the target utterance where the style is consistent with prompt utterance. However, generating audio in such an autoregressive manner Wang et al. (2023b); Peng et al. (2024)can lead to unstable prosody, word skipping, and repeating issues Ren et al. (2020); Tan et al. (2021); Shen et al. (2024). To ensure the robustness of the system, non-autoregressive methods such as NaturalSpeech2 Shen et al. (2024) and Voicebox Le et al. (2023) utilize diffusion-style model (VP-diffusion Song et al. (2020) or flow-matching Lipman et al. (2022)) to learn the distribution of a continuous intermediate vector such as mel-spectrogram or latent vector of codec. Both LM-based methods Zhao et al. (2023) and diffusion-based methods show superior performance in speech generation tasks. However, their generation is slow due to the iterative computation. Considering that many speech generation scenarios require real-time inference and low computational costs, we employ the latent consistency model for large-scale speech generation that inference with one or two steps while maintaining high audio quality. 2.2 Acceleration of Speech Synthesis Since early neural speech generation models Tan et al. (2021) use autoregressive models such as Tacotron Wang et al. (2017) and TransformerTTS Li et al. (2019), causing slow inference speed, with O(N) computation, where N is the sequence length. To address the slow inference speed, FastSpeech Ren et al. (2020, 2019) proposes to generate a mel-spectrogram in a non-autoregressive manner. However, these models Ren et al. (2022) result in blurred and over-smoothed mel-spectrograms due to the regression loss they used and the capability of modeling methods. To further enhance the speech quality, diffusion models are utilized Popov et al. (2021a); Jeong et al. (2021); Popov et al. (2021b) which increase the computation to O(T), where T is the diffusion steps. Therefore, distillation techniques Luo (2023) for diffusion-based methods such as CoMoSpeech Ye et al. (2023), CoMoSVC Lu et al. (2024) and Reflow-TTS Guan et al. (2023) emerge to reduce the sampling steps back to O(1), but require additional pre-trained diffusion as the teacher model. Unlike previous distillation techniques, which require extra training for the diffusion model as a teacher and are limited by its performance, our proposed adversarial consistency training technique can directly train from scratch, significantly reducing training costs. In addition, previous acceleration methods only validate speaker-limited recording-studio datasets with limited data diversity. To the best of our knowledge, FlashSpeech is the first work that reduces the computation of a large-scale speech generation system back to O(1). 2.3 Consistency Model The consistency model is proposed in Song et al. (2023); Song and Dhariwal (2023) to generate high-quality samples by directly mapping noise to data. Furthermore, many variants Kong et al. (2023); Lu et al. (2023); Sauer et al. (2023); Kim et al. (2023a) are proposed to further increase the generation quality of images. The latent consistency model is proposed by Luo et al. (2023) which can directly predict the solution of PF-ODE in latent space. However, the original LCM employs consistency distillation on the pre-trained latent diffusion model (LDM) which leverages large-scale off-the-shelf image diffusion models Rombach et al. (2022). Since there are no pre-trained large-scale TTS models in the speech community, and inspired by the techniques Song and Dhariwal (2023); 3 Kim et al. (2023a); Lu et al. (2023); Sauer et al. (2023); Kong et al. (2023), we propose the novel adversarial consistency training method which can directly train the large-scale latent consistency model from scratch utilizing the large pre-trained speech language model Chen et al. (2022b); Hsu et al. (2021); Baevski et al. (2020) such as WavLM for speech generation.",
+                    "pre_questions": [],
+                    "main_content": "Introduction In recent years, the landscape of speech synthesis has been transformed by the advent of large-scale generative models. Consequently, the latest research efforts have achieved notable advancements in zero-shot speech synthesis systems by significantly increasing the size of both datasets and models. Zero-shot speech synthesis, such as text-to-speech (TTS), voice conversion (VC) and Editing, aims to generate speech that incorporates unseen speaker characteristics from a reference audio segment during inference, without the need for additional training. Current advanced zero-shot speech synthesis systems typically leverage language models (LMs) Wang et al. (2023a); Yang et al. (2023); Zhang et al. (2023); Kharitonov et al. (2023); Wang et al. (2023b); Peng et al. (2024); Kim et al. (2024) and diffusion-style models Shen et al. (2024); Kim et al. (2023b); Le et al. (2023); Jiang et al. (2023b) for in-context speech generation on the large-scale dataset. However, the generation process of these methods needs a long-time iteration. For example, VALL-E Wang et al. (2023a) builds on the language model to predict 75 audio token sequences for a 1-second speech, in its first-stage autoregressive (AR) token sequence generation. When using a non-autoregressive (NAR) latent diffusion model Rombach et al. (2022) based framework, NaturalSpeech 2 Shen et al. (2024) still requires 150 sampling steps. As a result, although these methods can produce human-like speech, they require significant computational time and cost. Some efforts have been made to accelerate the Preprint. Under review. \u2020: Corresponding authors. arXiv:2404.14700v3  [eess.AS]  25 Apr 2024 Figure 1: The inference time comparisons of different zero-shot speech synthesis systems using the real-time factor (RTF). generation process. Voicebox Le et al. (2023) adopts flow-matching Lipman et al. (2022) so that fewer sampling steps (NFE1: 64) can be achieved because of the optimal transport path. ClaM-TTS Kim et al. (2024) proposes a mel-codec with a superior compression rate and a latent language model that generates a stack of tokens at once. Although the slow generation speed issue has been somewhat alleviated, the inference speed is still far from satisfactory for practical applications. Moreover, the substantial computational time of these approaches leads to significant computational cost overheads, presenting another challenge. The fundamental limitation of speech generation stems from the intrinsic mechanisms of language models and diffusion models, which require considerable time either auto-regressively or through a large number of denoising steps. Hence, the primary objective of this work is to accelerate inference speed and reduce computational costs while preserving generation quality at levels comparable to the prior research. In this paper, we propose FlashSpeech as the next step towards efficient zeroshot speech synthesis. To address the challenge of slow generation speed, we leverage the latent consistency model (LCM) Luo et al. (2023), a recent advancement in generative models. Building upon the previous non-autoregressive TTS system Shen et al. (2024), we adopt the encoder of a neural audio codec to convert speech waveforms into latent vectors as the training target for our LCM. To train this model, we propose a novel technique called adversarial consistency training, which utilizes the capabilities of pre-trained speech language models Chen et al. (2022b); Hsu et al. (2021); Baevski et al. (2020) as discriminators. This facilitates the transfer of knowledge from large pre-trained speech language models to speech generation tasks, efficiently integrating adversarial and consistency training to improve performance. The LCM is conditioned on prior vectors obtained from a phoneme encoder, a prompt encoder, and a prosody generator. Furthermore, we demonstrate that our proposed prosody generator leads to more diverse expressions and prosody while preserving stability. Our contributions can be summarized as follows: \u2022 We propose FlashSpeech, an efficient zero-shot speech synthesis system that generates voice with high audio quality and speaker similarity in zero-shot scenarios. \u2022 We introduce adversarial consistency training, a novel combination of consistency and adversarial training leveraging pre-trained speech language models, for training the latent consistency model from scratch, achieving speech generation in one or two steps. 1NFE: number of function evaluations. 2 \u2022 We propose a prosody generator module that enhances the diversity of prosody while maintaining stability. \u2022 FlashSpeech significantly outperforms strong baselines in audio quality and matches them in speaker similarity. Remarkably, it achieves this at a speed approximately 20 times faster than comparable systems, demonstrating unprecedented efficiency. Codec Encoder Codec Decoder Phoneme Codec Decoder Synthesized Speech ynthesize Speech Raw Speech Reconstructed Speech construct Speech Latent Consistency Model Latent Vector Z Conditional Feature Noise Encoder \ud835\udc33\ud835\udc91\ud835\udc93\ud835\udc90\ud835\udc8e\ud835\udc91\ud835\udc95 \ud835\udc33\ud835\udc95\ud835\udc82\ud835\udc93\ud835\udc88\ud835\udc86\ud835\udc95 Random Segment \u0ddc \ud835\udc9b\ud835\udc95\ud835\udc82\ud835\udc93\ud835\udc88\ud835\udc86\ud835\udc95 \ud835\udc33\ud835\udc91\ud835\udc93\ud835\udc90\ud835\udc8e\ud835\udc91\ud835\udc95 Prosody Generator Discriminator Real / Fake Figure 2: Overall architecture of FlashSpeech. Our FlashSpeech consists of a codec encoder/decoder and a latent consistency model conditioned on feature from a phoneme and zprompt encoder and a prosody generator. A discriminator is used during training. 3.1 Overview Our work is dedicated to advancing the speech synthesis efficiency, achieving O(1) computation cost while maintaining comparable performance to prior studies that require O(T) or O(N) computations. The framework of the proposed method, FlashSpeech, is illustrated in Fig. 2. FlashSpeech integrates a neural codec, an encoder for phonemes and prompts, a prosody generator, and an LCM, which are utilized during both the training and inference stages. Exclusively during training, a conditional discriminator is employed. FlashSpeech adopts the in-context learning paradigm Wang et al. (2023a), initially segmenting the latent vector z, extracted from the codec, into ztarget and zprompt. Subsequently, the phoneme and zprompt are processed through the encoder to produce the hidden feature. A prosody generator then predicts pitch and duration based on the hidden feature. The pitch and duration embeddings are combined with the hidden feature and inputted into the LCM as the conditional feature. The LCM model is trained from scratch using adversarial consistency training. After training, FlashSpeech can achieve efficient generation within one or two sampling steps. 3.2 Latent Consistency Model The consistency model Song et al. (2023) is a new family of generative models that enables one-step or few-step generation. Let us denote the data distribution by pdata(x). The core idea of the consistency model is to learn the function that maps any points on a trajectory of the PF-ODE to that trajectory\u2019s origin, which can be formulated as: f(x\u03c3, \u03c3) = x\u03c3min (1) where f(\u00b7, \u00b7) is the consistency function and x\u03c3 represents the data x perturbed by adding zero-mean Gaussian noise with standard deviation \u03c3. \u03c3min is a fixed small positive number. Then x\u03c3min can then be viewed as an approximate sample from the data distribution pdata(x). To satisfy property in equation (1), following Song et al. (2023), we parameterize the consistency model as f\u03b8(x\u03c3, \u03c3) = cskip(\u03c3)x + cout(\u03c3)F\u03b8(x\u03c3, \u03c3) (2) 4 where f\u03b8 is to estimate consistency function f by learning from data, F\u03b8 is a deep neural network with parameter \u03b8, cskip(\u03c3) and cout(\u03c3) are are differentiable functions with cskip(\u03c3min) = 1 and cout(\u03c3min) = 0 to ensure boundary condition. A valid consistency model should satisfy the selfconsistency property Song et al. (2023) f\u03b8(x\u03c3, \u03c3) = f\u03b8(x\u03c3\u2032, \u03c3\u2032), \u2200\u03c3, \u03c3\u2032 \u2208[\u03c3min, \u03c3max]. (3) where \u03c3max = 80 and \u03c3min = 0.002 following Karras et al. (2022); Song et al. (2023); Song and Dhariwal (2023). Then the model can generate samples in one step by evaluating x\u03c3min = f\u03b8(x\u03c3max, \u03c3max) (4) from distribution x\u03c3max \u223cN(0, \u03c32 maxI). As we apply a consistency model on the latent space of audio, we use the latent features z which are extracted prior to the residual quantization layer of the codec, z = CodecEncoder(y) (5) where y is the speech waveform. Furthermore, we add the feature from the prosody generator and encoder as the conditional feature c, our objective has changed to achieve f\u03b8(z\u03c3, \u03c3, c) = f\u03b8(z\u03c3\u2032, \u03c3\u2032, c) \u2200\u03c3, \u03c3\u2032 \u2208[\u03c3min, \u03c3max]. (6) During inference, the synthesized waveform \u02c6 y is transformed from \u02c6 z via the codec decoder. The predicted \u02c6 z is obtained by one sampling step \u02c6 z = f\u03b8(\u03f5 \u2217\u03c3max, \u03c3max) (7) or two sampling steps \u02c6 zinter = f\u03b8(\u03f5 \u2217\u03c3max, \u03c3max) (8) \u02c6 z = f\u03b8(\u02c6 zinter + \u03f5 \u2217\u03c3inter, \u03c3inter) (9) where \u02c6 zinter means the intermediate step, \u03c3inter is set to 2 empirically. \u03f5 is sampled from a standard Gaussian distribution. 3.3 Adversarial Consistency Training A major drawback of the LCM Luo et al. (2023) is that it needs to pre-train a diffusion-based teacher model in the first stage, and then perform distillation to produce the final model. This would make the training process complicated, and the performance would be limited as a result of the distillation. To eliminate the reliance on the teacher model training, in this paper, we propose a novel adversarial consistency training method to train LCM from scratch. Our training procedure is outlined in Fig. 3, which has three parts: 3.3.1 Consistency Training To achieve the property in equation (3), we adopt following consistency loss LN ct(\u03b8, \u03b8\u2212) = E[\u03bb(\u03c3i)d(f\u03b8(zi+1, \u03c3i+1, c), f\u03b8\u2212(zi, \u03c3i, c))]. (10) where \u03c3i represents the noise level at discrete time step i, d(\u00b7, \u00b7) is the distance function, f\u03b8(zi+1, \u03c3i+1, c) and f\u03b8\u2212(zi, \u03c3i, c) are the student with the higher noise level and the teacher with the lower noise level, respectively. The discrete time steps denoted as \u03c3min = \u03c30 < \u03c31 < \u00b7 \u00b7 \u00b7 < \u03c3N = \u03c3max are divided from the time interval [\u03c3min, \u03c3max], where the discretization curriculum N increases correspondingly as the number of training steps grows N(k) = min(s02\u230ak K\u2032 \u230b, s1) + 1 (11) where K\u2032 = j K log2\u230as1/s0\u230b+1 k , k is the current training step and K is the total training steps. s1 and s0 are hyperparameters to control the size of N(k). The distance function d(\u00b7, \u00b7) uses the Pseudo-Huber metric Charbonnier et al. (1997) d(x, y) = p \u2225x \u2212y\u22252 + a2 \u2212a, (12) 5 Denoiser Denoiser                      \uf071\u2212 \uf071 Student Teacher Consistency Loss Discriminator Adversarial Loss Stop Grad \\\\ \ud835\udc33\ud835\udf0e\ud835\udc56+1 \ud835\udc33\ud835\udf0e\ud835\udc56 \ud835\udc33 Codec Decoder waveform \ud835\udc53 \ud835\udf03(\ud835\udc33\ud835\udf0e\ud835\udc56+1, \ud835\udf0e\ud835\udc56+1, c) \ud835\udc53 \ud835\udf03(\ud835\udc33\ud835\udf0e\ud835\udc56, \ud835\udf0e\ud835\udc56,c) \u0ddc \ud835\udc33 Figure 3: An illustration of adversarial consistency training. where a is an adjustable constant, making the training more robust to outliers as it imposes a smaller penalty for large errors than \u21132 loss. The parameters \u03b8\u2212of teacher model are \u03b8\u2212\u2190 \u2212stopgrad(\u03b8), (13) which are identical to the student parameters \u03b8. This approach Song and Dhariwal (2023) has been demonstrated to improve sample quality of previous strategies that employ varying decay rates Song et al. (2023). The weighting function refers to \u03bb(\u03c3i) = 1 \u03c3i+1 \u2212\u03c3i (14) which emphasizes the loss of smaller noise levels. LCM through consistency training can generate speech with acceptable quality in a few steps, but it still falls short of previous methods. Therefore, to further enhance the quality of the generated samples, we integrate adversarial training. 3.3.2 Adversarial Training For the adversarial objective, the generated samples \u02c6 z \u2190f\u03b8(z\u03c3, \u03c3, c) and real samples z are passed to the discriminator D\u03b7 which aims to distinguish between them, where \u03b7 refers to the trainable parameters. Thus, we employ adversarial training loss Ladv(\u03b8, \u03b7) = Ez[log D\u03b7(z)] + E\u03c3Ez\u03c3[log(1 \u2212D\u03b7(f\u03b8(z\u03c3, \u03c3, c)))]. (15) In this way, the error signal from the discriminator guides f\u03b8 to produce more realistic outputs. For details, we use a frozen pre-trained speech language model SLM and a trainable lightweight discriminator head Dhead to build the discriminator. Since the current SLM is trained on the speech waveform, we covert both z and \u02c6 z to ground truth waveform and predicted waveform using the codec decoder. To further increase the similarity between prompt audio and generated audio, our discriminator is conditioned on the prompt audio feature. This prompt feature Fprompt is extracted using SLM on prompt audio and applies average pooling on the time axis. Therefore, D\u03b7 = Dhead(Fprompt \u2299Fgt, Fprompt \u2299Fpred) (16) where Fgt and Fpred refer to feature extracted through SLM for ground truth waveform and predicted waveform. The discriminator head consists of several 1D convolution layers. The input feature of the discriminator is conditioned on Fprompt via projection Miyato and Koyama (2018). 3.3.3 Combined Together Since there is a large gap on the loss scale between consistency loss and adversarial loss, it can lead to instability and failure in training. Therefore, we follow Esser et al. (2021) to compute the adaptive weight with \u03bbadv = \u2225\u2207\u03b8LLN ct (\u03b8, \u03b8\u2212)\u2225 \u2225\u2207\u03b8LLadv(\u03b8, \u03b7)\u2225 (17) where \u03b8L is the last layer of the neural network in LCM. The final loss of training LCM is defined as LN ct (\u03b8, \u03b8\u2212)+\u03bbadvLadv(\u03b8, \u03b7). This adaptive weighting significantly stabilizes the training by balancing the gradient scale of each term. 6 Prosody  Regression Prosody  Refinement Initial  Prediction Residual + Prosody  Feature Predicted Prosody  Noise deterministic stochastic \ud835\udf36 \u2217Residual Figure 4: An illustration of prosody generator. 3.4 Prosody Generator 3.4.1 Analysis of Prosody Prediction Previous regression methods for prosody prediction Ren et al. (2020); Shen et al. (2024), due to their deterministic mappings and assumptions of unimodal distribution, often fail to capture the inherent diversity and expressiveness of human speech prosody. This leads to predictions that lack variation and can appear over-smoothed. On the other hand, diffusion methods Le et al. (2023); Li et al. (2023) for prosody prediction offer a promising alternative by providing greater prosody diversity. However, they come with challenges regarding stability, and the potential for unnatural prosody. Additionally, the iterative inference process in DMs requires a significant number of sampling steps that may also hinder real-time application. Meanwhile, LM-based methods Jiang et al. (2024a); Wang et al. (2023a) also need a long time for inference. To alleviate these issues, our prosody generator consists of a prosody regression module and a prosody refinement module to enhance the diversity of prosody regression results with efficient one-step consistency model sampling. 3.4.2 Prosody Refinement via Consistency Model As shown in 4, our prosody generator consists of two parts which are prosody regression and prosody refinement. We first train the prosody regression module to get a deterministic output. Next, we freeze the parameters of the prosody regression module and use the residual of ground truth prosody and deterministic predicted prosody as the training target for prosody refinement. We adopt a consistency model as a prosody refinement module. The conditional feature of the consistency model is the feature from prosody regression before the final projection layer. Thus, the residual from a stochastic sampler refines the output of a deterministic prosody regression and produces a diverse set of plausible prosody under the same transcription and audio prompt. One option for the final prosody output pfinal can be represented as: pfinal = pres + pinit, (18) where pfinal denotes the final prosody output, pres represents the residual output from the prosody refinement module, capturing the variations between the ground truth prosody and the deterministic prediction, pinit is the initial deterministic prosody prediction from the prosody regression module. However, this formulation may negatively affect prosody stability, a similar observation is found in Vyas et al. (2023); Le et al. (2023). More specifically, higher diversity may cause less stability and sometimes produce unnatural prosody. To address this, we introduce a control factor \u03b1 that finely tunes the balance between stability and diversity in the prosodic output: pfinal = \u03b1pres + pinit (19) where \u03b1 is a scalar value ranging between 0 and 1. This adjustment allows for controlled incorporation of variability into the prosody, mitigating issues related to stability while still benefiting from the diversity offered by the prosody refinement module. 3.5 Applications This section elaborates on the practical applications of FlashSpeech. We delve into its deployment across various tasks such as zero-shot TTS, speech editing, voice conversion, and diverse speech sampling. All the sample audios of applications are available on the demo page. 7 3.5.1 Zero-Shot TTS Given a target text and reference audio, we first convert the text to phoneme using g2p (grapheme-tophoneme conversion). Then we use the codec encoder to convert the reference audio into zprompt. Speech can be synthesized efficiently through FlashSpeech with the phoneme input and zprompt, achieving high-quality text-to-speech results without requiring pre-training on the specific voice. 3.5.2 Voice Conversion Voice conversion aims to convert the source audio into the target audio using the speaker\u2019s voice of the reference audio. Following Shen et al. (2024); Preechakul et al. (2022), we first apply the reverse of ODE to diffuse the source audio into a starting point that still maintains some information in the source audio. After that, we run the sampling process from this starting point with the reference audio as zprompt and condition c. The condition c uses the phoneme and duration from the source audio and the pitch is predicted by the prosody generator. This method allows for zero-shot voice conversion while preserving the linguistic content of the source audio, and achieving the same timbre as the reference audio. 3.5.3 Speech Editing Given the speech, the original transcription, and the new transcription, we first use MFA (Montreal Forced Aligner) to align the speech and the original transcription to get the duration of each word. Then we remove the part that needs to be edited to construct the reference audio. Next, we use the new transcription and reference to synthesize new speech. Since this task is consistent with the in-context learning, we can concatenate the remaining part of the raw speech and the synthesized part as the final speech, thus enabling precise and seamless speech editing. 3.5.4 Diverse Speech Sampling FlashSpeech leverages its inherent stochasticity to generate a variety of speech outputs under the same conditions. By employing stochastic sampling in its prosody generation and LCM, FlashSpeech can produce diverse variations in pitch, duration, and overall audio characteristics from the same phoneme input and audio prompt. This feature is particularly useful for generating a wide range of speech expressions and styles from a single input, enhancing applications like voice acting, synthetic voice variation for virtual assistants, and more personalized speech synthesis. In addition, the synthetic data via speech sampling can also benefit other tasks such as ASR Rossenbach et al. (2020). 4 Experiment Table 1: The evaluation results for FlashSpeech and the baseline methods on LibriSpeech testclean. \u22c6 means the evaluation is conducted with 1 NVIDIA V100 GPU. \u2662means the device is not available. Abbreviations: MLS (Multilingual LibriSpeech Pratap et al. (2020)), G (GigaSpeech Chen et al. (2021)), L (LibriTTS-R Koizumi et al. (2023)), V (VCTK Yamagishi et al. (2019)), LJ (LJSpeech Ito and Johnson (2017)), W (WenetSpeech Zhang et al. (2022)). Model Data RTF \u2193 Sim-O \u2191 Sim-R \u2191 WER \u2193 CMOS \u2191 SMOS \u2191 GroundTruth 0.68 1.9 0.11 4.39 VALL-E reproduce Librilight 0.62 \u2662 0.47 0.51 6.1 -0.48 4.11 NaturalSpeech 2 MLS 0.37 \u22c6 0.53 0.60 1.9 -0.31 4.20 Voicebox reproduce Librilight 0.66\u2662 0.48 0.50 2.1 -0.58 3.95 Mega-TTS G+W 0.39 \u2662 3.0 CLaM-TTS MLS+G+L +V+LJ 0.42 \u2662 0.50 0.54 5.1 FlashSpeech (ours) MLS 0.02 \u22c6 0.52 0.57 2.7 0.00 4.29 8 FlashSpeech (RTF: 0.02) FlashSpeech (RTF: 0.02) FlashSpeech (RTF: 0.02) FlashSpeech (RTF: 0.02) FlashSpeech (RTF: 0.02) FlashSpeech (RTF: 0.02) FlashSpeech (RTF: 0.02) FlashSpeech (RTF: 0.02) FlashSpeech (RTF: 0.02) FlashSpeech (RTF: 0.02) Voicebox (RTF: 0.64) Mega-TTS (RTF: 0.39) ClaM-TTS (RTF: 0.42) VALL-E (RTF: 0.62) NaturalSpeech 2 (RTF: 0.37) Voicebox (RTF: 0.64) Mega-TTS (RTF: 0.39) ClaM-TTS (RTF: 0.42) VALL-E (RTF: 0.62) NaturalSpeech 2 (RTF: 0.37) Audio Quality Speaker Similarity Figure 5: User preference study. We compare the audio quality and speaker similarity of FlashSpeech against baselines with their official demo. In the experimental section, we begin by introducing the datasets and the configurations for training in our experiments. Following this, we show the evaluation metrics and demonstrate the comparative results against various zero-shot TTS models. Subsequently, ablation studies are conducted to test the effectiveness of several design choices. Finally, we also validate the effectiveness of other tasks such as voice conversion. We show our speech editing and diverse speech sampling results on our demo page. 4.1 Experimental Settings 4.1.1 Data and Preprocessing We use the English subset of Multilingual LibriSpeech (MLS) Pratap et al. (2020), including 44.5k hours of transcribed audiobook data and it contains 5490 distinct speakers. The audio data is resampled at a frequency of 16kHz. The input text is transformed into a sequence of phonemes through grapheme-to-phoneme conversion Sun et al. (2019) and then we use our internal alignment tool aligned with speech to obtain the phoneme-level duration. We adopt a hop size of 200 for all frame-level features. The pitch sequence is extracted using PyWorld2. we adopt Encodec D\u00e9fossez et al. (2022) as our audio codec. We use a modified version 3 and train it on MLS. We use the dense features extracted before the residual quantization layer as our latent vector z. 4.1.2 Training Details Our training consists of two stages, in the first stage we train LCM and the prosody regression part. We use 8 H800 80GB GPUs with a batch size of 20k frames of latent vectors per GPU for 650k steps. We use the AdamW optimizer with a learning rate of 3e-4, warm up the learning rate for the first 30k updates and then linear decay it. We deactivate adversarial training with \u03bbadv = 0 before 600K training iterations. For hyper-parameters, we set a in Equation (12) to 0.03. In equation (10), \u03c3i = \u0010 \u03c31/\u03c1 min + i\u22121 N(k)\u22121 \u0010 \u03c31/\u03c1 max \u2212\u03c31/\u03c1 min \u0011\u0011\u03c1 , where i \u2208[1, N(k)], \u03c1 = 7, \u03c3min = 0.002, \u03c3max = 80. For N(k) in Equation (11), we set s0 = 10, s1 = 1280, K = 600k. After 600k steps, we activate adversarial loss, and N(k) can be considered as fixed to 1280. We crop the waveform length fed into the discriminator into minimum waveform length in a minibatch. In addition, the weight of the feature extractor WavLM and the codec decoder are frozen. In the second stage, we train 150k steps for the prosody refinement module with consistency training in Equation (10). Different from the above setting, we empirically set s1 = 160, K = 150k. During training, only the weight of the prosody refinement part is updated. 2https://github.com/JeremyCCHsu/Python-Wrapper-for-World-Vocoder 3https://github.com/yangdongchao/UniAudio/tree/main/codec 9 4.1.3 Model Details The model structures of the prompt encoder and phoneme encoder are followShen et al. (2024). The neural function part in LCM is almost the same as the Shen et al. (2024). We rescale the sinusoidal position embedding in the neural function part by a factor of 1000. As for the prosody generator, we adopt 30 non-casual wavenet Oord et al. (2016) layers for the neural function part in the prosody refinement module and the same configurations for prosody regression parts in Shen et al. (2024). And we set \u03b1 = 0.2 for the prosody refinement module empirically. For the discriminator\u2019s head, we stack 5 convolutional layers with weight normalization Salimans and Kingma (2016) for binary classification. 4.2 Evaluation Metrics We use both objective and subjective evaluation metrics, including \u2022 RTF: Real-time-factor (RTF) measures the time taken for the system to generate one second of speech. This metric is crucial for evaluating the efficiency of our system, particularly for applications requiring real-time processing. We measure the time of our system end-to-end on an NVIDIA V100 GPU following Shen et al. (2024). \u2022 Sim-O and Sim-R: These metrics assess the speaker similarity. Sim-R measures the objective similarity between the synthesized speech and the reconstruction reference speech through the audio codec, using features embedding extracted from the pre-trained speaker verification model Wang et al. (2023a); Kim et al. (2024)4. Sim-O is calculated with the original reference speech. Higher scores in Sim-O and Sim-R indicate a higher speaker similarity. \u2022 WER (Word Error Rate): To evaluate the accuracy and clarity of synthesized speech from the TTS system, we employ the Automatic Speech Recognition (ASR) model Wang et al. (2023a) 5 to transcribe generated audio. The discrepancies between these transcriptions and original texts are quantified using the Word Error Rate (WER), a crucial metric indicating intelligibility and robustness. \u2022 CMOS, SMOS, UTMOS: we rank the comparative mean option score (CMOS) and similarity mean option score (SMOS) using mturk. The prompt for CMOS refers to \u2019Please focus on the audio quality and naturalness and ignore other factors.\u2019. The prompt for SMOS refers to \u2019Please focus on the similarity of the speaker to the reference, and ignore the differences of content, grammar or audio quality.\u2019 Each audio has been listened to by at least 10 listeners. UTMOS Saeki et al. (2022) is a Speech MOS predictor6 to measure the naturalness of speech. We use it in ablation studies which reduced the cost for evaluation. \u2022 Prosody JS Divergence: To evaluate the diversity and accuracy of the prosody prediction in our TTS system, we include the Prosody JS Divergence metric. This metric employs the Jensen-Shannon (JS) divergence Men\u00e9ndez et al. (1997) to quantify the divergence between the predicted and ground truth prosody feature distributions. Prosody features, including pitch, and duration, are quantized and their distributions in both synthesized and natural speech are compared. Lower JS divergence values indicate closer similarity between the predicted prosody features and those of the ground truth, suggesting a higher diversity of the synthesized speech. 4.3 Experimental Results on Zero-shot TTS Following Wang et al. (2023a), We employ LibriSpeech Panayotov et al. (2015) test-clean for zeroshot TTS evaluation. We adopt the cross-sentence setting in Wang et al. (2023a) that we randomly select 3-second clips as prompts from the same speaker\u2019s speech. The results are summarized in table 1 and figure 5. 4https://github.com/microsoft/UniSpeech/tree/main/downstreams/speaker_verification 5https://huggingface.co/facebook/hubert-large-ls960-ft 6https://github.com/tarepan/SpeechMOS 10 4.3.1 Evaluation Baselines \u2022 VALL-E Wang et al. (2023a): VALL-E predicts codec tokens using both AR and NAR models. RTF7 is obtained from Kim et al. (2024); Le et al. (2023). We use our reproduced results for MOS, Sim, and WER. Additionally, we do a preference test with their official demo. \u2022 Voicebox Le et al. (2023): Voicebox uses flow-matching to predict maksed mel-spectrogram. RTF is from the original paper. We use our reproduced results for MOS, Sim, and WER. We also implement a preference test with their official demo. \u2022 NaturalSpeech2 Shen et al. (2024): NaturalSpeech2 uses a latent diffusion model to predict latent features of codec. The RTF is from the original paper. the Sim, WER and samples for MOS are obtained through communication with the authors. We also do a preference test with their official demo. \u2022 Mega-TTS Jiang et al. (2023a)8: Mega-TTS uses both language model and GAN to predict mel-spectrogram. We obtain RTF from mobilespeech Ji et al. (2024) and WER from the original paper. We do a preference test with their official demo. \u2022 ClaM-TTS Kim et al. (2024): ClaM-TTS uses the AR model to predict mel codec tokens. We obtain the objective evaluation results from the original paper and do a preference test with their official demo. 4.3.2 Generation Quality FlashSpeech stands out significantly in terms of speaker quality, surpassing other baselines in both CMOS and audio quality preference tests. Notably, our method closely approaches ground truth recordings, underscoring its effectiveness. These results affirm the superior quality of FlashSpeech in speech synthesis. our method. 4.3.3 Generation Similarity Our evaluation of speaker similarity utilizes Sim, SMOS, and speaker similarity preference tests, where our methods achieve 1st, 2nd, and 3rd place rankings, respectively. These findings validate our methods\u2019 ability to achieve comparable speaker similarity to other methods. Despite our training data (MLS) containing approximately 5k speakers, fewer than most other methods (e.g., Librilight with about 7k speakers or self-collected data), we believe that increasing the number of speakers in our methods can further enhance speaker similarity. 4.3.4 Robustness Our methods achieve a WER of 2.7, placing them in the first echelon. This is due to the nonautoregressive nature of our methods, which ensures robustness. 4.3.5 Generation Speed FlashSpeech achieves a remarkable approximately 20x faster inference speed compared to previous work. Considering its excellent audio quality, robustness, and comparable speaker similarity, our method stands out as an efficient and effective solution in the field of large-scale speech synthesis. 4.4 Ablation Studies 4.4.1 Ablation studies of LCM We explored the impact of different pre-trained models in adversarial training on UTMOS and Sim-O. As shown in the table 2, the baseline, which employs consistency training alone, achieved a UTMOS 7In CLaM-TTS and Voicebox, they report the inference time for generating 10 seconds of speech. Therefore, we divide by 10 to obtain the time for generating 1 second of speech (RTF). 8Since we do not find any audio samples for Mega-TTS2 Jiang et al. (2024b) under the 3-second crosssentence setting, we are not able to compare with them. 11 Table 2: The ablation study of discriminator design. Method UTMOS \u2191 Sim-O \u2191 Consistency training baseline 3.62 0.45 + Adversarial training (Wav2Vec2-large) 3.92 0.50 + Adversarial training (Hubert-large) 3.83 0.47 + Adversarial training (Wavlm-large) 4.00 0.52 prompt projection 3.97 0.51 Table 3: The ablation study of sampling steps for LCM NFE UTMOS \u2191 Sim-O \u2191 1 3.99 0.51 2 4.00 0.52 4 3.91 0.51 of 3.62 and a Sim-O of 0.45. Incorporating adversarial training using wav2vec2-large9, hubert-large10, and wavlm-large11 as discriminators significantly improved both UTMOS and Sim-O scores. Notably, the application of adversarial training with Wavlm-large achieved the highest scores (UTMOS: 4.00, Sim-O: 0.52), underscoring the efficacy of this pre-trained model in enhancing the quality and speaker similarity of synthesized speech. Additionally, without using the audio prompt\u2019s feature as a condition the discriminator shows a slight decrease in performance (UTMOS: 3.97, Sim-O: 0.51), highlighting the importance of conditional features in guiding the adversarial training process. As shown in table 3, the effect of sampling steps (NFE) on UTMOS and Sim-O revealed that increasing NFE from 1 to 2 marginally improves UTMOS (3.99 to 4.00) and Sim-O (0.51 to 0.52). However, further increasing to 4 sampling steps slightly reduced UTMOS to 3.91 due to the accumulation of score estimation errors Chen et al. (2022a); Lyu et al. (2024). Therefore, we use 2 steps as the default setting for LCM. 4.4.2 Ablation studies of Prosody Generator In this part, we investigated the effects of a control factor, denoted as \u03b1, on the prosodic features of pitch and duration in speech synthesis, by setting another influencing factor to zero. Our study specifically conducted an ablation analysis to assess how \u03b1 influences these features, emphasizing its critical role in balancing stability and diversity within our framework\u2019s prosodic outputs. Table 4 elucidates the effects of varying \u03b1 on the pitch component. With \u03b1 set to 0, indicating no inclusion of the residual output from prosody refinement, we observed a Pitch JSD of 0.072 and a WER of 2.8. A slight modification to \u03b1 = 0.2 resulted in a reduced Pitch JSD of 0.067, maintaining the same WER. Notably, setting \u03b1 to 1, fully incorporating the prosody refinement\u2019s residual output, further decreased the Pitch JSD to 0.063, albeit at the cost of increased WER to 3.7, suggesting a trade-off between prosody diversity and speech intelligibility. Similar trends in table 5 are observed in the duration component analysis. With \u03b1 = 0, the Duration JSD was 0.0175 with a WER of 2.8. Adjusting \u03b1 to 0.2 slightly improved the Duration JSD to 0.0168, without affecting WER. However, fully embracing the refinement module\u2019s output by setting \u03b1 = 1 yielded the most significant improvement in Duration JSD to 0.0153, which, similar to pitch analysis, came with an increased WER of 3.9. The results underline the delicate balance required in tuning \u03b1 to optimize between diversity and stability of prosody without compromising speech intelligibility. 9https://huggingface.co/facebook/wav2vec2-large 10https://huggingface.co/facebook/hubert-large-ll60k 11https://huggingface.co/microsoft/wavlm-large 12 Table 4: The ablation study of control factor for pitch \u03b1 Pitch JSD \u2193 WER\u2193 0 0.072 2.8 0.2 0.067 2.8 1 0.063 3.7 Table 5: The ablation study of control factor for duration \u03b1 Duration JSD \u2193 WER \u2193 0 0.0175 2.8 0.2 0.0168 2.8 1 0.0153 3.9 4.5 Evaluation Results for Voice Conversion In this section, we present the evaluation results of our voice conversion system, FlashSpeech, in comparison with state-of-the-art methods, including YourTTS 12 Casanova et al. (2022) and DDDMVC 13 Choi et al. (2024). We conduct the experiments with their official checkpoints in our internal test set. Table 6: Voice Conversion Method CMOS \u2191 SMOS \u2191 Sim-O \u2191 YourTTS Casanova et al. (2022) -0.16 3.26 0.23 DDDM-VC Choi et al. (2024) -0.28 3.43 0.28 Ours 0.00 3.50 0.35 Our system outperforms both YourTTS and DDDM-VC in terms of CMOS, SMOS and Sim-O, demonstrating its capability to produce converted voices with high quality and similarity to the target speaker. These results confirm the effectiveness of our FlashSpeech approach in voice conversion tasks. 4.6 Conclusions and Future Work In this paper, we presented FlashSpeech, a novel speech generation system that significantly reduces computational costs while maintaining high-quality speech output. Utilizing a novel adversarial consistency training method and an LCM, FlashSpeech outperforms existing zero-shot TTS systems in efficiency, achieving speeds about 20 times faster without compromising on voice quality, similarity, and robustness. In the future, we aim to further refine the model to improve the inference speed and reduce computational demands. In addition, we will expand the data scale and enhance the system\u2019s ability to convey a broader range of emotions and more nuanced prosody. For future applications, FlashSpeech can be integrated for real-time interactions in applications such as virtual assistants and educational tools. 12https://github.com/coqui-ai/TTS 13https://github.com/hayeong0/DDDM-VC 13"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2306.15687v2",
+                    "title": "Voicebox: Text-Guided Multilingual Universal Speech Generation at Scale",
+                    "abstract": "Large-scale generative models such as GPT and DALL-E have revolutionized the\nresearch community. These models not only generate high fidelity outputs, but\nare also generalists which can solve tasks not explicitly taught. In contrast,\nspeech generative models are still primitive in terms of scale and task\ngeneralization. In this paper, we present Voicebox, the most versatile\ntext-guided generative model for speech at scale. Voicebox is a\nnon-autoregressive flow-matching model trained to infill speech, given audio\ncontext and text, trained on over 50K hours of speech that are not filtered or\nenhanced. Similar to GPT, Voicebox can perform many different tasks through\nin-context learning, but is more flexible as it can also condition on future\ncontext. Voicebox can be used for mono or cross-lingual zero-shot\ntext-to-speech synthesis, noise removal, content editing, style conversion, and\ndiverse sample generation. In particular, Voicebox outperforms the\nstate-of-the-art zero-shot TTS model VALL-E on both intelligibility (5.9% vs\n1.9% word error rates) and audio similarity (0.580 vs 0.681) while being up to\n20 times faster. Audio samples can be found in\n\\url{https://voicebox.metademolab.com}.",
+                    "authors": "Matthew Le, Apoorv Vyas, Bowen Shi, Brian Karrer, Leda Sari, Rashel Moritz, Mary Williamson, Vimal Manohar, Yossi Adi, Jay Mahadeokar, Wei-Ning Hsu",
+                    "published": "2023-06-23",
+                    "updated": "2023-10-19",
+                    "primary_cat": "eess.AS",
+                    "cats": [
+                        "eess.AS",
+                        "cs.CL",
+                        "cs.LG",
+                        "cs.SD"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2301.02111v1",
+                    "title": "Neural Codec Language Models are Zero-Shot Text to Speech Synthesizers",
+                    "abstract": "We introduce a language modeling approach for text to speech synthesis (TTS).\nSpecifically, we train a neural codec language model (called Vall-E) using\ndiscrete codes derived from an off-the-shelf neural audio codec model, and\nregard TTS as a conditional language modeling task rather than continuous\nsignal regression as in previous work. During the pre-training stage, we scale\nup the TTS training data to 60K hours of English speech which is hundreds of\ntimes larger than existing systems. Vall-E emerges in-context learning\ncapabilities and can be used to synthesize high-quality personalized speech\nwith only a 3-second enrolled recording of an unseen speaker as an acoustic\nprompt. Experiment results show that Vall-E significantly outperforms the\nstate-of-the-art zero-shot TTS system in terms of speech naturalness and\nspeaker similarity. In addition, we find Vall-E could preserve the speaker's\nemotion and acoustic environment of the acoustic prompt in synthesis. See\nhttps://aka.ms/valle for demos of our work.",
+                    "authors": "Chengyi Wang, Sanyuan Chen, Yu Wu, Ziqiang Zhang, Long Zhou, Shujie Liu, Zhuo Chen, Yanqing Liu, Huaming Wang, Jinyu Li, Lei He, Sheng Zhao, Furu Wei",
+                    "published": "2023-01-05",
+                    "updated": "2023-01-05",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL",
+                        "cs.SD",
+                        "eess.AS"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2310.04378v1",
+                    "title": "Latent Consistency Models: Synthesizing High-Resolution Images with Few-Step Inference",
+                    "abstract": "Latent Diffusion models (LDMs) have achieved remarkable results in\nsynthesizing high-resolution images. However, the iterative sampling process is\ncomputationally intensive and leads to slow generation. Inspired by Consistency\nModels (song et al.), we propose Latent Consistency Models (LCMs), enabling\nswift inference with minimal steps on any pre-trained LDMs, including Stable\nDiffusion (rombach et al). Viewing the guided reverse diffusion process as\nsolving an augmented probability flow ODE (PF-ODE), LCMs are designed to\ndirectly predict the solution of such ODE in latent space, mitigating the need\nfor numerous iterations and allowing rapid, high-fidelity sampling. Efficiently\ndistilled from pre-trained classifier-free guided diffusion models, a\nhigh-quality 768 x 768 2~4-step LCM takes only 32 A100 GPU hours for training.\nFurthermore, we introduce Latent Consistency Fine-tuning (LCF), a novel method\nthat is tailored for fine-tuning LCMs on customized image datasets. Evaluation\non the LAION-5B-Aesthetics dataset demonstrates that LCMs achieve\nstate-of-the-art text-to-image generation performance with few-step inference.\nProject Page: https://latent-consistency-models.github.io/",
+                    "authors": "Simian Luo, Yiqin Tan, Longbo Huang, Jian Li, Hang Zhao",
+                    "published": "2023-10-06",
+                    "updated": "2023-10-06",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.LG"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2105.06337v2",
+                    "title": "Grad-TTS: A Diffusion Probabilistic Model for Text-to-Speech",
+                    "abstract": "Recently, denoising diffusion probabilistic models and generative score\nmatching have shown high potential in modelling complex data distributions\nwhile stochastic calculus has provided a unified point of view on these\ntechniques allowing for flexible inference schemes. In this paper we introduce\nGrad-TTS, a novel text-to-speech model with score-based decoder producing\nmel-spectrograms by gradually transforming noise predicted by encoder and\naligned with text input by means of Monotonic Alignment Search. The framework\nof stochastic differential equations helps us to generalize conventional\ndiffusion probabilistic models to the case of reconstructing data from noise\nwith different parameters and allows to make this reconstruction flexible by\nexplicitly controlling trade-off between sound quality and inference speed.\nSubjective human evaluation shows that Grad-TTS is competitive with\nstate-of-the-art text-to-speech approaches in terms of Mean Opinion Score. We\nwill make the code publicly available shortly.",
+                    "authors": "Vadim Popov, Ivan Vovk, Vladimir Gogoryan, Tasnima Sadekova, Mikhail Kudinov",
+                    "published": "2021-05-13",
+                    "updated": "2021-08-05",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.CL",
+                        "stat.ML"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2310.02279v3",
+                    "title": "Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion",
+                    "abstract": "Consistency Models (CM) (Song et al., 2023) accelerate score-based diffusion\nmodel sampling at the cost of sample quality but lack a natural way to\ntrade-off quality for speed. To address this limitation, we propose Consistency\nTrajectory Model (CTM), a generalization encompassing CM and score-based models\nas special cases. CTM trains a single neural network that can -- in a single\nforward pass -- output scores (i.e., gradients of log-density) and enables\nunrestricted traversal between any initial and final time along the Probability\nFlow Ordinary Differential Equation (ODE) in a diffusion process. CTM enables\nthe efficient combination of adversarial training and denoising score matching\nloss to enhance performance and achieves new state-of-the-art FIDs for\nsingle-step diffusion model sampling on CIFAR-10 (FID 1.73) and ImageNet at\n64x64 resolution (FID 1.92). CTM also enables a new family of sampling schemes,\nboth deterministic and stochastic, involving long jumps along the ODE solution\ntrajectories. It consistently improves sample quality as computational budgets\nincrease, avoiding the degradation seen in CM. Furthermore, unlike CM, CTM's\naccess to the score function can streamline the adoption of established\ncontrollable/conditional generation methods from the diffusion community. This\naccess also enables the computation of likelihood. The code is available at\nhttps://github.com/sony/ctm.",
+                    "authors": "Dongjun Kim, Chieh-Hsin Lai, Wei-Hsiang Liao, Naoki Murata, Yuhta Takida, Toshimitsu Uesaka, Yutong He, Yuki Mitsufuji, Stefano Ermon",
+                    "published": "2023-10-01",
+                    "updated": "2024-03-30",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI",
+                        "cs.CV",
+                        "stat.ML"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2110.13900v5",
+                    "title": "WavLM: Large-Scale Self-Supervised Pre-Training for Full Stack Speech Processing",
+                    "abstract": "Self-supervised learning (SSL) achieves great success in speech recognition,\nwhile limited exploration has been attempted for other speech processing tasks.\nAs speech signal contains multi-faceted information including speaker identity,\nparalinguistics, spoken content, etc., learning universal representations for\nall speech tasks is challenging. To tackle the problem, we propose a new\npre-trained model, WavLM, to solve full-stack downstream speech tasks. WavLM\njointly learns masked speech prediction and denoising in pre-training. By this\nmeans, WavLM does not only keep the speech content modeling capability by the\nmasked speech prediction, but also improves the potential to non-ASR tasks by\nthe speech denoising. In addition, WavLM employs gated relative position bias\nfor the Transformer structure to better capture the sequence ordering of input\nspeech. We also scale up the training dataset from 60k hours to 94k hours.\nWavLM Large achieves state-of-the-art performance on the SUPERB benchmark, and\nbrings significant improvements for various speech processing tasks on their\nrepresentative benchmarks. The code and pre-trained models are available at\nhttps://aka.ms/wavlm.",
+                    "authors": "Sanyuan Chen, Chengyi Wang, Zhengyang Chen, Yu Wu, Shujie Liu, Zhuo Chen, Jinyu Li, Naoyuki Kanda, Takuya Yoshioka, Xiong Xiao, Jian Wu, Long Zhou, Shuo Ren, Yanmin Qian, Yao Qian, Jian Wu, Michael Zeng, Xiangzhan Yu, Furu Wei",
+                    "published": "2021-10-26",
+                    "updated": "2022-06-17",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL",
+                        "cs.SD",
+                        "eess.AS"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2310.14189v1",
+                    "title": "Improved Techniques for Training Consistency Models",
+                    "abstract": "Consistency models are a nascent family of generative models that can sample\nhigh quality data in one step without the need for adversarial training.\nCurrent consistency models achieve optimal sample quality by distilling from\npre-trained diffusion models and employing learned metrics such as LPIPS.\nHowever, distillation limits the quality of consistency models to that of the\npre-trained diffusion model, and LPIPS causes undesirable bias in evaluation.\nTo tackle these challenges, we present improved techniques for consistency\ntraining, where consistency models learn directly from data without\ndistillation. We delve into the theory behind consistency training and identify\na previously overlooked flaw, which we address by eliminating Exponential\nMoving Average from the teacher consistency model. To replace learned metrics\nlike LPIPS, we adopt Pseudo-Huber losses from robust statistics. Additionally,\nwe introduce a lognormal noise schedule for the consistency training objective,\nand propose to double total discretization steps every set number of training\niterations. Combined with better hyperparameter tuning, these modifications\nenable consistency models to achieve FID scores of 2.51 and 3.25 on CIFAR-10\nand ImageNet $64\\times 64$ respectively in a single sampling step. These scores\nmark a 3.5$\\times$ and 4$\\times$ improvement compared to prior consistency\ntraining approaches. Through two-step sampling, we further reduce FID scores to\n2.24 and 2.77 on these two datasets, surpassing those obtained via distillation\nin both one-step and two-step settings, while narrowing the gap between\nconsistency models and other state-of-the-art generative models.",
+                    "authors": "Yang Song, Prafulla Dhariwal",
+                    "published": "2023-10-22",
+                    "updated": "2023-10-22",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2303.01469v2",
+                    "title": "Consistency Models",
+                    "abstract": "Diffusion models have significantly advanced the fields of image, audio, and\nvideo generation, but they depend on an iterative sampling process that causes\nslow generation. To overcome this limitation, we propose consistency models, a\nnew family of models that generate high quality samples by directly mapping\nnoise to data. They support fast one-step generation by design, while still\nallowing multistep sampling to trade compute for sample quality. They also\nsupport zero-shot data editing, such as image inpainting, colorization, and\nsuper-resolution, without requiring explicit training on these tasks.\nConsistency models can be trained either by distilling pre-trained diffusion\nmodels, or as standalone generative models altogether. Through extensive\nexperiments, we demonstrate that they outperform existing distillation\ntechniques for diffusion models in one- and few-step sampling, achieving the\nnew state-of-the-art FID of 3.55 on CIFAR-10 and 6.20 on ImageNet 64x64 for\none-step generation. When trained in isolation, consistency models become a new\nfamily of generative models that can outperform existing one-step,\nnon-adversarial generative models on standard benchmarks such as CIFAR-10,\nImageNet 64x64 and LSUN 256x256.",
+                    "authors": "Yang Song, Prafulla Dhariwal, Mark Chen, Ilya Sutskever",
+                    "published": "2023-03-02",
+                    "updated": "2023-05-31",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.CV",
+                        "stat.ML"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2305.06908v4",
+                    "title": "CoMoSpeech: One-Step Speech and Singing Voice Synthesis via Consistency Model",
+                    "abstract": "Denoising diffusion probabilistic models (DDPMs) have shown promising\nperformance for speech synthesis. However, a large number of iterative steps\nare required to achieve high sample quality, which restricts the inference\nspeed. Maintaining sample quality while increasing sampling speed has become a\nchallenging task. In this paper, we propose a \"Co\"nsistency \"Mo\"del-based\n\"Speech\" synthesis method, CoMoSpeech, which achieve speech synthesis through a\nsingle diffusion sampling step while achieving high audio quality. The\nconsistency constraint is applied to distill a consistency model from a\nwell-designed diffusion-based teacher model, which ultimately yields superior\nperformances in the distilled CoMoSpeech. Our experiments show that by\ngenerating audio recordings by a single sampling step, the CoMoSpeech achieves\nan inference speed more than 150 times faster than real-time on a single NVIDIA\nA100 GPU, which is comparable to FastSpeech2, making diffusion-sampling based\nspeech synthesis truly practical. Meanwhile, objective and subjective\nevaluations on text-to-speech and singing voice synthesis show that the\nproposed teacher models yield the best audio quality, and the one-step sampling\nbased CoMoSpeech achieves the best inference speed with better or comparable\naudio quality to other conventional multi-step diffusion model baselines. Audio\nsamples are available at https://comospeech.github.io/.",
+                    "authors": "Zhen Ye, Wei Xue, Xu Tan, Jie Chen, Qifeng Liu, Yike Guo",
+                    "published": "2023-05-11",
+                    "updated": "2023-10-29",
+                    "primary_cat": "cs.SD",
+                    "cats": [
+                        "cs.SD",
+                        "cs.AI",
+                        "cs.CL",
+                        "cs.LG",
+                        "cs.MM",
+                        "eess.AS"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2402.09378v1",
+                    "title": "MobileSpeech: A Fast and High-Fidelity Framework for Mobile Zero-Shot Text-to-Speech",
+                    "abstract": "Zero-shot text-to-speech (TTS) has gained significant attention due to its\npowerful voice cloning capabilities, requiring only a few seconds of unseen\nspeaker voice prompts. However, all previous work has been developed for\ncloud-based systems. Taking autoregressive models as an example, although these\napproaches achieve high-fidelity voice cloning, they fall short in terms of\ninference speed, model size, and robustness. Therefore, we propose\nMobileSpeech, which is a fast, lightweight, and robust zero-shot text-to-speech\nsystem based on mobile devices for the first time. Specifically: 1) leveraging\ndiscrete codec, we design a parallel speech mask decoder module called SMD,\nwhich incorporates hierarchical information from the speech codec and weight\nmechanisms across different codec layers during the generation process.\nMoreover, to bridge the gap between text and speech, we introduce a high-level\nprobabilistic mask that simulates the progression of information flow from less\nto more during speech generation. 2) For speaker prompts, we extract\nfine-grained prompt duration from the prompt speech and incorporate text,\nprompt speech by cross attention in SMD. We demonstrate the effectiveness of\nMobileSpeech on multilingual datasets at different levels, achieving\nstate-of-the-art results in terms of generating speed and speech quality.\nMobileSpeech achieves RTF of 0.09 on a single A100 GPU and we have successfully\ndeployed MobileSpeech on mobile devices. Audio samples are available at\n\\url{https://mobilespeech.github.io/} .",
+                    "authors": "Shengpeng Ji, Ziyue Jiang, Hanting Wang, Jialong Zuo, Zhou Zhao",
+                    "published": "2024-02-14",
+                    "updated": "2024-02-14",
+                    "primary_cat": "eess.AS",
+                    "cats": [
+                        "eess.AS",
+                        "cs.SD"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2304.09116v3",
+                    "title": "NaturalSpeech 2: Latent Diffusion Models are Natural and Zero-Shot Speech and Singing Synthesizers",
+                    "abstract": "Scaling text-to-speech (TTS) to large-scale, multi-speaker, and in-the-wild\ndatasets is important to capture the diversity in human speech such as speaker\nidentities, prosodies, and styles (e.g., singing). Current large TTS systems\nusually quantize speech into discrete tokens and use language models to\ngenerate these tokens one by one, which suffer from unstable prosody, word\nskipping/repeating issue, and poor voice quality. In this paper, we develop\nNaturalSpeech 2, a TTS system that leverages a neural audio codec with residual\nvector quantizers to get the quantized latent vectors and uses a diffusion\nmodel to generate these latent vectors conditioned on text input. To enhance\nthe zero-shot capability that is important to achieve diverse speech synthesis,\nwe design a speech prompting mechanism to facilitate in-context learning in the\ndiffusion model and the duration/pitch predictor. We scale NaturalSpeech 2 to\nlarge-scale datasets with 44K hours of speech and singing data and evaluate its\nvoice quality on unseen speakers. NaturalSpeech 2 outperforms previous TTS\nsystems by a large margin in terms of prosody/timbre similarity, robustness,\nand voice quality in a zero-shot setting, and performs novel zero-shot singing\nsynthesis with only a speech prompt. Audio samples are available at\nhttps://speechresearch.github.io/naturalspeech2.",
+                    "authors": "Kai Shen, Zeqian Ju, Xu Tan, Yanqing Liu, Yichong Leng, Lei He, Tao Qin, Sheng Zhao, Jiang Bian",
+                    "published": "2023-04-18",
+                    "updated": "2023-05-30",
+                    "primary_cat": "eess.AS",
+                    "cats": [
+                        "eess.AS",
+                        "cs.AI",
+                        "cs.CL",
+                        "cs.LG",
+                        "cs.SD"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2104.01409v1",
+                    "title": "Diff-TTS: A Denoising Diffusion Model for Text-to-Speech",
+                    "abstract": "Although neural text-to-speech (TTS) models have attracted a lot of attention\nand succeeded in generating human-like speech, there is still room for\nimprovements to its naturalness and architectural efficiency. In this work, we\npropose a novel non-autoregressive TTS model, namely Diff-TTS, which achieves\nhighly natural and efficient speech synthesis. Given the text, Diff-TTS\nexploits a denoising diffusion framework to transform the noise signal into a\nmel-spectrogram via diffusion time steps. In order to learn the mel-spectrogram\ndistribution conditioned on the text, we present a likelihood-based\noptimization method for TTS. Furthermore, to boost up the inference speed, we\nleverage the accelerated sampling method that allows Diff-TTS to generate raw\nwaveforms much faster without significantly degrading perceptual quality.\nThrough experiments, we verified that Diff-TTS generates 28 times faster than\nthe real-time with a single NVIDIA 2080Ti GPU.",
+                    "authors": "Myeonghun Jeong, Hyeongju Kim, Sung Jun Cheon, Byoung Jin Choi, Nam Soo Kim",
+                    "published": "2021-04-03",
+                    "updated": "2021-04-03",
+                    "primary_cat": "eess.AS",
+                    "cats": [
+                        "eess.AS",
+                        "cs.AI",
+                        "cs.SD"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2109.13821v2",
+                    "title": "Diffusion-Based Voice Conversion with Fast Maximum Likelihood Sampling Scheme",
+                    "abstract": "Voice conversion is a common speech synthesis task which can be solved in\ndifferent ways depending on a particular real-world scenario. The most\nchallenging one often referred to as one-shot many-to-many voice conversion\nconsists in copying the target voice from only one reference utterance in the\nmost general case when both source and target speakers do not belong to the\ntraining dataset. We present a scalable high-quality solution based on\ndiffusion probabilistic modeling and demonstrate its superior quality compared\nto state-of-the-art one-shot voice conversion approaches. Moreover, focusing on\nreal-time applications, we investigate general principles which can make\ndiffusion models faster while keeping synthesis quality at a high level. As a\nresult, we develop a novel Stochastic Differential Equations solver suitable\nfor various diffusion model types and generative tasks as shown through\nempirical studies and justify it by theoretical analysis.",
+                    "authors": "Vadim Popov, Ivan Vovk, Vladimir Gogoryan, Tasnima Sadekova, Mikhail Kudinov, Jiansheng Wei",
+                    "published": "2021-09-28",
+                    "updated": "2022-08-04",
+                    "primary_cat": "cs.SD",
+                    "cats": [
+                        "cs.SD",
+                        "cs.LG",
+                        "stat.ML"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2011.13456v2",
+                    "title": "Score-Based Generative Modeling through Stochastic Differential Equations",
+                    "abstract": "Creating noise from data is easy; creating data from noise is generative\nmodeling. We present a stochastic differential equation (SDE) that smoothly\ntransforms a complex data distribution to a known prior distribution by slowly\ninjecting noise, and a corresponding reverse-time SDE that transforms the prior\ndistribution back into the data distribution by slowly removing the noise.\nCrucially, the reverse-time SDE depends only on the time-dependent gradient\nfield (\\aka, score) of the perturbed data distribution. By leveraging advances\nin score-based generative modeling, we can accurately estimate these scores\nwith neural networks, and use numerical SDE solvers to generate samples. We\nshow that this framework encapsulates previous approaches in score-based\ngenerative modeling and diffusion probabilistic modeling, allowing for new\nsampling procedures and new modeling capabilities. In particular, we introduce\na predictor-corrector framework to correct errors in the evolution of the\ndiscretized reverse-time SDE. We also derive an equivalent neural ODE that\nsamples from the same distribution as the SDE, but additionally enables exact\nlikelihood computation, and improved sampling efficiency. In addition, we\nprovide a new way to solve inverse problems with score-based models, as\ndemonstrated with experiments on class-conditional generation, image\ninpainting, and colorization. Combined with multiple architectural\nimprovements, we achieve record-breaking performance for unconditional image\ngeneration on CIFAR-10 with an Inception score of 9.89 and FID of 2.20, a\ncompetitive likelihood of 2.99 bits/dim, and demonstrate high fidelity\ngeneration of 1024 x 1024 images for the first time from a score-based\ngenerative model.",
+                    "authors": "Yang Song, Jascha Sohl-Dickstein, Diederik P. Kingma, Abhishek Kumar, Stefano Ermon, Ben Poole",
+                    "published": "2020-11-26",
+                    "updated": "2021-02-10",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "stat.ML"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2310.04378v1",
+                    "title": "Latent Consistency Models: Synthesizing High-Resolution Images with Few-Step Inference",
+                    "abstract": "Latent Diffusion models (LDMs) have achieved remarkable results in\nsynthesizing high-resolution images. However, the iterative sampling process is\ncomputationally intensive and leads to slow generation. Inspired by Consistency\nModels (song et al.), we propose Latent Consistency Models (LCMs), enabling\nswift inference with minimal steps on any pre-trained LDMs, including Stable\nDiffusion (rombach et al). Viewing the guided reverse diffusion process as\nsolving an augmented probability flow ODE (PF-ODE), LCMs are designed to\ndirectly predict the solution of such ODE in latent space, mitigating the need\nfor numerous iterations and allowing rapid, high-fidelity sampling. Efficiently\ndistilled from pre-trained classifier-free guided diffusion models, a\nhigh-quality 768 x 768 2~4-step LCM takes only 32 A100 GPU hours for training.\nFurthermore, we introduce Latent Consistency Fine-tuning (LCF), a novel method\nthat is tailored for fine-tuning LCMs on customized image datasets. Evaluation\non the LAION-5B-Aesthetics dataset demonstrates that LCMs achieve\nstate-of-the-art text-to-image generation performance with few-step inference.\nProject Page: https://latent-consistency-models.github.io/",
+                    "authors": "Simian Luo, Yiqin Tan, Longbo Huang, Jian Li, Hang Zhao",
+                    "published": "2023-10-06",
+                    "updated": "2023-10-06",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.LG"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2112.10752v2",
+                    "title": "High-Resolution Image Synthesis with Latent Diffusion Models",
+                    "abstract": "By decomposing the image formation process into a sequential application of\ndenoising autoencoders, diffusion models (DMs) achieve state-of-the-art\nsynthesis results on image data and beyond. Additionally, their formulation\nallows for a guiding mechanism to control the image generation process without\nretraining. However, since these models typically operate directly in pixel\nspace, optimization of powerful DMs often consumes hundreds of GPU days and\ninference is expensive due to sequential evaluations. To enable DM training on\nlimited computational resources while retaining their quality and flexibility,\nwe apply them in the latent space of powerful pretrained autoencoders. In\ncontrast to previous work, training diffusion models on such a representation\nallows for the first time to reach a near-optimal point between complexity\nreduction and detail preservation, greatly boosting visual fidelity. By\nintroducing cross-attention layers into the model architecture, we turn\ndiffusion models into powerful and flexible generators for general conditioning\ninputs such as text or bounding boxes and high-resolution synthesis becomes\npossible in a convolutional manner. Our latent diffusion models (LDMs) achieve\na new state of the art for image inpainting and highly competitive performance\non various tasks, including unconditional image generation, semantic scene\nsynthesis, and super-resolution, while significantly reducing computational\nrequirements compared to pixel-based DMs. Code is available at\nhttps://github.com/CompVis/latent-diffusion .",
+                    "authors": "Robin Rombach, Andreas Blattmann, Dominik Lorenz, Patrick Esser, Bj\u00f6rn Ommer",
+                    "published": "2021-12-20",
+                    "updated": "2022-04-13",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2006.04558v8",
+                    "title": "FastSpeech 2: Fast and High-Quality End-to-End Text to Speech",
+                    "abstract": "Non-autoregressive text to speech (TTS) models such as FastSpeech can\nsynthesize speech significantly faster than previous autoregressive models with\ncomparable quality. The training of FastSpeech model relies on an\nautoregressive teacher model for duration prediction (to provide more\ninformation as input) and knowledge distillation (to simplify the data\ndistribution in output), which can ease the one-to-many mapping problem (i.e.,\nmultiple speech variations correspond to the same text) in TTS. However,\nFastSpeech has several disadvantages: 1) the teacher-student distillation\npipeline is complicated and time-consuming, 2) the duration extracted from the\nteacher model is not accurate enough, and the target mel-spectrograms distilled\nfrom teacher model suffer from information loss due to data simplification,\nboth of which limit the voice quality. In this paper, we propose FastSpeech 2,\nwhich addresses the issues in FastSpeech and better solves the one-to-many\nmapping problem in TTS by 1) directly training the model with ground-truth\ntarget instead of the simplified output from teacher, and 2) introducing more\nvariation information of speech (e.g., pitch, energy and more accurate\nduration) as conditional inputs. Specifically, we extract duration, pitch and\nenergy from speech waveform and directly take them as conditional inputs in\ntraining and use predicted values in inference. We further design FastSpeech\n2s, which is the first attempt to directly generate speech waveform from text\nin parallel, enjoying the benefit of fully end-to-end inference. Experimental\nresults show that 1) FastSpeech 2 achieves a 3x training speed-up over\nFastSpeech, and FastSpeech 2s enjoys even faster inference speed; 2) FastSpeech\n2 and 2s outperform FastSpeech in voice quality, and FastSpeech 2 can even\nsurpass autoregressive models. Audio samples are available at\nhttps://speechresearch.github.io/fastspeech2/.",
+                    "authors": "Yi Ren, Chenxu Hu, Xu Tan, Tao Qin, Sheng Zhao, Zhou Zhao, Tie-Yan Liu",
+                    "published": "2020-06-08",
+                    "updated": "2022-08-08",
+                    "primary_cat": "eess.AS",
+                    "cats": [
+                        "eess.AS",
+                        "cs.CL",
+                        "cs.LG",
+                        "cs.SD"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2202.13066v1",
+                    "title": "Revisiting Over-Smoothness in Text to Speech",
+                    "abstract": "Non-autoregressive text to speech (NAR-TTS) models have attracted much\nattention from both academia and industry due to their fast generation speed.\nOne limitation of NAR-TTS models is that they ignore the correlation in time\nand frequency domains while generating speech mel-spectrograms, and thus cause\nblurry and over-smoothed results. In this work, we revisit this over-smoothing\nproblem from a novel perspective: the degree of over-smoothness is determined\nby the gap between the complexity of data distributions and the capability of\nmodeling methods. Both simplifying data distributions and improving modeling\nmethods can alleviate the problem. Accordingly, we first study methods reducing\nthe complexity of data distributions. Then we conduct a comprehensive study on\nNAR-TTS models that use some advanced modeling methods. Based on these studies,\nwe find that 1) methods that provide additional condition inputs reduce the\ncomplexity of data distributions to model, thus alleviating the over-smoothing\nproblem and achieving better voice quality. 2) Among advanced modeling methods,\nLaplacian mixture loss performs well at modeling multimodal distributions and\nenjoys its simplicity, while GAN and Glow achieve the best voice quality while\nsuffering from increased training or model complexity. 3) The two categories of\nmethods can be combined to further alleviate the over-smoothness and improve\nthe voice quality. 4) Our experiments on the multi-speaker dataset lead to\nsimilar conclusions as above and providing more variance information can reduce\nthe difficulty of modeling the target data distribution and alleviate the\nrequirements for model capacity.",
+                    "authors": "Yi Ren, Xu Tan, Tao Qin, Zhou Zhao, Tie-Yan Liu",
+                    "published": "2022-02-26",
+                    "updated": "2022-02-26",
+                    "primary_cat": "eess.AS",
+                    "cats": [
+                        "eess.AS",
+                        "cs.SD"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2310.14189v1",
+                    "title": "Improved Techniques for Training Consistency Models",
+                    "abstract": "Consistency models are a nascent family of generative models that can sample\nhigh quality data in one step without the need for adversarial training.\nCurrent consistency models achieve optimal sample quality by distilling from\npre-trained diffusion models and employing learned metrics such as LPIPS.\nHowever, distillation limits the quality of consistency models to that of the\npre-trained diffusion model, and LPIPS causes undesirable bias in evaluation.\nTo tackle these challenges, we present improved techniques for consistency\ntraining, where consistency models learn directly from data without\ndistillation. We delve into the theory behind consistency training and identify\na previously overlooked flaw, which we address by eliminating Exponential\nMoving Average from the teacher consistency model. To replace learned metrics\nlike LPIPS, we adopt Pseudo-Huber losses from robust statistics. Additionally,\nwe introduce a lognormal noise schedule for the consistency training objective,\nand propose to double total discretization steps every set number of training\niterations. Combined with better hyperparameter tuning, these modifications\nenable consistency models to achieve FID scores of 2.51 and 3.25 on CIFAR-10\nand ImageNet $64\\times 64$ respectively in a single sampling step. These scores\nmark a 3.5$\\times$ and 4$\\times$ improvement compared to prior consistency\ntraining approaches. Through two-step sampling, we further reduce FID scores to\n2.24 and 2.77 on these two datasets, surpassing those obtained via distillation\nin both one-step and two-step settings, while narrowing the gap between\nconsistency models and other state-of-the-art generative models.",
+                    "authors": "Yang Song, Prafulla Dhariwal",
+                    "published": "2023-10-22",
+                    "updated": "2023-10-22",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2303.01469v2",
+                    "title": "Consistency Models",
+                    "abstract": "Diffusion models have significantly advanced the fields of image, audio, and\nvideo generation, but they depend on an iterative sampling process that causes\nslow generation. To overcome this limitation, we propose consistency models, a\nnew family of models that generate high quality samples by directly mapping\nnoise to data. They support fast one-step generation by design, while still\nallowing multistep sampling to trade compute for sample quality. They also\nsupport zero-shot data editing, such as image inpainting, colorization, and\nsuper-resolution, without requiring explicit training on these tasks.\nConsistency models can be trained either by distilling pre-trained diffusion\nmodels, or as standalone generative models altogether. Through extensive\nexperiments, we demonstrate that they outperform existing distillation\ntechniques for diffusion models in one- and few-step sampling, achieving the\nnew state-of-the-art FID of 3.55 on CIFAR-10 and 6.20 on ImageNet 64x64 for\none-step generation. When trained in isolation, consistency models become a new\nfamily of generative models that can outperform existing one-step,\nnon-adversarial generative models on standard benchmarks such as CIFAR-10,\nImageNet 64x64 and LSUN 256x256.",
+                    "authors": "Yang Song, Prafulla Dhariwal, Mark Chen, Ilya Sutskever",
+                    "published": "2023-03-02",
+                    "updated": "2023-05-31",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.CV",
+                        "stat.ML"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2401.01792v1",
+                    "title": "CoMoSVC: Consistency Model-based Singing Voice Conversion",
+                    "abstract": "The diffusion-based Singing Voice Conversion (SVC) methods have achieved\nremarkable performances, producing natural audios with high similarity to the\ntarget timbre. However, the iterative sampling process results in slow\ninference speed, and acceleration thus becomes crucial. In this paper, we\npropose CoMoSVC, a consistency model-based SVC method, which aims to achieve\nboth high-quality generation and high-speed sampling. A diffusion-based teacher\nmodel is first specially designed for SVC, and a student model is further\ndistilled under self-consistency properties to achieve one-step sampling.\nExperiments on a single NVIDIA GTX4090 GPU reveal that although CoMoSVC has a\nsignificantly faster inference speed than the state-of-the-art (SOTA)\ndiffusion-based SVC system, it still achieves comparable or superior conversion\nperformance based on both subjective and objective metrics. Audio samples and\ncodes are available at https://comosvc.github.io/.",
+                    "authors": "Yiwen Lu, Zhen Ye, Wei Xue, Xu Tan, Qifeng Liu, Yike Guo",
+                    "published": "2024-01-03",
+                    "updated": "2024-01-03",
+                    "primary_cat": "eess.AS",
+                    "cats": [
+                        "eess.AS",
+                        "cs.AI",
+                        "cs.LG",
+                        "cs.SD"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2306.10521v2",
+                    "title": "LM-VC: Zero-shot Voice Conversion via Speech Generation based on Language Models",
+                    "abstract": "Language model (LM) based audio generation frameworks, e.g., AudioLM, have\nrecently achieved new state-of-the-art performance in zero-shot audio\ngeneration. In this paper, we explore the feasibility of LMs for zero-shot\nvoice conversion. An intuitive approach is to follow AudioLM - Tokenizing\nspeech into semantic and acoustic tokens respectively by HuBERT and\nSoundStream, and converting source semantic tokens to target acoustic tokens\nconditioned on acoustic tokens of the target speaker. However, such an approach\nencounters several issues: 1) the linguistic content contained in semantic\ntokens may get dispersed during multi-layer modeling while the lengthy speech\ninput in the voice conversion task makes contextual learning even harder; 2)\nthe semantic tokens still contain speaker-related information, which may be\nleaked to the target speech, lowering the target speaker similarity; 3) the\ngeneration diversity in the sampling of the LM can lead to unexpected outcomes\nduring inference, leading to unnatural pronunciation and speech quality\ndegradation. To mitigate these problems, we propose LM-VC, a two-stage language\nmodeling approach that generates coarse acoustic tokens for recovering the\nsource linguistic content and target speaker's timbre, and then reconstructs\nthe fine for acoustic details as converted speech. Specifically, to enhance\ncontent preservation and facilitates better disentanglement, a masked prefix LM\nwith a mask prediction strategy is used for coarse acoustic modeling. This\nmodel is encouraged to recover the masked content from the surrounding context\nand generate target speech based on the target speaker's utterance and\ncorrupted semantic tokens. Besides, to further alleviate the sampling error in\nthe generation, an external LM, which employs window attention to capture the\nlocal acoustic relations, is introduced to participate in the coarse acoustic\nmodeling.",
+                    "authors": "Zhichao Wang, Yuanzhe Chen, Lei Xie, Qiao Tian, Yuping Wang",
+                    "published": "2023-06-18",
+                    "updated": "2023-08-21",
+                    "primary_cat": "eess.AS",
+                    "cats": [
+                        "eess.AS",
+                        "cs.SD"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1809.08895v3",
+                    "title": "Neural Speech Synthesis with Transformer Network",
+                    "abstract": "Although end-to-end neural text-to-speech (TTS) methods (such as Tacotron2)\nare proposed and achieve state-of-the-art performance, they still suffer from\ntwo problems: 1) low efficiency during training and inference; 2) hard to model\nlong dependency using current recurrent neural networks (RNNs). Inspired by the\nsuccess of Transformer network in neural machine translation (NMT), in this\npaper, we introduce and adapt the multi-head attention mechanism to replace the\nRNN structures and also the original attention mechanism in Tacotron2. With the\nhelp of multi-head self-attention, the hidden states in the encoder and decoder\nare constructed in parallel, which improves the training efficiency. Meanwhile,\nany two inputs at different times are connected directly by self-attention\nmechanism, which solves the long range dependency problem effectively. Using\nphoneme sequences as input, our Transformer TTS network generates mel\nspectrograms, followed by a WaveNet vocoder to output the final audio results.\nExperiments are conducted to test the efficiency and performance of our new\nnetwork. For the efficiency, our Transformer TTS network can speed up the\ntraining about 4.25 times faster compared with Tacotron2. For the performance,\nrigorous human tests show that our proposed model achieves state-of-the-art\nperformance (outperforms Tacotron2 with a gap of 0.048) and is very close to\nhuman quality (4.39 vs 4.44 in MOS).",
+                    "authors": "Naihan Li, Shujie Liu, Yanqing Liu, Sheng Zhao, Ming Liu, Ming Zhou",
+                    "published": "2018-09-19",
+                    "updated": "2019-01-30",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2106.15561v3",
+                    "title": "A Survey on Neural Speech Synthesis",
+                    "abstract": "Text to speech (TTS), or speech synthesis, which aims to synthesize\nintelligible and natural speech given text, is a hot research topic in speech,\nlanguage, and machine learning communities and has broad applications in the\nindustry. As the development of deep learning and artificial intelligence,\nneural network-based TTS has significantly improved the quality of synthesized\nspeech in recent years. In this paper, we conduct a comprehensive survey on\nneural TTS, aiming to provide a good understanding of current research and\nfuture trends. We focus on the key components in neural TTS, including text\nanalysis, acoustic models and vocoders, and several advanced topics, including\nfast TTS, low-resource TTS, robust TTS, expressive TTS, and adaptive TTS, etc.\nWe further summarize resources related to TTS (e.g., datasets, opensource\nimplementations) and discuss future research directions. This survey can serve\nboth academic researchers and industry practitioners working on TTS.",
+                    "authors": "Xu Tan, Tao Qin, Frank Soong, Tie-Yan Liu",
+                    "published": "2021-06-29",
+                    "updated": "2021-07-23",
+                    "primary_cat": "eess.AS",
+                    "cats": [
+                        "eess.AS",
+                        "cs.CL",
+                        "cs.LG",
+                        "cs.MM",
+                        "cs.SD"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2210.02747v2",
+                    "title": "Flow Matching for Generative Modeling",
+                    "abstract": "We introduce a new paradigm for generative modeling built on Continuous\nNormalizing Flows (CNFs), allowing us to train CNFs at unprecedented scale.\nSpecifically, we present the notion of Flow Matching (FM), a simulation-free\napproach for training CNFs based on regressing vector fields of fixed\nconditional probability paths. Flow Matching is compatible with a general\nfamily of Gaussian probability paths for transforming between noise and data\nsamples -- which subsumes existing diffusion paths as specific instances.\nInterestingly, we find that employing FM with diffusion paths results in a more\nrobust and stable alternative for training diffusion models. Furthermore, Flow\nMatching opens the door to training CNFs with other, non-diffusion probability\npaths. An instance of particular interest is using Optimal Transport (OT)\ndisplacement interpolation to define the conditional probability paths. These\npaths are more efficient than diffusion paths, provide faster training and\nsampling, and result in better generalization. Training CNFs using Flow\nMatching on ImageNet leads to consistently better performance than alternative\ndiffusion-based methods in terms of both likelihood and sample quality, and\nallows fast and reliable sample generation using off-the-shelf numerical ODE\nsolvers.",
+                    "authors": "Yaron Lipman, Ricky T. Q. Chen, Heli Ben-Hamu, Maximilian Nickel, Matt Le",
+                    "published": "2022-10-06",
+                    "updated": "2023-02-08",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI",
+                        "stat.ML"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1703.10135v2",
+                    "title": "Tacotron: Towards End-to-End Speech Synthesis",
+                    "abstract": "A text-to-speech synthesis system typically consists of multiple stages, such\nas a text analysis frontend, an acoustic model and an audio synthesis module.\nBuilding these components often requires extensive domain expertise and may\ncontain brittle design choices. In this paper, we present Tacotron, an\nend-to-end generative text-to-speech model that synthesizes speech directly\nfrom characters. Given <text, audio> pairs, the model can be trained completely\nfrom scratch with random initialization. We present several key techniques to\nmake the sequence-to-sequence framework perform well for this challenging task.\nTacotron achieves a 3.82 subjective 5-scale mean opinion score on US English,\noutperforming a production parametric system in terms of naturalness. In\naddition, since Tacotron generates speech at the frame level, it's\nsubstantially faster than sample-level autoregressive methods.",
+                    "authors": "Yuxuan Wang, RJ Skerry-Ryan, Daisy Stanton, Yonghui Wu, Ron J. Weiss, Navdeep Jaitly, Zongheng Yang, Ying Xiao, Zhifeng Chen, Samy Bengio, Quoc Le, Yannis Agiomyrgiannakis, Rob Clark, Rif A. Saurous",
+                    "published": "2017-03-29",
+                    "updated": "2017-04-06",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL",
+                        "cs.LG",
+                        "cs.SD"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2309.17056v2",
+                    "title": "ReFlow-TTS: A Rectified Flow Model for High-fidelity Text-to-Speech",
+                    "abstract": "The diffusion models including Denoising Diffusion Probabilistic Models\n(DDPM) and score-based generative models have demonstrated excellent\nperformance in speech synthesis tasks. However, its effectiveness comes at the\ncost of numerous sampling steps, resulting in prolonged sampling time required\nto synthesize high-quality speech. This drawback hinders its practical\napplicability in real-world scenarios. In this paper, we introduce ReFlow-TTS,\na novel rectified flow based method for speech synthesis with high-fidelity.\nSpecifically, our ReFlow-TTS is simply an Ordinary Differential Equation (ODE)\nmodel that transports Gaussian distribution to the ground-truth Mel-spectrogram\ndistribution by straight line paths as much as possible. Furthermore, our\nproposed approach enables high-quality speech synthesis with a single sampling\nstep and eliminates the need for training a teacher model. Our experiments on\nLJSpeech Dataset show that our ReFlow-TTS method achieves the best performance\ncompared with other diffusion based models. And the ReFlow-TTS with one step\nsampling achieves competitive performance compared with existing one-step TTS\nmodels.",
+                    "authors": "Wenhao Guan, Qi Su, Haodong Zhou, Shiyu Miao, Xingjia Xie, Lin Li, Qingyang Hong",
+                    "published": "2023-09-29",
+                    "updated": "2024-01-31",
+                    "primary_cat": "cs.SD",
+                    "cats": [
+                        "cs.SD",
+                        "eess.AS"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/0805.0647v1",
+                    "title": "Scaling of Rough Surfaces: Effects of Surface Diffusion on Growth and Roughness Exponents",
+                    "abstract": "Random deposition model with surface diffusion over several next nearest\nneighbours is studied. The results agree with the results obtained by Family\nfor the case of nearest neighbour diffusion [F. Family, J. Phys. A 19(8), L441,\n1986]. However for larger diffusion steps, the growth exponent and the\nroughness exponent show interesting dependence on diffusion length.",
+                    "authors": "Baisakhi Mal, Subhankar Ray, J. Shamanna",
+                    "published": "2008-05-06",
+                    "updated": "2008-05-06",
+                    "primary_cat": "cond-mat.soft",
+                    "cats": [
+                        "cond-mat.soft",
+                        "cond-mat.stat-mech"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/astro-ph/0012545v1",
+                    "title": "Diffusion and the occurrence of hydrogen shell flashes in helium white dwarf stars",
+                    "abstract": "We investigate the effects of element diffusion on the structure and\nevolution of low-mass helium white dwarfs (WD). Attention is focused on the\noccurrence of hydrogen shell flashes induced by diffusion processes during\ncooling phases. Initial models from 0.406 to 0.161 solar masses are constructed\nby applying mass loss rates at different stages of the RGB evolution of a solar\nmodel. The multicomponent flow equations describing gravitational settling, and\nchemical and thermal diffusion are solved and the diffusion calculations are\ncoupled to an evolutionary code. In addition, the same sequences are computed\nbut neglecting diffusion. We find that element diffusion strongly affects the\nstructure and cooling history of helium WD. In particular, diffusion induces\nthe occurrence of hydrogen shell flashes in models with masses ranging from\n0.18 to 0.41 solar masses, which is in sharp contrast from the situation when\ndiffusion is neglected. In connection with the further evolution, these\ndiffusion-induced flashes lead to much thinner hydrogen envelopes, preventing\nstable nuclear burning from being an appreciable energy source at advanced\nstages of evolution. This implies much shorter cooling ages than in the case\nwhen diffusion is neglected. These new WD models are discussed in light of\nrecent observational data of some millisecond pulsar systems with WD\ncompanions. We find that age discrepancies between the predictions of standard\nevolutionary models and such observations appear to be the result of ignoring\nelement diffusion in such models. Indeed, such discrepancies vanish when\naccount is made of diffusion.",
+                    "authors": "L. G. Althaus, A. M. Serenelli, O. G. Benvenuto",
+                    "published": "2000-12-29",
+                    "updated": "2000-12-29",
+                    "primary_cat": "astro-ph",
+                    "cats": [
+                        "astro-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2403.01742v2",
+                    "title": "Diffusion-TS: Interpretable Diffusion for General Time Series Generation",
+                    "abstract": "Denoising diffusion probabilistic models (DDPMs) are becoming the leading\nparadigm for generative models. It has recently shown breakthroughs in audio\nsynthesis, time series imputation and forecasting. In this paper, we propose\nDiffusion-TS, a novel diffusion-based framework that generates multivariate\ntime series samples of high quality by using an encoder-decoder transformer\nwith disentangled temporal representations, in which the decomposition\ntechnique guides Diffusion-TS to capture the semantic meaning of time series\nwhile transformers mine detailed sequential information from the noisy model\ninput. Different from existing diffusion-based approaches, we train the model\nto directly reconstruct the sample instead of the noise in each diffusion step,\ncombining a Fourier-based loss term. Diffusion-TS is expected to generate time\nseries satisfying both interpretablity and realness. In addition, it is shown\nthat the proposed Diffusion-TS can be easily extended to conditional generation\ntasks, such as forecasting and imputation, without any model changes. This also\nmotivates us to further explore the performance of Diffusion-TS under irregular\nsettings. Finally, through qualitative and quantitative experiments, results\nshow that Diffusion-TS achieves the state-of-the-art results on various\nrealistic analyses of time series.",
+                    "authors": "Xinyu Yuan, Yan Qiao",
+                    "published": "2024-03-04",
+                    "updated": "2024-03-14",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1705.07063v1",
+                    "title": "Double diffusivity model under stochastic forcing",
+                    "abstract": "The \"double diffusivity\" model was proposed in the late 1970s, and reworked\nin the early 1980s, as a continuum counterpart to existing discrete models of\ndiffusion corresponding to high diffusivity paths, such as grain boundaries and\ndislocation lines. Technically, the model pans out as a system of coupled {\\it\nFick type} diffusion equations to represent \"regular\" and \"high\" diffusivity\npaths with \"source terms\" accounting for the mass exchange between the two\npaths. The model remit was extended by analogy to describe flow in porous media\nwith double porosity, as well as to model heat conduction in media with two\nnon-equilibrium local temperature baths e.g. ion and electron baths. Uncoupling\nof the two partial differential equations leads to a higher-ordered diffusion\nequation, solutions of which could be obtained in terms of classical diffusion\nequation solutions. Similar equations could also be derived within an \"internal\nlength\" gradient (ILG) mechanics formulation applied to diffusion problems,\n{\\it i.e.}, by introducing nonlocal effects, together with inertia and\nviscosity, in a mechanics based formulation of diffusion theory. This issue\nbecomes particularly important in the case of diffusion in nanopolycrystals\nwhose deterministic ILG based theoretical calculations predict a relaxation\ntime that is only about one-tenth of the actual experimentally verified\ntimescale. This article provides the \"missing link\" in this estimation by\nadding a vital element in the ILG structure, that of stochasticity, that takes\ninto account all boundary layer fluctuations. Our stochastic-ILG diffusion\ncalculation confirms rapprochement between theory and experiment, thereby\nbenchmarking a new generation of gradient-based continuum models that conform\ncloser to real life fluctuating environments.",
+                    "authors": "Amit K Chattopadhyay, Elias C Aifantis",
+                    "published": "2017-05-19",
+                    "updated": "2017-05-19",
+                    "primary_cat": "cond-mat.soft",
+                    "cats": [
+                        "cond-mat.soft",
+                        "cond-mat.mtrl-sci",
+                        "cond-mat.stat-mech"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2010.02514v1",
+                    "title": "Diffusion model and analysis of diffusion process at lagrangian method",
+                    "abstract": "Based on Fick's 2nd law the development of moving particle semi-implicit\nmethod for predicting diffusion process is proposed in this study",
+                    "authors": "Ziqi Zhou",
+                    "published": "2020-10-06",
+                    "updated": "2020-10-06",
+                    "primary_cat": "physics.flu-dyn",
+                    "cats": [
+                        "physics.flu-dyn"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/math/0204289v1",
+                    "title": "On diffusion approximation with discontinuous coefficients",
+                    "abstract": "Convergence of stochastic processes with jumps to diffusion processes is\ninvestigated in the case when the limit process has discontinuous coefficients.\n  An example is given in which the diffusion approximation of a queueing model\nyields a diffusion process with discontinuous diffusion and drift coefficients.",
+                    "authors": "N. V. Krylov, R. Liptser",
+                    "published": "2002-04-24",
+                    "updated": "2002-04-24",
+                    "primary_cat": "math.PR",
+                    "cats": [
+                        "math.PR",
+                        "math.SG",
+                        "60B10; 60K25}"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2301.00527v1",
+                    "title": "Diffusion Probabilistic Models for Scene-Scale 3D Categorical Data",
+                    "abstract": "In this paper, we learn a diffusion model to generate 3D data on a\nscene-scale. Specifically, our model crafts a 3D scene consisting of multiple\nobjects, while recent diffusion research has focused on a single object. To\nrealize our goal, we represent a scene with discrete class labels, i.e.,\ncategorical distribution, to assign multiple objects into semantic categories.\nThus, we extend discrete diffusion models to learn scene-scale categorical\ndistributions. In addition, we validate that a latent diffusion model can\nreduce computation costs for training and deploying. To the best of our\nknowledge, our work is the first to apply discrete and latent diffusion for 3D\ncategorical data on a scene-scale. We further propose to perform semantic scene\ncompletion (SSC) by learning a conditional distribution using our diffusion\nmodel, where the condition is a partial observation in a sparse point cloud. In\nexperiments, we empirically show that our diffusion models not only generate\nreasonable scenes, but also perform the scene completion task better than a\ndiscriminative model. Our code and models are available at\nhttps://github.com/zoomin-lee/scene-scale-diffusion",
+                    "authors": "Jumin Lee, Woobin Im, Sebin Lee, Sung-Eui Yoon",
+                    "published": "2023-01-02",
+                    "updated": "2023-01-02",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2305.10028v1",
+                    "title": "Pyramid Diffusion Models For Low-light Image Enhancement",
+                    "abstract": "Recovering noise-covered details from low-light images is challenging, and\nthe results given by previous methods leave room for improvement. Recent\ndiffusion models show realistic and detailed image generation through a\nsequence of denoising refinements and motivate us to introduce them to\nlow-light image enhancement for recovering realistic details. However, we found\ntwo problems when doing this, i.e., 1) diffusion models keep constant\nresolution in one reverse process, which limits the speed; 2) diffusion models\nsometimes result in global degradation (e.g., RGB shift). To address the above\nproblems, this paper proposes a Pyramid Diffusion model (PyDiff) for low-light\nimage enhancement. PyDiff uses a novel pyramid diffusion method to perform\nsampling in a pyramid resolution style (i.e., progressively increasing\nresolution in one reverse process). Pyramid diffusion makes PyDiff much faster\nthan vanilla diffusion models and introduces no performance degradation.\nFurthermore, PyDiff uses a global corrector to alleviate the global degradation\nthat may occur in the reverse process, significantly improving the performance\nand making the training of diffusion models easier with little additional\ncomputational consumption. Extensive experiments on popular benchmarks show\nthat PyDiff achieves superior performance and efficiency. Moreover, PyDiff can\ngeneralize well to unseen noise and illumination distributions.",
+                    "authors": "Dewei Zhou, Zongxin Yang, Yi Yang",
+                    "published": "2023-05-17",
+                    "updated": "2023-05-17",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2305.12377v1",
+                    "title": "The vanishing diffusion limit for an Oldroyd-B model in $\\mathbb{R}^2_+$",
+                    "abstract": "We consider the initial-boundary value problem for an incompressible\nOldroyd-B model with stress diffusion in two-dimensional upper half plane which\ndescribes the motion of viscoelastic polymeric fluids. From the physical point\nof view, the diffusive coefficient is several orders of magnitude smaller than\nother parameters in the model, and is usually assumed to be zero. However, the\nlink between the diffusive model and the standard one (zero diffusion) via\nvanishing diffusion limit is still unknown from the mathematical point of view,\nin particular for the problem with boundary. Some numerical results [13]\nsuggest that this should be true. In this work, we provide a rigorous\njustification for the vanishing diffusion in $L^\\infty$-norm.",
+                    "authors": "Yinghui Wang, Huanyao Wen",
+                    "published": "2023-05-21",
+                    "updated": "2023-05-21",
+                    "primary_cat": "math.AP",
+                    "cats": [
+                        "math.AP",
+                        "35Q35, 76A10, 76D10"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2006.00003v1",
+                    "title": "Coupling particle-based reaction-diffusion simulations with reservoirs mediated by reaction-diffusion PDEs",
+                    "abstract": "Open biochemical systems of interacting molecules are ubiquitous in\nlife-related processes. However, established computational methodologies, like\nmolecular dynamics, are still mostly constrained to closed systems and\ntimescales too small to be relevant for life processes. Alternatively,\nparticle-based reaction-diffusion models are currently the most accurate and\ncomputationally feasible approach at these scales. Their efficiency lies in\nmodeling entire molecules as particles that can diffuse and interact with each\nother. In this work, we develop modeling and numerical schemes for\nparticle-based reaction-diffusion in an open setting, where the reservoirs are\nmediated by reaction-diffusion PDEs. We derive two important theoretical\nresults. The first one is the mean-field for open systems of diffusing\nparticles; the second one is the mean-field for a particle-based\nreaction-diffusion system with second-order reactions. We employ these two\nresults to develop a numerical scheme that consistently couples particle-based\nreaction-diffusion processes with reaction-diffusion PDEs. This allows modeling\nopen biochemical systems in contact with reservoirs that are time-dependent and\nspatially inhomogeneous, as in many relevant real-world applications.",
+                    "authors": "Margarita Kostr\u00e9, Christof Sch\u00fctte, Frank No\u00e9, Mauricio J. del Razo",
+                    "published": "2020-05-29",
+                    "updated": "2020-05-29",
+                    "primary_cat": "q-bio.QM",
+                    "cats": [
+                        "q-bio.QM",
+                        "physics.chem-ph",
+                        "physics.comp-ph",
+                        "92C40, 92C45, 60J70, 60Gxx, 70Lxx"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2301.00059v2",
+                    "title": "Describing NMR chemical exchange by effective phase diffusion approach",
+                    "abstract": "This paper proposes an effective phase diffusion method to analyze chemical\nexchange in nuclear magnetic resonance (NMR). The chemical exchange involves\nspin jumps around different sites where the spin angular frequencies vary,\nwhich leads to a random phase walk viewed from the rotating frame reference.\nTherefore, the random walk in phase space can be treated by the effective phase\ndiffusion method. Both the coupled and uncoupled phase diffusions are\nconsidered; additionally, it includes normal diffusion as well as fractional\ndiffusion. Based on these phase diffusion equations, the line shape of NMR\nexchange spectrum can be analyzed. By comparing these theoretical results with\nthe conventional theory, this phase diffusion approach works for fast exchange,\nranging from slightly faster than intermediate exchange to very fast exchange.\nFor normal diffusion models, the theoretically predicted curves agree with\nthose predicted from traditional models in the literature, and the\ncharacteristic exchange time obtained from phase diffusion with a fixed jump\ntime is the same as that obtained from the conventional model. However, the\nphase diffusion with a monoexponential time distribution gives a characteristic\nexchange time constant which is half of that obtained from the traditional\nmodel. Additionally, the fractional diffusion obtains a significantly different\nline shape than that predicted based on normal diffusion.",
+                    "authors": "Guoxing Lin",
+                    "published": "2022-12-30",
+                    "updated": "2023-05-17",
+                    "primary_cat": "physics.chem-ph",
+                    "cats": [
+                        "physics.chem-ph",
+                        "cond-mat.stat-mech"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/nlin/0212039v2",
+                    "title": "Front dynamics in reaction-diffusion systems with Levy flights: a fractional diffusion approach",
+                    "abstract": "The use of reaction-diffusion models rests on the key assumption that the\nunderlying diffusive process is Gaussian. However, a growing number of studies\nhave pointed out the prevalence of anomalous diffusion, and there is a need to\nunderstand the dynamics of reactive systems in the presence of this type of\nnon-Gaussian diffusion. Here we present a study of front dynamics in\nreaction-diffusion systems where anomalous diffusion is due to the presence of\nasymmetric Levy flights. Our approach consists of replacing the Laplacian\ndiffusion operator by a fractional diffusion operator, whose fundamental\nsolutions are Levy $\\alpha$-stable distributions. Numerical simulation of the\nfractional Fisher-Kolmogorov equation, and analytical arguments show that\nanomalous diffusion leads to the exponential acceleration of fronts and a\nuniversal power law decay, $x^{-\\alpha}$, of the tail, where $\\alpha$, the\nindex of the Levy distribution, is the order of the fractional derivative.",
+                    "authors": "D. del-Castillo-Negrete, B. A. Carreras, V. E. Lynch",
+                    "published": "2002-12-17",
+                    "updated": "2003-06-30",
+                    "primary_cat": "nlin.PS",
+                    "cats": [
+                        "nlin.PS",
+                        "nlin.CD"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2302.05737v2",
+                    "title": "A Reparameterized Discrete Diffusion Model for Text Generation",
+                    "abstract": "This work studies discrete diffusion probabilistic models with applications\nto natural language generation. We derive an alternative yet equivalent\nformulation of the sampling from discrete diffusion processes and leverage this\ninsight to develop a family of reparameterized discrete diffusion models. The\nderived generic framework is highly flexible, offers a fresh perspective of the\ngeneration process in discrete diffusion models, and features more effective\ntraining and decoding techniques. We conduct extensive experiments to evaluate\nthe text generation capability of our model, demonstrating significant\nimprovements over existing diffusion models.",
+                    "authors": "Lin Zheng, Jianbo Yuan, Lei Yu, Lingpeng Kong",
+                    "published": "2023-02-11",
+                    "updated": "2024-02-03",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL",
+                        "cs.LG"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1503.03201v2",
+                    "title": "Fractional Diffusion Equations for Lattice and Continuum: Grunwald-Letnikov Differences and Derivatives Approach",
+                    "abstract": "Fractional diffusion equations for three-dimensional lattice models based on\nfractional-order differences of the Grunwald-Letnikov type are suggested. These\nlattice fractional diffusion equations contain difference operators that\ndescribe long-range jumps from one lattice site to other. In continuum limit,\nthe suggested lattice diffusion equations with non-integer order differences\ngive the diffusion equations with the Grunwald-Letnikov fractional derivatives\nfor continuum. We propose a consistent derivation of the fractional diffusion\nequation with the fractional derivatives of Grunwald-Letnikov type. The\nsuggested lattice diffusion equations can be considered as a new\nmicrostructural basis of space-fractional diffusion in nonlocal media.",
+                    "authors": "Vasily E. Tarasov",
+                    "published": "2015-03-11",
+                    "updated": "2015-03-12",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2207.09786v1",
+                    "title": "Non-Uniform Diffusion Models",
+                    "abstract": "Diffusion models have emerged as one of the most promising frameworks for\ndeep generative modeling. In this work, we explore the potential of non-uniform\ndiffusion models. We show that non-uniform diffusion leads to multi-scale\ndiffusion models which have similar structure to this of multi-scale\nnormalizing flows. We experimentally find that in the same or less training\ntime, the multi-scale diffusion model achieves better FID score than the\nstandard uniform diffusion model. More importantly, it generates samples $4.4$\ntimes faster in $128\\times 128$ resolution. The speed-up is expected to be\nhigher in higher resolutions where more scales are used. Moreover, we show that\nnon-uniform diffusion leads to a novel estimator for the conditional score\nfunction which achieves on par performance with the state-of-the-art\nconditional denoising estimator. Our theoretical and experimental findings are\naccompanied by an open source library MSDiff which can facilitate further\nresearch of non-uniform diffusion models.",
+                    "authors": "Georgios Batzolis, Jan Stanczuk, Carola-Bibiane Sch\u00f6nlieb, Christian Etmann",
+                    "published": "2022-07-20",
+                    "updated": "2022-07-20",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1709.05336v1",
+                    "title": "Cs diffusion in SiC high-energy grain boundaries",
+                    "abstract": "Cesium (Cs) is a radioactive fission product whose release is of concern for\nTristructural-Isotropic (TRISO) fuel particles. In this work, Cs diffusion\nthrough high energy grain boundaries (HEGBs) of cubic-SiC is studied using an\nab-initio based kinetic Monte Carlo (kMC) model. The HEGB environment was\nmodeled as an amorphous SiC (a-SiC), and Cs defect energies were calculated\nusing density functional theory (DFT). From defect energies, it was suggested\nthat the fastest diffusion mechanism as Cs interstitial in an amorphous SiC.\nThe diffusion of Cs interstitial was simulated using a kMC, based on the site\nand transition state energies sampled from the DFT. The Cs HEGB diffusion\nexhibited an Arrhenius type diffusion in the range of 1200-1600{\\deg}C. The\ncomparison between HEGB results and the other studies suggests not only that\nthe GB diffusion dominates the bulk diffusion, but also that the HEGB is one of\nthe fastest grain boundary paths for the Cs diffusion. The diffusion\ncoefficients in HEGB are clearly a few orders of magnitude lower than the\nreported diffusion coefficients from in- and out-of- pile samples, suggesting\nthat other contributions are responsible, such as a radiation enhanced\ndiffusion.",
+                    "authors": "Hyunseok Ko, Izabela Szlufarska, Dane Morgan",
+                    "published": "2017-09-11",
+                    "updated": "2017-09-11",
+                    "primary_cat": "cond-mat.mtrl-sci",
+                    "cats": [
+                        "cond-mat.mtrl-sci",
+                        "nucl-th"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2212.10777v4",
+                    "title": "Hierarchically branched diffusion models leverage dataset structure for class-conditional generation",
+                    "abstract": "Class-labeled datasets, particularly those common in scientific domains, are\nrife with internal structure, yet current class-conditional diffusion models\nignore these relationships and implicitly diffuse on all classes in a flat\nfashion. To leverage this structure, we propose hierarchically branched\ndiffusion models as a novel framework for class-conditional generation.\nBranched diffusion models rely on the same diffusion process as traditional\nmodels, but learn reverse diffusion separately for each branch of a hierarchy.\nWe highlight several advantages of branched diffusion models over the current\nstate-of-the-art methods for class-conditional diffusion, including extension\nto novel classes in a continual-learning setting, a more sophisticated form of\nanalogy-based conditional generation (i.e. transmutation), and a novel\ninterpretability into the generation process. We extensively evaluate branched\ndiffusion models on several benchmark and large real-world scientific datasets\nspanning many data modalities.",
+                    "authors": "Alex M. Tseng, Max Shen, Tommaso Biancalani, Gabriele Scalia",
+                    "published": "2022-12-21",
+                    "updated": "2024-02-01",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2403.05794v2",
+                    "title": "Privacy-Preserving Diffusion Model Using Homomorphic Encryption",
+                    "abstract": "In this paper, we introduce a privacy-preserving stable diffusion framework\nleveraging homomorphic encryption, called HE-Diffusion, which primarily focuses\non protecting the denoising phase of the diffusion process. HE-Diffusion is a\ntailored encryption framework specifically designed to align with the unique\narchitecture of stable diffusion, ensuring both privacy and functionality. To\naddress the inherent computational challenges, we propose a novel\nmin-distortion method that enables efficient partial image encryption,\nsignificantly reducing the overhead without compromising the model's output\nquality. Furthermore, we adopt a sparse tensor representation to expedite\ncomputational operations, enhancing the overall efficiency of the\nprivacy-preserving diffusion process. We successfully implement HE-based\nprivacy-preserving stable diffusion inference. The experimental results show\nthat HE-Diffusion achieves 500 times speedup compared with the baseline method,\nand reduces time cost of the homomorphically encrypted inference to the minute\nlevel. Both the performance and accuracy of the HE-Diffusion are on par with\nthe plaintext counterpart. Our approach marks a significant step towards\nintegrating advanced cryptographic techniques with state-of-the-art generative\nmodels, paving the way for privacy-preserving and efficient image generation in\ncritical applications.",
+                    "authors": "Yaojian Chen, Qiben Yan",
+                    "published": "2024-03-09",
+                    "updated": "2024-05-02",
+                    "primary_cat": "cs.CR",
+                    "cats": [
+                        "cs.CR",
+                        "cs.AI"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2404.08926v2",
+                    "title": "Diffusion Models Meet Remote Sensing: Principles, Methods, and Perspectives",
+                    "abstract": "As a newly emerging advance in deep generative models, diffusion models have\nachieved state-of-the-art results in many fields, including computer vision,\nnatural language processing, and molecule design. The remote sensing community\nhas also noticed the powerful ability of diffusion models and quickly applied\nthem to a variety of tasks for image processing. Given the rapid increase in\nresearch on diffusion models in the field of remote sensing, it is necessary to\nconduct a comprehensive review of existing diffusion model-based remote sensing\npapers, to help researchers recognize the potential of diffusion models and\nprovide some directions for further exploration. Specifically, this paper first\nintroduces the theoretical background of diffusion models, and then\nsystematically reviews the applications of diffusion models in remote sensing,\nincluding image generation, enhancement, and interpretation. Finally, the\nlimitations of existing remote sensing diffusion models and worthy research\ndirections for further exploration are discussed and summarized.",
+                    "authors": "Yidan Liu, Jun Yue, Shaobo Xia, Pedram Ghamisi, Weiying Xie, Leyuan Fang",
+                    "published": "2024-04-13",
+                    "updated": "2024-04-17",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2312.14589v1",
+                    "title": "Non-Denoising Forward-Time Diffusions",
+                    "abstract": "The scope of this paper is generative modeling through diffusion processes.\nAn approach falling within this paradigm is the work of Song et al. (2021),\nwhich relies on a time-reversal argument to construct a diffusion process\ntargeting the desired data distribution. We show that the time-reversal\nargument, common to all denoising diffusion probabilistic modeling proposals,\nis not necessary. We obtain diffusion processes targeting the desired data\ndistribution by taking appropriate mixtures of diffusion bridges. The resulting\ntransport is exact by construction, allows for greater flexibility in choosing\nthe dynamics of the underlying diffusion, and can be approximated by means of a\nneural network via novel training objectives. We develop a unifying view of the\ndrift adjustments corresponding to our and to time-reversal approaches and make\nuse of this representation to inspect the inner workings of diffusion-based\ngenerative models. Finally, we leverage on scalable simulation and inference\ntechniques common in spatial statistics to move beyond fully factorial\ndistributions in the underlying diffusion dynamics. The methodological advances\ncontained in this work contribute toward establishing a general framework for\ngenerative modeling based on diffusion processes.",
+                    "authors": "Stefano Peluchetti",
+                    "published": "2023-12-22",
+                    "updated": "2023-12-22",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "stat.ML"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2404.07771v1",
+                    "title": "An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimization",
+                    "abstract": "Diffusion models, a powerful and universal generative AI technology, have\nachieved tremendous success in computer vision, audio, reinforcement learning,\nand computational biology. In these applications, diffusion models provide\nflexible high-dimensional data modeling, and act as a sampler for generating\nnew samples under active guidance towards task-desired properties. Despite the\nsignificant empirical success, theory of diffusion models is very limited,\npotentially slowing down principled methodological innovations for further\nharnessing and improving diffusion models. In this paper, we review emerging\napplications of diffusion models, understanding their sample generation under\nvarious controls. Next, we overview the existing theories of diffusion models,\ncovering their statistical properties and sampling capabilities. We adopt a\nprogressive routine, beginning with unconditional diffusion models and\nconnecting to conditional counterparts. Further, we review a new avenue in\nhigh-dimensional structured optimization through conditional diffusion models,\nwhere searching for solutions is reformulated as a conditional sampling problem\nand solved by diffusion models. Lastly, we discuss future directions about\ndiffusion models. The purpose of this paper is to provide a well-rounded\ntheoretical exposure for stimulating forward-looking theories and methods of\ndiffusion models.",
+                    "authors": "Minshuo Chen, Song Mei, Jianqing Fan, Mengdi Wang",
+                    "published": "2024-04-11",
+                    "updated": "2024-04-11",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "math.ST",
+                        "stat.ML",
+                        "stat.TH"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2310.05264v3",
+                    "title": "The Emergence of Reproducibility and Consistency in Diffusion Models",
+                    "abstract": "In this work, we investigate an intriguing and prevalent phenomenon of\ndiffusion models which we term as \"consistent model reproducibility\": given the\nsame starting noise input and a deterministic sampler, different diffusion\nmodels often yield remarkably similar outputs. We confirm this phenomenon\nthrough comprehensive experiments, implying that different diffusion models\nconsistently reach the same data distribution and scoring function regardless\nof diffusion model frameworks, model architectures, or training procedures.\nMore strikingly, our further investigation implies that diffusion models are\nlearning distinct distributions affected by the training data size. This is\nsupported by the fact that the model reproducibility manifests in two distinct\ntraining regimes: (i) \"memorization regime\", where the diffusion model overfits\nto the training data distribution, and (ii) \"generalization regime\", where the\nmodel learns the underlying data distribution. Our study also finds that this\nvaluable property generalizes to many variants of diffusion models, including\nthose for conditional use, solving inverse problems, and model fine-tuning.\nFinally, our work raises numerous intriguing theoretical questions for future\ninvestigation and highlights practical implications regarding training\nefficiency, model privacy, and the controlled generation of diffusion models.",
+                    "authors": "Huijie Zhang, Jinfan Zhou, Yifu Lu, Minzhe Guo, Peng Wang, Liyue Shen, Qing Qu",
+                    "published": "2023-10-08",
+                    "updated": "2024-02-21",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.CV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2303.06574v2",
+                    "title": "Diffusion Models for Non-autoregressive Text Generation: A Survey",
+                    "abstract": "Non-autoregressive (NAR) text generation has attracted much attention in the\nfield of natural language processing, which greatly reduces the inference\nlatency but has to sacrifice the generation accuracy. Recently, diffusion\nmodels, a class of latent variable generative models, have been introduced into\nNAR text generation, showing an improved text generation quality. In this\nsurvey, we review the recent progress in diffusion models for NAR text\ngeneration. As the background, we first present the general definition of\ndiffusion models and the text diffusion models, and then discuss their merits\nfor NAR generation. As the core content, we further introduce two mainstream\ndiffusion models in existing work of text diffusion, and review the key designs\nof the diffusion process. Moreover, we discuss the utilization of pre-trained\nlanguage models (PLMs) for text diffusion models and introduce optimization\ntechniques for text data. Finally, we discuss several promising directions and\nconclude this paper. Our survey aims to provide researchers with a systematic\nreference of related research on text diffusion models for NAR generation. We\npresent our collection of text diffusion models at\nhttps://github.com/RUCAIBox/Awesome-Text-Diffusion-Models.",
+                    "authors": "Yifan Li, Kun Zhou, Wayne Xin Zhao, Ji-Rong Wen",
+                    "published": "2023-03-12",
+                    "updated": "2023-05-13",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2403.15766v1",
+                    "title": "BEND: Bagging Deep Learning Training Based on Efficient Neural Network Diffusion",
+                    "abstract": "Bagging has achieved great success in the field of machine learning by\nintegrating multiple base classifiers to build a single strong classifier to\nreduce model variance. The performance improvement of bagging mainly relies on\nthe number and diversity of base classifiers. However, traditional deep\nlearning model training methods are expensive to train individually and\ndifficult to train multiple models with low similarity in a restricted dataset.\nRecently, diffusion models, which have been tremendously successful in the\nfields of imaging and vision, have been found to be effective in generating\nneural network model weights and biases with diversity. We creatively propose a\nBagging deep learning training algorithm based on Efficient Neural network\nDiffusion (BEND). The originality of BEND comes from the first use of a neural\nnetwork diffusion model to efficiently build base classifiers for bagging. Our\napproach is simple but effective, first using multiple trained model weights\nand biases as inputs to train autoencoder and latent diffusion model to realize\na diffusion model from noise to valid neural network parameters. Subsequently,\nwe generate several base classifiers using the trained diffusion model.\nFinally, we integrate these ba se classifiers for various inference tasks using\nthe Bagging method. Resulting experiments on multiple models and datasets show\nthat our proposed BEND algorithm can consistently outperform the mean and\nmedian accuracies of both the original trained model and the diffused model. At\nthe same time, new models diffused using the diffusion model have higher\ndiversity and lower cost than multiple models trained using traditional\nmethods. The BEND approach successfully introduces diffusion models into the\nnew deep learning training domain and provides a new paradigm for future deep\nlearning training and inference.",
+                    "authors": "Jia Wei, Xingjun Zhang, Witold Pedrycz",
+                    "published": "2024-03-23",
+                    "updated": "2024-03-23",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2005.00562v1",
+                    "title": "Unexpected crossovers in correlated random-diffusivity processes",
+                    "abstract": "The passive and active motion of micron-sized tracer particles in crowded\nliquids and inside living biological cells is ubiquitously characterised by\n\"viscoelastic\" anomalous diffusion, in which the increments of the motion\nfeature long-ranged negative and positive correlations. While viscoelastic\nanomalous diffusion is typically modelled by a Gaussian process with correlated\nincrements, so-called fractional Gaussian noise, an increasing number of\nsystems are reported, in which viscoelastic anomalous diffusion is paired with\nnon-Gaussian displacement distributions. Following recent advances in Brownian\nyet non-Gaussian diffusion we here introduce and discuss several possible\nversions of random-diffusivity models with long-ranged correlations. While all\nthese models show a crossover from non-Gaussian to Gaussian distributions\nbeyond some correlation time, their mean squared displacements exhibit\nstrikingly different behaviours: depending on the model crossovers from\nanomalous to normal diffusion are observed, as well as unexpected dependencies\nof the effective diffusion coefficient on the correlation exponent. Our\nobservations of the strong non-universality of random-diffusivity viscoelastic\nanomalous diffusion are important for the analysis of experiments and a better\nunderstanding of the physical origins of \"viscoelastic yet non-Gaussian\"\ndiffusion.",
+                    "authors": "Wei Wang, Flavio Seno, Igor M. Sokolov, Aleksei V. Chechkin, Ralf Metzler",
+                    "published": "2020-05-01",
+                    "updated": "2020-05-01",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech",
+                        "physics.bio-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2206.12327v1",
+                    "title": "Source Localization of Graph Diffusion via Variational Autoencoders for Graph Inverse Problems",
+                    "abstract": "Graph diffusion problems such as the propagation of rumors, computer viruses,\nor smart grid failures are ubiquitous and societal. Hence it is usually crucial\nto identify diffusion sources according to the current graph diffusion\nobservations. Despite its tremendous necessity and significance in practice,\nsource localization, as the inverse problem of graph diffusion, is extremely\nchallenging as it is ill-posed: different sources may lead to the same graph\ndiffusion patterns. Different from most traditional source localization\nmethods, this paper focuses on a probabilistic manner to account for the\nuncertainty of different candidate sources. Such endeavors require overcoming\nchallenges including 1) the uncertainty in graph diffusion source localization\nis hard to be quantified; 2) the complex patterns of the graph diffusion\nsources are difficult to be probabilistically characterized; 3) the\ngeneralization under any underlying diffusion patterns is hard to be imposed.\nTo solve the above challenges, this paper presents a generic framework: Source\nLocalization Variational AutoEncoder (SL-VAE) for locating the diffusion\nsources under arbitrary diffusion patterns. Particularly, we propose a\nprobabilistic model that leverages the forward diffusion estimation model along\nwith deep generative models to approximate the diffusion source distribution\nfor quantifying the uncertainty. SL-VAE further utilizes prior knowledge of the\nsource-observation pairs to characterize the complex patterns of diffusion\nsources by a learned generative prior. Lastly, a unified objective that\nintegrates the forward diffusion estimation model is derived to enforce the\nmodel to generalize under arbitrary diffusion patterns. Extensive experiments\nare conducted on 7 real-world datasets to demonstrate the superiority of SL-VAE\nin reconstructing the diffusion sources by excelling other methods on average\n20% in AUC score.",
+                    "authors": "Chen Ling, Junji Jiang, Junxiang Wang, Liang Zhao",
+                    "published": "2022-06-24",
+                    "updated": "2022-06-24",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.IT",
+                        "math.IT"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2304.05060v2",
+                    "title": "SPIRiT-Diffusion: Self-Consistency Driven Diffusion Model for Accelerated MRI",
+                    "abstract": "Diffusion models have emerged as a leading methodology for image generation\nand have proven successful in the realm of magnetic resonance imaging (MRI)\nreconstruction. However, existing reconstruction methods based on diffusion\nmodels are primarily formulated in the image domain, making the reconstruction\nquality susceptible to inaccuracies in coil sensitivity maps (CSMs). k-space\ninterpolation methods can effectively address this issue but conventional\ndiffusion models are not readily applicable in k-space interpolation. To\novercome this challenge, we introduce a novel approach called SPIRiT-Diffusion,\nwhich is a diffusion model for k-space interpolation inspired by the iterative\nself-consistent SPIRiT method. Specifically, we utilize the iterative solver of\nthe self-consistent term (i.e., k-space physical prior) in SPIRiT to formulate\na novel stochastic differential equation (SDE) governing the diffusion process.\nSubsequently, k-space data can be interpolated by executing the diffusion\nprocess. This innovative approach highlights the optimization model's role in\ndesigning the SDE in diffusion models, enabling the diffusion process to align\nclosely with the physics inherent in the optimization model, a concept referred\nto as model-driven diffusion. We evaluated the proposed SPIRiT-Diffusion method\nusing a 3D joint intracranial and carotid vessel wall imaging dataset. The\nresults convincingly demonstrate its superiority over image-domain\nreconstruction methods, achieving high reconstruction quality even at a\nsubstantial acceleration rate of 10.",
+                    "authors": "Zhuo-Xu Cui, Chentao Cao, Yue Wang, Sen Jia, Jing Cheng, Xin Liu, Hairong Zheng, Dong Liang, Yanjie Zhu",
+                    "published": "2023-04-11",
+                    "updated": "2024-04-20",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1009.5965v1",
+                    "title": "Sensitivity of a Babcock-Leighton Flux-Transport Dynamo to Magnetic Diffusivity Profiles",
+                    "abstract": "We study the influence of various magnetic diffusivity profiles on the\nevolution of the poloidal and toroidal magnetic fields in a kinematic flux\ntransport dynamo model for the Sun. The diffusivity is a poorly understood\ningredient in solar dynamo models. We mathematically construct various\ntheoretical profiles of the depth-dependent diffusivity, based on constraints\nfrom mixing length theory and turbulence, and on comparisons of poloidal field\nevolution on the Sun with that from the flux-transport dynamo model.\n  We then study the effect of each diffusivity profile in the cyclic evolution\nof the magnetic fields in the Sun, by solving the mean-field dynamo equations.\nWe investigate effects on the solar cycle periods, the maximum tachocline field\nstrengths, and the evolution of the toroidal and poloidal field structures\ninside the convection zone, due to different diffusivity profiles.\n  We conduct three experiments: (I) comparing very different magnetic\ndiffusivity profiles; (II) comparing different locations of diffusivity\ngradient near the tachocline for the optimal profile; and (III) comparing\ndifferent slopes of diffusivity gradient for an optimal profile.\n  Based on these simulations, we discuss which aspects of depth-dependent\ndiffusivity profiles may be most relevant for magnetic flux evolution in the\nSun, and how certain observations could help improve knowledge of this dynamo\ningredient.",
+                    "authors": "E. J. Zita",
+                    "published": "2010-09-29",
+                    "updated": "2010-09-29",
+                    "primary_cat": "astro-ph.SR",
+                    "cats": [
+                        "astro-ph.SR",
+                        "physics.flu-dyn"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1905.04004v2",
+                    "title": "Well-posedness of a cross-diffusion population model with nonlocal diffusion",
+                    "abstract": "We prove the existence and uniqueness of solution of a nonlocal\ncross-diffusion competitive population model for two species. The model may be\nconsidered as a version, or even an approximation, of the paradigmatic\nShigesada-Kawasaki-Teramoto cross-diffusion model, in which the usual diffusion\ndifferential operator is replaced by an integral diffusion operator. The proof\nof existence of solutions is based on a compactness argument, while the\nuniqueness of solution is achieved through a duality technique.",
+                    "authors": "Gonzalo Galiano, Juli\u00e1n Velasco",
+                    "published": "2019-05-10",
+                    "updated": "2024-01-24",
+                    "primary_cat": "math.AP",
+                    "cats": [
+                        "math.AP"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2303.16203v3",
+                    "title": "Your Diffusion Model is Secretly a Zero-Shot Classifier",
+                    "abstract": "The recent wave of large-scale text-to-image diffusion models has\ndramatically increased our text-based image generation abilities. These models\ncan generate realistic images for a staggering variety of prompts and exhibit\nimpressive compositional generalization abilities. Almost all use cases thus\nfar have solely focused on sampling; however, diffusion models can also provide\nconditional density estimates, which are useful for tasks beyond image\ngeneration. In this paper, we show that the density estimates from large-scale\ntext-to-image diffusion models like Stable Diffusion can be leveraged to\nperform zero-shot classification without any additional training. Our\ngenerative approach to classification, which we call Diffusion Classifier,\nattains strong results on a variety of benchmarks and outperforms alternative\nmethods of extracting knowledge from diffusion models. Although a gap remains\nbetween generative and discriminative approaches on zero-shot recognition\ntasks, our diffusion-based approach has significantly stronger multimodal\ncompositional reasoning ability than competing discriminative approaches.\nFinally, we use Diffusion Classifier to extract standard classifiers from\nclass-conditional diffusion models trained on ImageNet. Our models achieve\nstrong classification performance using only weak augmentations and exhibit\nqualitatively better \"effective robustness\" to distribution shift. Overall, our\nresults are a step toward using generative over discriminative models for\ndownstream tasks. Results and visualizations at\nhttps://diffusion-classifier.github.io/",
+                    "authors": "Alexander C. Li, Mihir Prabhudesai, Shivam Duggal, Ellis Brown, Deepak Pathak",
+                    "published": "2023-03-28",
+                    "updated": "2023-09-13",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI",
+                        "cs.CV",
+                        "cs.NE",
+                        "cs.RO"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1603.05605v1",
+                    "title": "Multiscale modeling of diffusion in a crowded environment",
+                    "abstract": "We present a multiscale approach to model diffusion in a crowded environment\nand its effect on the reaction rates. Diffusion in biological systems is often\nmodeled by a discrete space jump process in order to capture the inherent noise\nof biological systems, which becomes important in the low copy number regime.\nTo model diffusion in the crowded cell environment efficiently, we compute the\njump rates in this mesoscopic model from local first exit times, which account\nfor the microscopic positions of the crowding molecules, while the diffusing\nmolecules jump on a coarser Cartesian grid. We then extract a macroscopic\ndescription from the resulting jump rates, where the excluded volume effect is\nmodeled by a diffusion equation with space dependent diffusion coefficient. The\ncrowding molecules can be of arbitrary shape and size and numerical experiments\ndemonstrate that those factors together with the size of the diffusing molecule\nplay a crucial role on the magnitude of the decrease in diffusive motion. When\ncorrecting the reaction rates for the altered diffusion we can show that\nmolecular crowding either enhances or inhibits chemical reactions depending on\nlocal fluctuations of the obstacle density.",
+                    "authors": "Lina Meinecke",
+                    "published": "2016-03-12",
+                    "updated": "2016-03-12",
+                    "primary_cat": "q-bio.SC",
+                    "cats": [
+                        "q-bio.SC",
+                        "math.NA",
+                        "92-08"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1908.03076v3",
+                    "title": "The strategy of survival for a competition between normal and anomalous diffusion",
+                    "abstract": "In this paper, we study the competition of two diffusion processes for\nachieving the maximum possible diffusion in an area. This competition, however,\ndoes not occur in the same circumstance; one of these processes is a normal\ndiffusion with a higher growth rate, and another one is an anomalous diffusion\nwith a lower growth rate. The trivial solution of the proposed model suggests\nthat the winner is the one with the higher growth rate. But, the question is:\nwhat characteristics and strategies should the second diffusion include to\nprolong the survival in such a competition? The studied diffusion equations\ncorrespond to the SI model such that the anomalous diffusion has memory\ndescribed by a fractional order derivative. The strategy promise that anomalous\ndiffusion reaches maximum survival in case of forgetting some parts of the\nmemory. This model can represent some of real phenomena, such as the contest of\ntwo companies in a market share, the spreading of two epidemic diseases, the\ndiffusion of two species, or any reaction-diffusion related to real-world\ncompetition.",
+                    "authors": "Moein Khalighi, Jamshid Ardalankia, Abbas Karimi Rizi, Haleh Ebadi, Gholamreza Jafari",
+                    "published": "2019-08-07",
+                    "updated": "2020-10-18",
+                    "primary_cat": "physics.soc-ph",
+                    "cats": [
+                        "physics.soc-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1801.09352v1",
+                    "title": "Distributed order Hausdorff derivative diffusion model to characterize non-Fickian diffusion in porous media",
+                    "abstract": "Many theoretical and experimental results show that solute transport in\nheterogeneous porous media exhibits multi-scaling behaviors. To describe such\nnon-Fickian diffusions, this work provides a distributed order Hausdorff\ndiffusion model to describe the tracer transport in porous media. This model is\nproved to be equivalent with the diffusion equation model with a nonlinear time\ndependent diffusion coefficient. In conjunction with the structural derivative,\nits mean squared displacement (MSD) of the tracer particles is explicitly\nderived as a dilogarithm function when the weight function of the order\ndistribution is a linear function of the time derivative order. This model can\ncapture both accelerating and decelerating anomalous and ultraslow diffusions\nby varying the weight parameter c. In this study, the tracer transport in\nwater-filled pore spaces of two-dimensional Euclidean is demonstrated as a\ndecelerating sub-diffusion, and can well be described by the distributed order\nHausdorff diffusion model with c = 1.73. While the Hausdorff diffusion model\ncan accurately fit the sub-diffusion experimental data of the tracer transport\nin the pore-solid prefractal porous media.",
+                    "authors": "Yingjie Liang, Wen Chen, Wei Xu, HongGuang Sun",
+                    "published": "2018-01-29",
+                    "updated": "2018-01-29",
+                    "primary_cat": "physics.flu-dyn",
+                    "cats": [
+                        "physics.flu-dyn"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2310.01221v2",
+                    "title": "Nonlocal diffusion model with maximum principle",
+                    "abstract": "In this paper, we propose nonlocal diffusion models with Dirichlet boundary.\nThese nonlocal diffusion models preserve the maximum principle and also have\ncorresponding variational form. With these good properties, It is relatively\neasy to prove the well-posedness and the vanishing nonlocality convergence.\nFurthermore, by specifically designed weight function, we can get a nonlocal\ndiffusion model with second order convergence which is optimal for nonlocal\ndiffusion models.",
+                    "authors": "Zuoqiang Shi",
+                    "published": "2023-10-02",
+                    "updated": "2023-10-12",
+                    "primary_cat": "math.AP",
+                    "cats": [
+                        "math.AP",
+                        "cs.NA",
+                        "math.NA"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1906.02405v1",
+                    "title": "Indirect interactions influence contact network structure and diffusion dynamics",
+                    "abstract": "Interaction patterns at the individual level influence the behaviour of\ndiffusion over contact networks. Most of the current diffusion models only\nconsider direct interactions among individuals to build underlying infectious\nitems transmission networks. However, delayed indirect interactions, where a\nsusceptible individual interacts with infectious items after the infected\nindividual has left the interaction space, can also cause transmission events.\nWe define a diffusion model called the same place different time transmission\n(SPDT) based diffusion that considers transmission links for these indirect\ninteractions. Our SPDT model changes the network dynamics where the\nconnectivity among individuals varies with the decay rates of link infectivity.\nWe investigate SPDT diffusion behaviours by simulating airborne disease\nspreading on data-driven contact networks. The SPDT model significantly\nincreases diffusion dynamics (particularly for networks with low link densities\nwhere indirect interactions create new infection pathways) and is capable of\nproducing realistic disease reproduction number. Our results show that the SPDT\nmodel is significantly more likely to lead to outbreaks compared to current\ndiffusion models with direct interactions. We find that the diffusion dynamics\nwith including indirect links are not reproducible by the current models,\nhighlighting the importance of the indirect links for predicting outbreaks.",
+                    "authors": "Md Shahzamal, Raja Jurdak, Bernard Mans, Frank de Hoog",
+                    "published": "2019-06-06",
+                    "updated": "2019-06-06",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "physics.soc-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1701.00257v2",
+                    "title": "Analyzing PFG anisotropic anomalous diffusions by instantaneous signal attenuation method",
+                    "abstract": "Anomalous diffusion has been investigated in many systems. Pulsed field\ngradient (PFG) anomalous diffusion is much more complicated than PFG normal\ndiffusion. There have been many theoretical and experimental studies for PFG\nisotropic anomalous diffusion, but there are very few theoretical treatments\nreported for anisotropic anomalous diffusion. Currently, there is not a general\nPFG signal attenuation expression, which includes the finite gradient pulse\neffect and can treat all three types of anisotropic fractional diffusions:\ngeneral fractional diffusion, time fractional diffusion, and space-fractional\ndiffusion. In this paper, the recently developed instantaneous signal\nattenuation (ISA) method was applied to obtain PFG signal attenuation\nexpression for free and restricted anisotropic anomalous diffusion with two\nmodels: fractal derivative and fractional derivative models. The obtained PFG\nsignal attenuation expression for anisotropic anomalous diffusion can reduce to\nthe reported result for PFG anisotropic normal diffusion. The results can also\nreduce to reported PFG isotropic anomalous diffusion results obtained by\neffective phase shift diffusion equation method and instantaneous signal\nattenuation method. For anisotropic space-fractional diffusion, the obtained\nresult agrees with that obtained by the modified Bloch equation method.\nAdditionally, The PFG signal attenuation expressions for free and restricted\nanisotropic curvilinear diffusions were derived by the traditional method, the\nresults of which agree with the PFG anisotropic fractional diffusion results\nbased on the fractional derivative model. The powder pattern of PFG anisotropic\ndiffusion was also discussed. The results here improve our understanding of PFG\nanomalous diffusion, and provide new formalisms for PFG anisotropic anomalous\ndiffusion in NMR and MRI.",
+                    "authors": "Guoxing Lin",
+                    "published": "2017-01-01",
+                    "updated": "2017-01-05",
+                    "primary_cat": "physics.chem-ph",
+                    "cats": [
+                        "physics.chem-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2401.06046v2",
+                    "title": "Quantifying the contributions to diffusion in complex materials",
+                    "abstract": "Using machine learning with a variational formula for diffusivity, we recast\ndiffusion as a sum of individual contributions to diffusion--called\n\"kinosons\"--and compute their statistical distribution to model a complex\nmulticomponent alloy. Calculating kinosons is orders of magnitude more\nefficient than computing whole trajectories, and elucidates kinetic mechanisms\nfor diffusion. The distribution of kinosons with temperature leads to new\naccurate analytic models for macroscale diffusivity. This combination of\nmachine learning with diffusion theory promises insight into other complex\nmaterials.",
+                    "authors": "Soham Chattopadhyay, Dallas R. Trinkle",
+                    "published": "2024-01-11",
+                    "updated": "2024-03-14",
+                    "primary_cat": "cond-mat.mtrl-sci",
+                    "cats": [
+                        "cond-mat.mtrl-sci"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1506.05574v1",
+                    "title": "Information Diffusion issues",
+                    "abstract": "In this report there will be a discussion for Information Diffusion. There\nwill be discussions on what information diffusion is, its key characteristics\nand on several other aspects of these kinds of networks. This report will focus\non peer to peer models in information diffusion. There will be discussions on\nepidemic model, OSN and other details related to information diffusion.",
+                    "authors": "Jonathan Helmigh",
+                    "published": "2015-06-18",
+                    "updated": "2015-06-18",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2305.08379v2",
+                    "title": "TESS: Text-to-Text Self-Conditioned Simplex Diffusion",
+                    "abstract": "Diffusion models have emerged as a powerful paradigm for generation,\nobtaining strong performance in various continuous domains. However, applying\ncontinuous diffusion models to natural language remains challenging due to its\ndiscrete nature and the need for a large number of diffusion steps to generate\ntext, making diffusion-based generation expensive. In this work, we propose\nText-to-text Self-conditioned Simplex Diffusion (TESS), a text diffusion model\nthat is fully non-autoregressive, employs a new form of self-conditioning, and\napplies the diffusion process on the logit simplex space rather than the\nlearned embedding space. Through extensive experiments on natural language\nunderstanding and generation tasks including summarization, text\nsimplification, paraphrase generation, and question generation, we demonstrate\nthat TESS outperforms state-of-the-art non-autoregressive models, requires\nfewer diffusion steps with minimal drop in performance, and is competitive with\npretrained autoregressive sequence-to-sequence models. We publicly release our\ncodebase at https://github.com/allenai/tess-diffusion.",
+                    "authors": "Rabeeh Karimi Mahabadi, Hamish Ivison, Jaesung Tae, James Henderson, Iz Beltagy, Matthew E. Peters, Arman Cohan",
+                    "published": "2023-05-15",
+                    "updated": "2024-02-21",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL",
+                        "cs.LG"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1404.3573v1",
+                    "title": "\"Diffusing diffusivity\": A model for anomalous and \"anomalous yet Brownian\" diffusion",
+                    "abstract": "Wang et al. [PNAS 106 (2009) 15160] have found that in several systems the\nlinear time dependence of the mean-square displacement (MSD) of diffusing\ncolloidal particles, typical of normal diffusion, is accompanied by a\nnon-Gaussian displacement distribution (DisD), with roughly exponential tails\nat short times, a situation they termed \"anomalous yet Brownian\" diffusion. The\ndiversity of systems in which this is observed calls for a generic model. We\npresent such a model where there is \"diffusivity memory\" but no \"direction\nmemory\" in the particle trajectory, and we show that it leads to both a linear\nMSD and a non-Gaussian DisD at short times. In our model, the diffusivity is\nundergoing a (perhaps biased) random walk, hence the expression \"diffusing\ndiffusivity\". The DisD is predicted to be exactly exponential at short times if\nthe distribution of diffusivities is itself exponential, but an exponential\nremains a good fit to the DisD for a variety of diffusivity distributions.\nMoreover, our generic model can be modified to produce subdiffusion.",
+                    "authors": "Mykyta V. Chubynsky, Gary W. Slater",
+                    "published": "2014-04-14",
+                    "updated": "2014-04-14",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech",
+                        "cond-mat.soft"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/0910.2253v1",
+                    "title": "Linearized Kompaneetz equation as a relativistic diffusion",
+                    "abstract": "We show that Kompaneetz equation describing photon diffusion in an\nenvironment of an electron gas, when linearized around its equilibrium\ndistribution, coincides with the relativistic diffusion discussed in recent\npublications. The model of the relativistic diffusion is related to soluble\nmodels of imaginary time quantum mechanics. We suggest some non-linear\ngeneralizations of the relativistic diffusion equation and their astrophysical\napplications (in particular to the Sunyaev-Zeldovich effect).",
+                    "authors": "Z. Haba",
+                    "published": "2009-10-12",
+                    "updated": "2009-10-12",
+                    "primary_cat": "astro-ph.CO",
+                    "cats": [
+                        "astro-ph.CO"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2306.03436v2",
+                    "title": "Intellectual Property Protection of Diffusion Models via the Watermark Diffusion Process",
+                    "abstract": "Diffusion models have rapidly become a vital part of deep generative\narchitectures, given today's increasing demands. Obtaining large,\nhigh-performance diffusion models demands significant resources, highlighting\ntheir importance as intellectual property worth protecting. However, existing\nwatermarking techniques for ownership verification are insufficient when\napplied to diffusion models. Very recent research in watermarking diffusion\nmodels either exposes watermarks during task generation, which harms the\nimperceptibility, or is developed for conditional diffusion models that require\nprompts to trigger the watermark. This paper introduces WDM, a novel\nwatermarking solution for diffusion models without imprinting the watermark\nduring task generation. It involves training a model to concurrently learn a\nWatermark Diffusion Process (WDP) for embedding watermarks alongside the\nstandard diffusion process for task generation. We provide a detailed\ntheoretical analysis of WDP training and sampling, relating it to a shifted\nGaussian diffusion process via the same reverse noise. Extensive experiments\nare conducted to validate the effectiveness and robustness of our approach in\nvarious trigger and watermark data configurations.",
+                    "authors": "Sen Peng, Yufei Chen, Cong Wang, Xiaohua Jia",
+                    "published": "2023-06-06",
+                    "updated": "2023-11-29",
+                    "primary_cat": "cs.CR",
+                    "cats": [
+                        "cs.CR",
+                        "cs.LG"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1210.5101v1",
+                    "title": "Global well-posedness and zero-diffusion limit of classical solutions to the 3D conservation laws arising in chemotaxis",
+                    "abstract": "In this paper, we study the relationship between a diffusive model and a\nnon-diffusive model which are both derived from the well-known Keller-Segel\nmodel, as a coefficient of diffusion $\\varepsilon$ goes to zero. First, we\nestablish the global well-posedness of classical solutions to the Cauchy\nproblem for the diffusive model with smooth initial data which is of small\n$L^2$ norm, together with some {\\it a priori} estimates uniform for $t$ and\n$\\varepsilon$. Then we investigate the zero-diffusion limit, and get the global\nwell-posedness of classical solutions to the Cauchy problem for the\nnon-diffusive model. Finally, we derive the convergence rate of the diffusive\nmodel toward the non-diffusive model. It is shown that the convergence rate in\n$L^\\infty$ norm is of the order $O(\\varepsilon^{1/2})$. It should be noted that\nthe initial data is small in $L^2$-norm but can be of large oscillations with\nconstant state at far field. As a byproduct, we improve the corresponding\nresult on the well-posedness of the non-difussive model which requires small\noscillations.",
+                    "authors": "Hongyun Peng, Huanyao Wen, Changjiang Zhu",
+                    "published": "2012-10-18",
+                    "updated": "2012-10-18",
+                    "primary_cat": "math.AP",
+                    "cats": [
+                        "math.AP"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2307.06272v1",
+                    "title": "Exposing the Fake: Effective Diffusion-Generated Images Detection",
+                    "abstract": "Image synthesis has seen significant advancements with the advent of\ndiffusion-based generative models like Denoising Diffusion Probabilistic Models\n(DDPM) and text-to-image diffusion models. Despite their efficacy, there is a\ndearth of research dedicated to detecting diffusion-generated images, which\ncould pose potential security and privacy risks. This paper addresses this gap\nby proposing a novel detection method called Stepwise Error for\nDiffusion-generated Image Detection (SeDID). Comprising statistical-based\n$\\text{SeDID}_{\\text{Stat}}$ and neural network-based\n$\\text{SeDID}_{\\text{NNs}}$, SeDID exploits the unique attributes of diffusion\nmodels, namely deterministic reverse and deterministic denoising computation\nerrors. Our evaluations demonstrate SeDID's superior performance over existing\nmethods when applied to diffusion models. Thus, our work makes a pivotal\ncontribution to distinguishing diffusion model-generated images, marking a\nsignificant step in the domain of artificial intelligence security.",
+                    "authors": "Ruipeng Ma, Jinhao Duan, Fei Kong, Xiaoshuang Shi, Kaidi Xu",
+                    "published": "2023-07-12",
+                    "updated": "2023-07-12",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.CR",
+                        "cs.LG"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2401.17181v1",
+                    "title": "Transfer Learning for Text Diffusion Models",
+                    "abstract": "In this report, we explore the potential for text diffusion to replace\nautoregressive (AR) decoding for the training and deployment of large language\nmodels (LLMs). We are particularly interested to see whether pretrained AR\nmodels can be transformed into text diffusion models through a lightweight\nadaptation procedure we call ``AR2Diff''. We begin by establishing a strong\nbaseline setup for training text diffusion models. Comparing across multiple\narchitectures and pretraining objectives, we find that training a decoder-only\nmodel with a prefix LM objective is best or near-best across several tasks.\nBuilding on this finding, we test various transfer learning setups for text\ndiffusion models. On machine translation, we find that text diffusion\nunderperforms the standard AR approach. However, on code synthesis and\nextractive QA, we find diffusion models trained from scratch outperform AR\nmodels in many cases. We also observe quality gains from AR2Diff -- adapting AR\nmodels to use diffusion decoding. These results are promising given that text\ndiffusion is relatively underexplored and can be significantly faster than AR\ndecoding for long text generation.",
+                    "authors": "Kehang Han, Kathleen Kenealy, Aditya Barua, Noah Fiedel, Noah Constant",
+                    "published": "2024-01-30",
+                    "updated": "2024-01-30",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/cond-mat/0210703v1",
+                    "title": "Membrane bound protein diffusion viewed by fluorescence recovery after bleaching experiments : models analysis",
+                    "abstract": "Diffusion processes in biological membranes are of interest to understand the\nmacromolecular organisation and function of several molecules. Fluorescence\nRecovery After Photobleaching (FRAP) has been widely used as a method to\nanalyse this processes using classical Brownian diffusion model. In the first\npart of this work, the analytical expression of the fluorescence recovery as a\nfunction of time has been established for anomalous diffusion due to long\nwaiting times. Then, experimental fluorescence recoveries recorded in living\ncells on a membrane-bound protein have been analysed using three different\nmodels : normal Brownian diffusion, Brownian diffusion with an immobile\nfraction and anomalous diffusion due to long waiting times.",
+                    "authors": "C. Favard, N. Olivi-Tran, J. -L. Meunier",
+                    "published": "2002-10-31",
+                    "updated": "2002-10-31",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech",
+                        "physics.bio-ph",
+                        "q-bio.BM"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2306.07491v2",
+                    "title": "Exact sharp-fronted solutions for nonlinear diffusion on evolving domains",
+                    "abstract": "Models of diffusive processes that occur on evolving domains are frequently\nemployed to describe biological and physical phenomena, such as diffusion\nwithin expanding tissues or substrates. Previous investigations into these\nmodels either report numerical solutions or require an assumption of linear\ndiffusion to determine exact solutions. Unfortunately, numerical solutions do\nnot reveal the relationship between the model parameters and the solution\nfeatures. Additionally, experimental observations typically report the presence\nof sharp fronts, which are not captured by linear diffusion. Here we address\nboth limitations by presenting exact sharp-fronted solutions to a model of\ndegenerate nonlinear diffusion on a growing domain. We obtain the solution by\nidentifying a series of transformations that converts the model of a nonlinear\ndiffusive process on an evolving domain to a nonlinear diffusion equation on a\nfixed domain, which admits known exact solutions for certain choices of\ndiffusivity functions. We determine expressions for critical time scales and\ndomain growth rates such that the diffusive population never reaches the domain\nboundaries and hence the solution remains valid.",
+                    "authors": "Stuart T. Johnston, Matthew J. Simpson",
+                    "published": "2023-06-13",
+                    "updated": "2023-10-06",
+                    "primary_cat": "q-bio.PE",
+                    "cats": [
+                        "q-bio.PE"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1609.09697v1",
+                    "title": "Anomalous diffusion in time-fluctuating non-stationary diffusivity landscapes",
+                    "abstract": "We investigate the ensemble and time averaged mean squared displacements for\nparticle diffusion in a simple model for disordered media by assuming that the\nlocal diffusivity is both fluctuating in time and has a deterministic average\ngrowth or decay in time. In this study we compare computer simulations of the\nstochastic Langevin equation for this random diffusion process with analytical\nresults. We explore the regimes of normal Brownian motion as well as anomalous\ndiffusion in the sub- and superdiffusive regimes. We also consider effects of\nthe inertial term on the particle motion. The investigation of the resulting\ndiffusion is performed for unconfined and confined motion.",
+                    "authors": "A. G. Cherstvy, R. Metzler",
+                    "published": "2016-09-30",
+                    "updated": "2016-09-30",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2402.01965v2",
+                    "title": "Analyzing Neural Network-Based Generative Diffusion Models through Convex Optimization",
+                    "abstract": "Diffusion models are becoming widely used in state-of-the-art image, video\nand audio generation. Score-based diffusion models stand out among these\nmethods, necessitating the estimation of score function of the input data\ndistribution. In this study, we present a theoretical framework to analyze\ntwo-layer neural network-based diffusion models by reframing score matching and\ndenoising score matching as convex optimization. Though existing diffusion\ntheory is mainly asymptotic, we characterize the exact predicted score function\nand establish the convergence result for neural network-based diffusion models\nwith finite data. This work contributes to understanding what neural\nnetwork-based diffusion model learns in non-asymptotic settings.",
+                    "authors": "Fangzhao Zhang, Mert Pilanci",
+                    "published": "2024-02-03",
+                    "updated": "2024-02-06",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "math.OC"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2404.12761v1",
+                    "title": "Universality of giant diffusion in tilted periodic potentials",
+                    "abstract": "Giant diffusion, where the diffusion coefficient of a Brownian particle in a\nperiodic potential with an external force is significantly enhanced by the\nexternal force, is a non-trivial non-equilibrium phenomenon. We propose a\nsimple stochastic model of giant diffusion, which is based on a biased\ncontinuous-time random walk (CTRW). In this model, we introduce a flight time\nin the biased CTRW. We derive the diffusion coefficients of this model by the\nrenewal theory and find that there is a maximum diffusion coefficient when the\nbias is changed. Giant diffusion is universally observed in the sense that\nthere is a peak of the diffusion coefficient for any tilted periodic potentials\nand the degree of the diffusivity is greatly enhanced especially for\nlow-temperature regimes. The biased CTRW models with flight times are applied\nto diffusion under three tilted periodic potentials. Furthermore, the\ntemperature dependence of the maximum diffusion coefficient and the external\nforce that attains the maximum are presented for diffusion under a tilted\nsawtooth potential.",
+                    "authors": "Kento Iida, Andreas Dechant, Takuma Akimoto",
+                    "published": "2024-04-19",
+                    "updated": "2024-04-19",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1611.06202v2",
+                    "title": "Brownian yet non-Gaussian diffusion: from superstatistics to subordination of diffusing diffusivities",
+                    "abstract": "A growing number of biological, soft, and active matter systems are observed\nto exhibit normal diffusive dynamics with a linear growth of the mean squared\ndisplacement, yet with a non-Gaussian distribution of increments. Based on the\nChubinsky-Slater idea of a diffusing diffusivity we here establish and analyze\na minimal model framework of diffusion processes with fluctuating diffusivity.\nIn particular, we demonstrate the equivalence of the diffusing diffusivity\nprocess with a superstatistical approach with a distribution of diffusivities,\nat times shorter than the diffusivity correlation time. At longer times a\ncrossover to a Gaussian distribution with an effective diffusivity emerges.\nSpecifically, we establish a subordination picture of Brownian but non-Gaussian\ndiffusion processes, that can be used for a wide class of diffusivity\nfluctuation statistics. Our results are shown to be in excellent agreement with\nsimulations and numerical evaluations.",
+                    "authors": "A. V. Chechkin, F. Seno, R. Metzler, I. M. Sokolov",
+                    "published": "2016-11-18",
+                    "updated": "2017-03-30",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech",
+                        "physics.bio-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2312.08873v1",
+                    "title": "Diffusion Cocktail: Fused Generation from Diffusion Models",
+                    "abstract": "Diffusion models excel at generating high-quality images and are easy to\nextend, making them extremely popular among active users who have created an\nextensive collection of diffusion models with various styles by fine-tuning\nbase models such as Stable Diffusion. Recent work has focused on uncovering\nsemantic and visual information encoded in various components of a diffusion\nmodel, enabling better generation quality and more fine-grained control.\nHowever, those methods target improving a single model and overlook the vastly\navailable collection of fine-tuned diffusion models. In this work, we study the\ncombinations of diffusion models. We propose Diffusion Cocktail (Ditail), a\ntraining-free method that can accurately transfer content information between\ntwo diffusion models. This allows us to perform diverse generations using a set\nof diffusion models, resulting in novel images that are unlikely to be obtained\nby a single model alone. We also explore utilizing Ditail for style transfer,\nwith the target style set by a diffusion model instead of an image. Ditail\noffers a more detailed manipulation of the diffusion generation, thereby\nenabling the vast community to integrate various styles and contents seamlessly\nand generate any content of any style.",
+                    "authors": "Haoming Liu, Yuanhe Guo, Shengjie Wang, Hongyi Wen",
+                    "published": "2023-12-12",
+                    "updated": "2023-12-12",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.AI"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2211.07804v3",
+                    "title": "Diffusion Models for Medical Image Analysis: A Comprehensive Survey",
+                    "abstract": "Denoising diffusion models, a class of generative models, have garnered\nimmense interest lately in various deep-learning problems. A diffusion\nprobabilistic model defines a forward diffusion stage where the input data is\ngradually perturbed over several steps by adding Gaussian noise and then learns\nto reverse the diffusion process to retrieve the desired noise-free data from\nnoisy data samples. Diffusion models are widely appreciated for their strong\nmode coverage and quality of the generated samples despite their known\ncomputational burdens. Capitalizing on the advances in computer vision, the\nfield of medical imaging has also observed a growing interest in diffusion\nmodels. To help the researcher navigate this profusion, this survey intends to\nprovide a comprehensive overview of diffusion models in the discipline of\nmedical image analysis. Specifically, we introduce the solid theoretical\nfoundation and fundamental concepts behind diffusion models and the three\ngeneric diffusion modelling frameworks: diffusion probabilistic models,\nnoise-conditioned score networks, and stochastic differential equations. Then,\nwe provide a systematic taxonomy of diffusion models in the medical domain and\npropose a multi-perspective categorization based on their application, imaging\nmodality, organ of interest, and algorithms. To this end, we cover extensive\napplications of diffusion models in the medical domain. Furthermore, we\nemphasize the practical use case of some selected approaches, and then we\ndiscuss the limitations of the diffusion models in the medical domain and\npropose several directions to fulfill the demands of this field. Finally, we\ngather the overviewed studies with their available open-source implementations\nat\nhttps://github.com/amirhossein-kz/Awesome-Diffusion-Models-in-Medical-Imaging.",
+                    "authors": "Amirhossein Kazerouni, Ehsan Khodapanah Aghdam, Moein Heidari, Reza Azad, Mohsen Fayyaz, Ilker Hacihaliloglu, Dorit Merhof",
+                    "published": "2022-11-14",
+                    "updated": "2023-06-03",
+                    "primary_cat": "eess.IV",
+                    "cats": [
+                        "eess.IV",
+                        "cs.CV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/cond-mat/0208120v1",
+                    "title": "Aging in a Chaotic System",
+                    "abstract": "We demonstrate aging behavior in a simple non-linear system. Our model is a\nchaotic map which generates deterministically sub-diffusion. Asymptotic\nbehaviors of the diffusion process are described using aging continuous time\nrandom walks, introduced previously to model diffusion in glasses.",
+                    "authors": "E. Barkai",
+                    "published": "2002-08-06",
+                    "updated": "2002-08-06",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech",
+                        "nlin.CD"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2210.07677v1",
+                    "title": "TransFusion: Transcribing Speech with Multinomial Diffusion",
+                    "abstract": "Diffusion models have shown exceptional scaling properties in the image\nsynthesis domain, and initial attempts have shown similar benefits for applying\ndiffusion to unconditional text synthesis. Denoising diffusion models attempt\nto iteratively refine a sampled noise signal until it resembles a coherent\nsignal (such as an image or written sentence). In this work we aim to see\nwhether the benefits of diffusion models can also be realized for speech\nrecognition. To this end, we propose a new way to perform speech recognition\nusing a diffusion model conditioned on pretrained speech features.\nSpecifically, we propose TransFusion: a transcribing diffusion model which\niteratively denoises a random character sequence into coherent text\ncorresponding to the transcript of a conditioning utterance. We demonstrate\ncomparable performance to existing high-performing contrastive models on the\nLibriSpeech speech recognition benchmark. To the best of our knowledge, we are\nthe first to apply denoising diffusion to speech recognition. We also propose\nnew techniques for effectively sampling and decoding multinomial diffusion\nmodels. These are required because traditional methods of sampling from\nacoustic models are not possible with our new discrete diffusion approach. Code\nand trained models are available: https://github.com/RF5/transfusion-asr",
+                    "authors": "Matthew Baas, Kevin Eloff, Herman Kamper",
+                    "published": "2022-10-14",
+                    "updated": "2022-10-14",
+                    "primary_cat": "eess.AS",
+                    "cats": [
+                        "eess.AS",
+                        "cs.AI",
+                        "cs.SD"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2210.05559v2",
+                    "title": "Unifying Diffusion Models' Latent Space, with Applications to CycleDiffusion and Guidance",
+                    "abstract": "Diffusion models have achieved unprecedented performance in generative\nmodeling. The commonly-adopted formulation of the latent code of diffusion\nmodels is a sequence of gradually denoised samples, as opposed to the simpler\n(e.g., Gaussian) latent space of GANs, VAEs, and normalizing flows. This paper\nprovides an alternative, Gaussian formulation of the latent space of various\ndiffusion models, as well as an invertible DPM-Encoder that maps images into\nthe latent space. While our formulation is purely based on the definition of\ndiffusion models, we demonstrate several intriguing consequences. (1)\nEmpirically, we observe that a common latent space emerges from two diffusion\nmodels trained independently on related domains. In light of this finding, we\npropose CycleDiffusion, which uses DPM-Encoder for unpaired image-to-image\ntranslation. Furthermore, applying CycleDiffusion to text-to-image diffusion\nmodels, we show that large-scale text-to-image diffusion models can be used as\nzero-shot image-to-image editors. (2) One can guide pre-trained diffusion\nmodels and GANs by controlling the latent codes in a unified, plug-and-play\nformulation based on energy-based models. Using the CLIP model and a face\nrecognition model as guidance, we demonstrate that diffusion models have better\ncoverage of low-density sub-populations and individuals than GANs. The code is\npublicly available at https://github.com/ChenWu98/cycle-diffusion.",
+                    "authors": "Chen Henry Wu, Fernando De la Torre",
+                    "published": "2022-10-11",
+                    "updated": "2022-12-07",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.GR",
+                        "cs.LG"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2305.14671v2",
+                    "title": "A Survey of Diffusion Models in Natural Language Processing",
+                    "abstract": "This survey paper provides a comprehensive review of the use of diffusion\nmodels in natural language processing (NLP). Diffusion models are a class of\nmathematical models that aim to capture the diffusion of information or signals\nacross a network or manifold. In NLP, diffusion models have been used in a\nvariety of applications, such as natural language generation, sentiment\nanalysis, topic modeling, and machine translation. This paper discusses the\ndifferent formulations of diffusion models used in NLP, their strengths and\nlimitations, and their applications. We also perform a thorough comparison\nbetween diffusion models and alternative generative models, specifically\nhighlighting the autoregressive (AR) models, while also examining how diverse\narchitectures incorporate the Transformer in conjunction with diffusion models.\nCompared to AR models, diffusion models have significant advantages for\nparallel generation, text interpolation, token-level controls such as syntactic\nstructures and semantic contents, and robustness. Exploring further\npermutations of integrating Transformers into diffusion models would be a\nvaluable pursuit. Also, the development of multimodal diffusion models and\nlarge-scale diffusion language models with notable capabilities for few-shot\nlearning would be important directions for the future advance of diffusion\nmodels in NLP.",
+                    "authors": "Hao Zou, Zae Myung Kim, Dongyeop Kang",
+                    "published": "2023-05-24",
+                    "updated": "2023-06-14",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2002.02101v1",
+                    "title": "Trace of anomalous diffusion in a biased quenched trap model",
+                    "abstract": "Diffusion on a quenched heterogeneous environment in the presence of bias is\nconsidered analytically. The first-passage-time statistics can be applied to\nobtain the drift and the diffusion coefficient in periodic quenched\nenvironments. We show several transition points at which sample-to-sample\nfluctuations of the drift or the diffusion coefficient remain large even when\nthe system size becomes large, i.e., non-self-averaging. Moreover, we find that\nthe disorder average of the diffusion coefficient diverges or becomes zero when\nthe corresponding annealed model generates superdiffusion or subdiffusion,\nrespectively. This result implies that anomalous diffusion in an annealed model\nis traced by anomaly of the diffusion coefficients in the corresponding\nquenched model.",
+                    "authors": "Takuma Akimoto, Keiji Saito",
+                    "published": "2020-02-06",
+                    "updated": "2020-02-06",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2302.07261v2",
+                    "title": "Where to Diffuse, How to Diffuse, and How to Get Back: Automated Learning for Multivariate Diffusions",
+                    "abstract": "Diffusion-based generative models (DBGMs) perturb data to a target noise\ndistribution and reverse this process to generate samples. The choice of\nnoising process, or inference diffusion process, affects both likelihoods and\nsample quality. For example, extending the inference process with auxiliary\nvariables leads to improved sample quality. While there are many such\nmultivariate diffusions to explore, each new one requires significant\nmodel-specific analysis, hindering rapid prototyping and evaluation. In this\nwork, we study Multivariate Diffusion Models (MDMs). For any number of\nauxiliary variables, we provide a recipe for maximizing a lower-bound on the\nMDMs likelihood without requiring any model-specific analysis. We then\ndemonstrate how to parameterize the diffusion for a specified target noise\ndistribution; these two points together enable optimizing the inference\ndiffusion process. Optimizing the diffusion expands easy experimentation from\njust a few well-known processes to an automatic search over all linear\ndiffusions. To demonstrate these ideas, we introduce two new specific\ndiffusions as well as learn a diffusion process on the MNIST, CIFAR10, and\nImageNet32 datasets. We show learned MDMs match or surpass bits-per-dims (BPDs)\nrelative to fixed choices of diffusions for a given dataset and model\narchitecture.",
+                    "authors": "Raghav Singhal, Mark Goldstein, Rajesh Ranganath",
+                    "published": "2023-02-14",
+                    "updated": "2023-03-03",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "stat.ML"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2202.05830v1",
+                    "title": "Learning Fast Samplers for Diffusion Models by Differentiating Through Sample Quality",
+                    "abstract": "Diffusion models have emerged as an expressive family of generative models\nrivaling GANs in sample quality and autoregressive models in likelihood scores.\nStandard diffusion models typically require hundreds of forward passes through\nthe model to generate a single high-fidelity sample. We introduce\nDifferentiable Diffusion Sampler Search (DDSS): a method that optimizes fast\nsamplers for any pre-trained diffusion model by differentiating through sample\nquality scores. We also present Generalized Gaussian Diffusion Models (GGDM), a\nfamily of flexible non-Markovian samplers for diffusion models. We show that\noptimizing the degrees of freedom of GGDM samplers by maximizing sample quality\nscores via gradient descent leads to improved sample quality. Our optimization\nprocedure backpropagates through the sampling process using the\nreparametrization trick and gradient rematerialization. DDSS achieves strong\nresults on unconditional image generation across various datasets (e.g., FID\nscores on LSUN church 128x128 of 11.6 with only 10 inference steps, and 4.82\nwith 20 steps, compared to 51.1 and 14.9 with strongest DDPM/DDIM baselines).\nOur method is compatible with any pre-trained diffusion model without\nfine-tuning or re-training required.",
+                    "authors": "Daniel Watson, William Chan, Jonathan Ho, Mohammad Norouzi",
+                    "published": "2022-02-11",
+                    "updated": "2022-02-11",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1411.2007v1",
+                    "title": "On large time behavior and selection principle for a diffusive Carr-Penrose Model",
+                    "abstract": "This paper is concerned with the study of a diffusive perturbation of the\nlinear LSW model introduced by Carr and Penrose. A main subject of interest is\nto understand how the presence of diffusion acts as a selection principle,\nwhich singles out a particular self-similar solution of the linear LSW model as\ndetermining the large time behavior of the diffusive model. A selection\nprinciple is rigorously proven for a model which is a semi-classical\napproximation to the diffusive model. Upper bounds on the rate of coarsening\nare also obtained for the full diffusive model.",
+                    "authors": "Joseph G. Conlon, Michael Dabkowski, Jingchen Wu",
+                    "published": "2014-11-07",
+                    "updated": "2014-11-07",
+                    "primary_cat": "math.AP",
+                    "cats": [
+                        "math.AP",
+                        "35F05"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1609.04658v1",
+                    "title": "Analyzing Signal Attenuation in PFG Anomalous Diffusion via a Modified Gaussian Phase Distribution Approximation Based on Fractal Derivative Model",
+                    "abstract": "Pulsed field gradient (PFG) has been increasingly employed to study anomalous\ndiffusions in Nuclear Magnetic Resonance (NMR) and Magnetic Resonance Imaging\n(MRI). However, the analysis of PFG anomalous diffusion is complicated. In this\npaper, a fractal derivative model based modified Gaussian phase distribution\nmethod is proposed to describe PFG anomalous diffusion. By using the phase\ndistribution obtained from the effective phase shift diffusion method based on\nfractal derivatives, and employing some of the traditional Gaussian phase\ndistribution approximation techniques, a general signal attenuation expression\nfor free fractional diffusion is derived. This expression describes a stretched\nexponential function based attenuation, which is distinct from both the\nexponential attenuation for normal diffusion obtained from conventional\nGaussian phase distribution approximation, and the Mittag-Leffler function\nbased attenuation for anomalous diffusion obtained from fractional derivative.\nThe obtained signal attenuation expression can analyze the finite gradient\npulse width (FGPW) effect. Additionally, it can generally be applied to all\nthree types of PFG fractional diffusions classified based on time derivative\norder alpha and space derivative order beta. These three types of fractional\ndiffusions include time-fractional diffusion, space-fractional diffusion, and\ngeneral fractional diffusion. The results in this paper are consistent with\nreported results based on effective phase shift diffusion equation method and\ninstantaneous signal attenuation method. This method provides a new, convenient\napproximation formalism for analyzing PFG anomalous diffusion experiments.",
+                    "authors": "Guoxing Lin",
+                    "published": "2016-09-15",
+                    "updated": "2016-09-15",
+                    "primary_cat": "physics.chem-ph",
+                    "cats": [
+                        "physics.chem-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1708.06890v1",
+                    "title": "Collaborative Inference of Coexisting Information Diffusions",
+                    "abstract": "Recently, \\textit{diffusion history inference} has become an emerging\nresearch topic due to its great benefits for various applications, whose\npurpose is to reconstruct the missing histories of information diffusion traces\naccording to incomplete observations. The existing methods, however, often\nfocus only on single information diffusion trace, while in a real-world social\nnetwork, there often coexist multiple information diffusions over the same\nnetwork. In this paper, we propose a novel approach called Collaborative\nInference Model (CIM) for the problem of the inference of coexisting\ninformation diffusions. By exploiting the synergism between the coexisting\ninformation diffusions, CIM holistically models multiple information diffusions\nas a sparse 4th-order tensor called Coexisting Diffusions Tensor (CDT) without\nany prior assumption of diffusion models, and collaboratively infers the\nhistories of the coexisting information diffusions via a low-rank approximation\nof CDT with a fusion of heterogeneous constraints generated from additional\ndata sources. To improve the efficiency, we further propose an optimal\nalgorithm called Time Window based Parallel Decomposition Algorithm (TWPDA),\nwhich can speed up the inference without compromise on the accuracy by\nutilizing the temporal locality of information diffusions. The extensive\nexperiments conducted on real world datasets and synthetic datasets verify the\neffectiveness and efficiency of CIM and TWPDA.",
+                    "authors": "Yanchao Sun, Cong Qian, Ning Yang, Philip S. Yu",
+                    "published": "2017-08-23",
+                    "updated": "2017-08-23",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2307.13949v1",
+                    "title": "How Does Diffusion Influence Pretrained Language Models on Out-of-Distribution Data?",
+                    "abstract": "Transformer-based pretrained language models (PLMs) have achieved great\nsuccess in modern NLP. An important advantage of PLMs is good\nout-of-distribution (OOD) robustness. Recently, diffusion models have attracted\na lot of work to apply diffusion to PLMs. It remains under-explored how\ndiffusion influences PLMs on OOD data. The core of diffusion models is a\nforward diffusion process which gradually applies Gaussian noise to inputs, and\na reverse denoising process which removes noise. The noised input\nreconstruction is a fundamental ability of diffusion models. We directly\nanalyze OOD robustness by measuring the reconstruction loss, including testing\nthe abilities to reconstruct OOD data, and to detect OOD samples. Experiments\nare conducted by analyzing different training parameters and data statistical\nfeatures on eight datasets. It shows that finetuning PLMs with diffusion\ndegrades the reconstruction ability on OOD data. The comparison also shows that\ndiffusion models can effectively detect OOD samples, achieving state-of-the-art\nperformance in most of the datasets with an absolute accuracy improvement up to\n18%. These results indicate that diffusion reduces OOD robustness of PLMs.",
+                    "authors": "Huazheng Wang, Daixuan Cheng, Haifeng Sun, Jingyu Wang, Qi Qi, Jianxin Liao, Jing Wang, Cong Liu",
+                    "published": "2023-07-26",
+                    "updated": "2023-07-26",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL",
+                        "cs.AI"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2308.06342v2",
+                    "title": "Mirror Diffusion Models",
+                    "abstract": "Diffusion models have successfully been applied to generative tasks in\nvarious continuous domains. However, applying diffusion to discrete categorical\ndata remains a non-trivial task. Moreover, generation in continuous domains\noften requires clipping in practice, which motivates the need for a theoretical\nframework for adapting diffusion to constrained domains. Inspired by the mirror\nLangevin algorithm for the constrained sampling problem, in this theoretical\nreport we propose Mirror Diffusion Models (MDMs). We demonstrate MDMs in the\ncontext of simplex diffusion and propose natural extensions to popular domains\nsuch as image and text generation.",
+                    "authors": "Jaesung Tae",
+                    "published": "2023-08-11",
+                    "updated": "2023-08-18",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2106.04745v2",
+                    "title": "Evaluation of diffuse mismatch model for phonon scattering at disordered interfaces",
+                    "abstract": "Diffuse phonon scattering strongly affects the phonon transport through a\ndisordered interface. The often-used diffuse mismatch model assumes that\nphonons lose memory of their origin after being scattered by the interface.\nUsing mode-resolved atomic Green's function simulation, we demonstrate that\ndiffuse phonon scattering by a single disordered interface cannot make a phonon\nlose its memory and thus the applicability of diffusive mismatch model is\nlimited. An analytical expression for diffuse scattering probability based on\nthe continuum approximation is also derived and shown to work reasonably well\nat low frequencies.",
+                    "authors": "Qichen Song, Gang Chen",
+                    "published": "2021-06-09",
+                    "updated": "2021-08-04",
+                    "primary_cat": "cond-mat.mes-hall",
+                    "cats": [
+                        "cond-mat.mes-hall"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2305.09605v1",
+                    "title": "Expressiveness Remarks for Denoising Diffusion Models and Samplers",
+                    "abstract": "Denoising diffusion models are a class of generative models which have\nrecently achieved state-of-the-art results across many domains. Gradual noise\nis added to the data using a diffusion process, which transforms the data\ndistribution into a Gaussian. Samples from the generative model are then\nobtained by simulating an approximation of the time reversal of this diffusion\ninitialized by Gaussian samples. Recent research has explored adapting\ndiffusion models for sampling and inference tasks. In this paper, we leverage\nknown connections to stochastic control akin to the F\\\"ollmer drift to extend\nestablished neural network approximation results for the F\\\"ollmer drift to\ndenoising diffusion models and samplers.",
+                    "authors": "Francisco Vargas, Teodora Reu, Anna Kerekes",
+                    "published": "2023-05-16",
+                    "updated": "2023-05-16",
+                    "primary_cat": "stat.ML",
+                    "cats": [
+                        "stat.ML",
+                        "cs.LG"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1907.09989v1",
+                    "title": "Rogue Heat and Diffusion Waves",
+                    "abstract": "In this paper, we numerically show and discuss the existence and\ncharacteristics of rogue heat and diffusion waves. More specifically, we use\ntwo different nonlinear heat (diffusion) models and show that modulation\ninstability leads to the generation of unexpected and large fluctuations in the\nframe of these models. These fluctuations can be named as rogue heat\n(diffusion) waves. We discuss the properties and statistics of such rogue\nwaves. Our results can find many important applications in many branches such\nas the nonlinear heat transfer, turbulence, financial mathematics, chemical or\nbiological diffusion, nuclear reactions, subsurface water infiltration, and\npore water pressure diffusion modeled in the frame of nonlinear Terzaghi\nconsolidation models, just to name a few.",
+                    "authors": "Cihan Bayindir",
+                    "published": "2019-07-18",
+                    "updated": "2019-07-18",
+                    "primary_cat": "nlin.PS",
+                    "cats": [
+                        "nlin.PS",
+                        "physics.flu-dyn"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2012.06816v1",
+                    "title": "Evaluation and Comparison of Diffusion Models with Motif Features",
+                    "abstract": "Diffusion models simulate the propagation of influence in networks. The\ndesign and evaluation of diffusion models has been subjective and empirical.\nWhen being applied to a network represented by a graph, the diffusion model\ngenerates a sequence of edges on which the influence flows, such sequence forms\na temporal network. In most scenarios, the statistical properties or the\ncharacteristics of a network are inferred by analyzing the temporal networks\ngenerated by diffusion models. To analyze real temporal networks, the motif has\nbeen proposed as a reliable feature. However, it is unclear how the network\ntopology and the diffusion model affect the motif feature of a generated\ntemporal network. In this paper, we adopt the motif feature to evaluate the\ntemporal graph generated by a diffusion model, thence the diffusion model\nitself. Two benchmarks for quantitively evaluating diffusion models with motif,\nstability and separability, are proposed and measured on numerous diffusion\nmodels. One motif-based metric is proposed to measure the similarity between\ndiffusion models. The experiments suggest that the motif of a generated\ntemporal network is dominated by the diffusion model, while the network\ntopology is almost ignored. This result indicates that more practical and\nreliable diffusion models have to be designed with delicacy in order to capture\nthe propagation patterns of real temporal networks.",
+                    "authors": "Fangqi Li",
+                    "published": "2020-12-12",
+                    "updated": "2020-12-12",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "cs.NI"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2402.13144v1",
+                    "title": "Neural Network Diffusion",
+                    "abstract": "Diffusion models have achieved remarkable success in image and video\ngeneration. In this work, we demonstrate that diffusion models can also\n\\textit{generate high-performing neural network parameters}. Our approach is\nsimple, utilizing an autoencoder and a standard latent diffusion model. The\nautoencoder extracts latent representations of a subset of the trained network\nparameters. A diffusion model is then trained to synthesize these latent\nparameter representations from random noise. It then generates new\nrepresentations that are passed through the autoencoder's decoder, whose\noutputs are ready to use as new subsets of network parameters. Across various\narchitectures and datasets, our diffusion process consistently generates models\nof comparable or improved performance over trained networks, with minimal\nadditional cost. Notably, we empirically find that the generated models perform\ndifferently with the trained networks. Our results encourage more exploration\non the versatile use of diffusion models.",
+                    "authors": "Kai Wang, Zhaopan Xu, Yukun Zhou, Zelin Zang, Trevor Darrell, Zhuang Liu, Yang You",
+                    "published": "2024-02-20",
+                    "updated": "2024-02-20",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.CV"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1304.0925v1",
+                    "title": "A new approach to multi-modal diffusions with applications to protein folding",
+                    "abstract": "This article demonstrates that flexible and statistically tractable\nmulti-modal diffusion models can be attained by transformation of simple\nwell-known diffusion models such as the Ornstein-Uhlenbeck model, or more\ngenerally a Pearson diffusion. The transformed diffusion inherits many\nproperties of the underlying simple diffusion including its mixing rates and\ndistributions of first passage times. Likelihood inference and martingale\nestimating functions are considered in the case of a discretely observed\nbimodal diffusion. It is further demonstrated that model parameters can be\nidentified and estimated when the diffusion is observed with additional\nmeasurement error. The new approach is applied to molecular dynamics data in\nform of a reaction coordinate of the small Trp-zipper protein, for which the\nfolding and unfolding rates are estimated. The new models provide a better fit\nto this type of protein folding data than previous models because the diffusion\ncoefficient is state-dependent.",
+                    "authors": "Julie Forman, Michael S\u00f8rensen",
+                    "published": "2013-04-03",
+                    "updated": "2013-04-03",
+                    "primary_cat": "stat.ME",
+                    "cats": [
+                        "stat.ME"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1212.2829v1",
+                    "title": "Spin diffusion in one-dimensional classical Heisenberg mode",
+                    "abstract": "The problem of spin diffusion is studied numerically in one-dimensional\nclassical Heisenberg model using a deterministic odd even spin precession\ndynamics. We demonstrate that spin diffusion in this model, like energy\ndiffusion, is normal and one obtains a long time diffusive tail in the decay of\nautocorrelation function (ACF). Some variations of the model with different\ncoupling schemes and with anisotropy are also studied and we find normal\ndiffusion in all of them. A systematic finite size analysis of the Heisenberg\nmodel also suggests diffusive spreading of fluctuation, contrary to previous\nclaims of anomalous diffusion.",
+                    "authors": "Debarshee Bagchi",
+                    "published": "2012-12-12",
+                    "updated": "2012-12-12",
+                    "primary_cat": "cond-mat.stat-mech",
+                    "cats": [
+                        "cond-mat.stat-mech"
+                    ],
+                    "category": "Diffusion AND Model"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1712.02290v2",
+                    "title": "Effects of nongaussian diffusion on \"isotropic diffusion measurements'': an ex-vivo microimaging and simulation study",
+                    "abstract": "Designing novel diffusion-weighted pulse sequences to probe tissue\nmicrostructure beyond the conventional Stejskal-Tanner family is currently of\nbroad interest. One such technique, multidimensional diffusion MRI, has been\nrecently proposed to afford model-free decomposition of diffusion signal\nkurtosis into terms originating from either ensemble variance of isotropic\ndiffusivity or microscopic diffusion anisotropy. This ability rests on the\nassumption that diffusion can be described as a sum of multiple Gaussian\ncompartments, but this is often not strictly fulfilled. The effects of\nnongaussian diffusion on single shot isotropic diffusion sequences were first\nconsidered in detail by de Swiet and Mitra in 1996. They showed theoretically\nthat anisotropic compartments lead to anisotropic time dependence of the\ndiffusion tensors, which causes the measured isotropic diffusivity to depend on\ngradient frame orientation. Here we show how such deviations from the multiple\nGaussian compartments assumption conflates orientation dispersion with ensemble\nvariance in isotropic diffusivity. Second, we consider additional contributions\nto the apparent variance in isotropic diffusivity arising due to\nintracompartmental kurtosis. These will likewise depend on gradient frame\norientation. We illustrate the potential importance of these confounds with\nanalytical expressions, numerical simulations in simple model geometries, and\nmicroimaging experiments in fixed spinal cord using isotropic diffusion\nencoding waveforms with 7.5 ms duration and 3000 mT/m maximum amplitude.",
+                    "authors": "Sune N\u00f8rh\u00f8j Jespersen, Jonas Lynge Olesen, Andrada Ianu\u015f, Noam Shemesh",
+                    "published": "2017-12-06",
+                    "updated": "2019-02-04",
+                    "primary_cat": "physics.bio-ph",
+                    "cats": [
+                        "physics.bio-ph"
+                    ],
+                    "category": "Diffusion AND Model"
+                }
+            ]
+        ]
+    },
+    {
+        "url": "http://arxiv.org/abs/2401.09417v2",
+        "title": "Vision Mamba: Efficient Visual Representation Learning with Bidirectional State Space Model",
+        "abstract": "Recently the state space models (SSMs) with efficient hardware-aware designs,\ni.e., the Mamba deep learning model, have shown great potential for long\nsequence modeling. Meanwhile building efficient and generic vision backbones\npurely upon SSMs is an appealing direction. However, representing visual data\nis challenging for SSMs due to the position-sensitivity of visual data and the\nrequirement of global context for visual understanding. In this paper, we show\nthat the reliance on self-attention for visual representation learning is not\nnecessary and propose a new generic vision backbone with bidirectional Mamba\nblocks (Vim), which marks the image sequences with position embeddings and\ncompresses the visual representation with bidirectional state space models. On\nImageNet classification, COCO object detection, and ADE20k semantic\nsegmentation tasks, Vim achieves higher performance compared to\nwell-established vision transformers like DeiT, while also demonstrating\nsignificantly improved computation & memory efficiency. For example, Vim is\n2.8$\\times$ faster than DeiT and saves 86.8% GPU memory when performing batch\ninference to extract features on images with a resolution of 1248$\\times$1248.\nThe results demonstrate that Vim is capable of overcoming the computation &\nmemory constraints on performing Transformer-style understanding for\nhigh-resolution images and it has great potential to be the next-generation\nbackbone for vision foundation models. Code is available at\nhttps://github.com/hustvl/Vim.",
+        "authors": "Lianghui Zhu, Bencheng Liao, Qian Zhang, Xinlong Wang, Wenyu Liu, Xinggang Wang",
+        "published": "2024-01-17",
+        "updated": "2024-02-10",
+        "primary_cat": "cs.CV",
+        "cats": [
+            "cs.CV",
+            "cs.LG"
+        ],
+        "label": "Related Work"
+    },
+    {
+        "url": "http://arxiv.org/abs/2112.02475v2",
+        "title": "Deblurring via Stochastic Refinement",
+        "abstract": "Image deblurring is an ill-posed problem with multiple plausible solutions\nfor a given input image. However, most existing methods produce a deterministic\nestimate of the clean image and are trained to minimize pixel-level distortion.\nThese metrics are known to be poorly correlated with human perception, and\noften lead to unrealistic reconstructions. We present an alternative framework\nfor blind deblurring based on conditional diffusion models. Unlike existing\ntechniques, we train a stochastic sampler that refines the output of a\ndeterministic predictor and is capable of producing a diverse set of plausible\nreconstructions for a given input. This leads to a significant improvement in\nperceptual quality over existing state-of-the-art methods across multiple\nstandard benchmarks. Our predict-and-refine approach also enables much more\nefficient sampling compared to typical diffusion models. Combined with a\ncarefully tuned network architecture and inference procedure, our method is\ncompetitive in terms of distortion metrics such as PSNR. These results show\nclear benefits of our diffusion-based method for deblurring and challenge the\nwidely used strategy of producing a single, deterministic reconstruction.",
+        "authors": "Jay Whang, Mauricio Delbracio, Hossein Talebi, Chitwan Saharia, Alexandros G. Dimakis, Peyman Milanfar",
+        "published": "2021-12-05",
+        "updated": "2021-12-28",
+        "primary_cat": "cs.CV",
+        "cats": [
+            "cs.CV",
+            "eess.IV"
+        ],
+        "label": "Related Work"
+    },
+    {
+        "url": "http://arxiv.org/abs/2401.10166v2",
+        "title": "VMamba: Visual State Space Model",
+        "abstract": "Convolutional Neural Networks (CNNs) and Vision Transformers (ViTs) have long\nbeen the predominant backbone networks for visual representation learning.\nWhile ViTs have recently gained prominence over CNNs due to their superior\nfitting capabilities, their scalability is largely constrained by the quadratic\ncomplexity of attention computation. Inspired by the capability of Mamba in\nefficiently modeling long sequences, we propose VMamba, a generic vision\nbackbone model aiming to reduce the computational complexity to linear while\nretaining ViTs' advantageous features. To enhance VMamba's adaptability in\nprocessing vision data, we introduce the Cross-Scan Module (CSM) to enable 1D\nselective scanning in 2D image space with global receptive fields.\nAdditionally, we make further improvements in implementation details and\narchitectural designs to enhance VMamba's performance and boost its inference\nspeed. Extensive experimental results demonstrate VMamba's promising\nperformance across various visual perception tasks, highlighting its pronounced\nadvantages in input scaling efficiency compared to existing benchmark models.\nSource code is available at https://github.com/MzeroMiko/VMamba.",
+        "authors": "Yue Liu, Yunjie Tian, Yuzhong Zhao, Hongtian Yu, Lingxi Xie, Yaowei Wang, Qixiang Ye, Yunfan Liu",
+        "published": "2024-01-18",
+        "updated": "2024-04-10",
+        "primary_cat": "cs.CV",
+        "cats": [
+            "cs.CV"
+        ],
+        "label": "Related Work"
+    },
+    {
+        "url": "http://arxiv.org/abs/2111.00396v3",
+        "title": "Efficiently Modeling Long Sequences with Structured State Spaces",
+        "abstract": "A central goal of sequence modeling is designing a single principled model\nthat can address sequence data across a range of modalities and tasks,\nparticularly on long-range dependencies. Although conventional models including\nRNNs, CNNs, and Transformers have specialized variants for capturing long\ndependencies, they still struggle to scale to very long sequences of $10000$ or\nmore steps. A promising recent approach proposed modeling sequences by\nsimulating the fundamental state space model (SSM) \\( x'(t) = Ax(t) + Bu(t),\ny(t) = Cx(t) + Du(t) \\), and showed that for appropriate choices of the state\nmatrix \\( A \\), this system could handle long-range dependencies mathematically\nand empirically. However, this method has prohibitive computation and memory\nrequirements, rendering it infeasible as a general sequence modeling solution.\nWe propose the Structured State Space sequence model (S4) based on a new\nparameterization for the SSM, and show that it can be computed much more\nefficiently than prior approaches while preserving their theoretical strengths.\nOur technique involves conditioning \\( A \\) with a low-rank correction,\nallowing it to be diagonalized stably and reducing the SSM to the well-studied\ncomputation of a Cauchy kernel. S4 achieves strong empirical results across a\ndiverse range of established benchmarks, including (i) 91\\% accuracy on\nsequential CIFAR-10 with no data augmentation or auxiliary losses, on par with\na larger 2-D ResNet, (ii) substantially closing the gap to Transformers on\nimage and language modeling tasks, while performing generation $60\\times$\nfaster (iii) SoTA on every task from the Long Range Arena benchmark, including\nsolving the challenging Path-X task of length 16k that all prior work fails on,\nwhile being as efficient as all competitors.",
+        "authors": "Albert Gu, Karan Goel, Christopher R\u00e9",
+        "published": "2021-10-31",
+        "updated": "2022-08-05",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG"
+        ],
+        "label": "Related Work"
+    },
+    {
+        "url": "http://arxiv.org/abs/2211.14461v2",
+        "title": "CDDFuse: Correlation-Driven Dual-Branch Feature Decomposition for Multi-Modality Image Fusion",
+        "abstract": "Multi-modality (MM) image fusion aims to render fused images that maintain\nthe merits of different modalities, e.g., functional highlight and detailed\ntextures. To tackle the challenge in modeling cross-modality features and\ndecomposing desirable modality-specific and modality-shared features, we\npropose a novel Correlation-Driven feature Decomposition Fusion (CDDFuse)\nnetwork. Firstly, CDDFuse uses Restormer blocks to extract cross-modality\nshallow features. We then introduce a dual-branch Transformer-CNN feature\nextractor with Lite Transformer (LT) blocks leveraging long-range attention to\nhandle low-frequency global features and Invertible Neural Networks (INN)\nblocks focusing on extracting high-frequency local information. A\ncorrelation-driven loss is further proposed to make the low-frequency features\ncorrelated while the high-frequency features uncorrelated based on the embedded\ninformation. Then, the LT-based global fusion and INN-based local fusion layers\noutput the fused image. Extensive experiments demonstrate that our CDDFuse\nachieves promising results in multiple fusion tasks, including infrared-visible\nimage fusion and medical image fusion. We also show that CDDFuse can boost the\nperformance in downstream infrared-visible semantic segmentation and object\ndetection in a unified benchmark. The code is available at\nhttps://github.com/Zhaozixiang1228/MMIF-CDDFuse.",
+        "authors": "Zixiang Zhao, Haowen Bai, Jiangshe Zhang, Yulun Zhang, Shuang Xu, Zudi Lin, Radu Timofte, Luc Van Gool",
+        "published": "2022-11-26",
+        "updated": "2023-04-10",
+        "primary_cat": "cs.CV",
+        "cats": [
+            "cs.CV"
+        ],
+        "label": "Related Work"
+    },
+    {
+        "url": "http://arxiv.org/abs/2312.00752v1",
+        "title": "Mamba: Linear-Time Sequence Modeling with Selective State Spaces",
+        "abstract": "Foundation models, now powering most of the exciting applications in deep\nlearning, are almost universally based on the Transformer architecture and its\ncore attention module. Many subquadratic-time architectures such as linear\nattention, gated convolution and recurrent models, and structured state space\nmodels (SSMs) have been developed to address Transformers' computational\ninefficiency on long sequences, but they have not performed as well as\nattention on important modalities such as language. We identify that a key\nweakness of such models is their inability to perform content-based reasoning,\nand make several improvements. First, simply letting the SSM parameters be\nfunctions of the input addresses their weakness with discrete modalities,\nallowing the model to selectively propagate or forget information along the\nsequence length dimension depending on the current token. Second, even though\nthis change prevents the use of efficient convolutions, we design a\nhardware-aware parallel algorithm in recurrent mode. We integrate these\nselective SSMs into a simplified end-to-end neural network architecture without\nattention or even MLP blocks (Mamba). Mamba enjoys fast inference (5$\\times$\nhigher throughput than Transformers) and linear scaling in sequence length, and\nits performance improves on real data up to million-length sequences. As a\ngeneral sequence model backbone, Mamba achieves state-of-the-art performance\nacross several modalities such as language, audio, and genomics. On language\nmodeling, our Mamba-3B model outperforms Transformers of the same size and\nmatches Transformers twice its size, both in pretraining and downstream\nevaluation.",
+        "authors": "Albert Gu, Tri Dao",
+        "published": "2023-12-01",
+        "updated": "2023-12-01",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG",
+            "cs.AI"
+        ],
+        "label": "Related Work"
+    },
+    {
+        "url": "http://arxiv.org/abs/2106.15282v3",
+        "title": "Cascaded Diffusion Models for High Fidelity Image Generation",
+        "abstract": "We show that cascaded diffusion models are capable of generating high\nfidelity images on the class-conditional ImageNet generation benchmark, without\nany assistance from auxiliary image classifiers to boost sample quality. A\ncascaded diffusion model comprises a pipeline of multiple diffusion models that\ngenerate images of increasing resolution, beginning with a standard diffusion\nmodel at the lowest resolution, followed by one or more super-resolution\ndiffusion models that successively upsample the image and add higher resolution\ndetails. We find that the sample quality of a cascading pipeline relies\ncrucially on conditioning augmentation, our proposed method of data\naugmentation of the lower resolution conditioning inputs to the\nsuper-resolution models. Our experiments show that conditioning augmentation\nprevents compounding error during sampling in a cascaded model, helping us to\ntrain cascading pipelines achieving FID scores of 1.48 at 64x64, 3.52 at\n128x128 and 4.88 at 256x256 resolutions, outperforming BigGAN-deep, and\nclassification accuracy scores of 63.02% (top-1) and 84.06% (top-5) at 256x256,\noutperforming VQ-VAE-2.",
+        "authors": "Jonathan Ho, Chitwan Saharia, William Chan, David J. Fleet, Mohammad Norouzi, Tim Salimans",
+        "published": "2021-05-30",
+        "updated": "2021-12-17",
+        "primary_cat": "cs.CV",
+        "cats": [
+            "cs.CV",
+            "cs.AI",
+            "cs.LG"
+        ],
+        "label": "Related Work"
+    },
+    {
+        "url": "http://arxiv.org/abs/2201.11793v3",
+        "title": "Denoising Diffusion Restoration Models",
+        "abstract": "Many interesting tasks in image restoration can be cast as linear inverse\nproblems. A recent family of approaches for solving these problems uses\nstochastic algorithms that sample from the posterior distribution of natural\nimages given the measurements. However, efficient solutions often require\nproblem-specific supervised training to model the posterior, whereas\nunsupervised methods that are not problem-specific typically rely on\ninefficient iterative methods. This work addresses these issues by introducing\nDenoising Diffusion Restoration Models (DDRM), an efficient, unsupervised\nposterior sampling method. Motivated by variational inference, DDRM takes\nadvantage of a pre-trained denoising diffusion generative model for solving any\nlinear inverse problem. We demonstrate DDRM's versatility on several image\ndatasets for super-resolution, deblurring, inpainting, and colorization under\nvarious amounts of measurement noise. DDRM outperforms the current leading\nunsupervised methods on the diverse ImageNet dataset in reconstruction quality,\nperceptual quality, and runtime, being 5x faster than the nearest competitor.\nDDRM also generalizes well for natural images out of the distribution of the\nobserved ImageNet training set.",
+        "authors": "Bahjat Kawar, Michael Elad, Stefano Ermon, Jiaming Song",
+        "published": "2022-01-27",
+        "updated": "2022-10-12",
+        "primary_cat": "eess.IV",
+        "cats": [
+            "eess.IV",
+            "cs.CV",
+            "cs.LG"
+        ],
+        "label": "Related Work"
+    },
+    {
+        "url": "http://arxiv.org/abs/1706.03762v7",
+        "title": "Attention Is All You Need",
+        "abstract": "The dominant sequence transduction models are based on complex recurrent or\nconvolutional neural networks in an encoder-decoder configuration. The best\nperforming models also connect the encoder and decoder through an attention\nmechanism. We propose a new simple network architecture, the Transformer, based\nsolely on attention mechanisms, dispensing with recurrence and convolutions\nentirely. Experiments on two machine translation tasks show these models to be\nsuperior in quality while being more parallelizable and requiring significantly\nless time to train. Our model achieves 28.4 BLEU on the WMT 2014\nEnglish-to-German translation task, improving over the existing best results,\nincluding ensembles by over 2 BLEU. On the WMT 2014 English-to-French\ntranslation task, our model establishes a new single-model state-of-the-art\nBLEU score of 41.8 after training for 3.5 days on eight GPUs, a small fraction\nof the training costs of the best models from the literature. We show that the\nTransformer generalizes well to other tasks by applying it successfully to\nEnglish constituency parsing both with large and limited training data.",
+        "authors": "Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N. Gomez, Lukasz Kaiser, Illia Polosukhin",
+        "published": "2017-06-12",
+        "updated": "2023-08-02",
+        "primary_cat": "cs.CL",
+        "cats": [
+            "cs.CL",
+            "cs.LG"
+        ],
+        "label": "Related Work"
+    },
+    {
+        "url": "http://arxiv.org/abs/2112.02991v1",
+        "title": "Cross-Modality Attentive Feature Fusion for Object Detection in Multispectral Remote Sensing Imagery",
+        "abstract": "Cross-modality fusing complementary information of multispectral remote\nsensing image pairs can improve the perception ability of detection algorithms,\nmaking them more robust and reliable for a wider range of applications, such as\nnighttime detection. Compared with prior methods, we think different features\nshould be processed specifically, the modality-specific features should be\nretained and enhanced, while the modality-shared features should be\ncherry-picked from the RGB and thermal IR modalities. Following this idea, a\nnovel and lightweight multispectral feature fusion approach with joint\ncommon-modality and differential-modality attentions are proposed, named\nCross-Modality Attentive Feature Fusion (CMAFF). Given the intermediate feature\nmaps of RGB and IR images, our module parallel infers attention maps from two\nseparate modalities, common- and differential-modality, then the attention maps\nare multiplied to the input feature map respectively for adaptive feature\nenhancement or selection. Extensive experiments demonstrate that our proposed\napproach can achieve the state-of-the-art performance at a low computation\ncost.",
+        "authors": "Qingyun Fang, Zhaokui Wang",
+        "published": "2021-12-06",
+        "updated": "2021-12-06",
+        "primary_cat": "cs.CV",
+        "cats": [
+            "cs.CV",
+            "cs.AI",
+            "eess.IV"
+        ],
+        "label": "Related Work"
+    },
+    {
+        "url": "http://arxiv.org/abs/2204.05289v2",
+        "title": "Towards Online Domain Adaptive Object Detection",
+        "abstract": "Existing object detection models assume both the training and test data are\nsampled from the same source domain. This assumption does not hold true when\nthese detectors are deployed in real-world applications, where they encounter\nnew visual domain. Unsupervised Domain Adaptation (UDA) methods are generally\nemployed to mitigate the adverse effects caused by domain shift. Existing UDA\nmethods operate in an offline manner where the model is first adapted towards\nthe target domain and then deployed in real-world applications. However, this\noffline adaptation strategy is not suitable for real-world applications as the\nmodel frequently encounters new domain shifts. Hence, it becomes critical to\ndevelop a feasible UDA method that generalizes to these domain shifts\nencountered during deployment time in a continuous online manner. To this end,\nwe propose a novel unified adaptation framework that adapts and improves\ngeneralization on the target domain in online settings. In particular, we\nintroduce MemXformer - a cross-attention transformer-based memory module where\nitems in the memory take advantage of domain shifts and record prototypical\npatterns of the target distribution. Further, MemXformer produces strong\npositive and negative pairs to guide a novel contrastive loss, which enhances\ntarget specific representation learning. Experiments on diverse detection\nbenchmarks show that the proposed strategy can produce state-of-the-art\nperformance in both online and offline settings. To the best of our knowledge,\nthis is the first work to address online and offline adaptation settings for\nobject detection. Code at https://github.com/Vibashan/memXformer-online-da",
+        "authors": "Vibashan VS, Poojan Oza, Vishal M. Patel",
+        "published": "2022-04-11",
+        "updated": "2022-10-21",
+        "primary_cat": "cs.CV",
+        "cats": [
+            "cs.CV"
+        ],
+        "label": "Related Work"
+    },
+    {
+        "url": "http://arxiv.org/abs/2010.04324v2",
+        "title": "Deep-Masking Generative Network: A Unified Framework for Background Restoration from Superimposed Images",
+        "abstract": "Restoring the clean background from the superimposed images containing a\nnoisy layer is the common crux of a classical category of tasks on image\nrestoration such as image reflection removal, image deraining and image\ndehazing. These tasks are typically formulated and tackled individually due to\nthe diverse and complicated appearance patterns of noise layers within the\nimage. In this work we present the Deep-Masking Generative Network (DMGN),\nwhich is a unified framework for background restoration from the superimposed\nimages and is able to cope with different types of noise. Our proposed DMGN\nfollows a coarse-to-fine generative process: a coarse background image and a\nnoise image are first generated in parallel, then the noise image is further\nleveraged to refine the background image to achieve a higher-quality background\nimage. In particular, we design the novel Residual Deep-Masking Cell as the\ncore operating unit for our DMGN to enhance the effective information and\nsuppress the negative information during image generation via learning a gating\nmask to control the information flow. By iteratively employing this Residual\nDeep-Masking Cell, our proposed DMGN is able to generate both high-quality\nbackground image and noisy image progressively. Furthermore, we propose a\ntwo-pronged strategy to effectively leverage the generated noise image as\ncontrasting cues to facilitate the refinement of the background image.\nExtensive experiments across three typical tasks for image background\nrestoration, including image reflection removal, image rain steak removal and\nimage dehazing, show that our DMGN consistently outperforms state-of-the-art\nmethods specifically designed for each single task.",
+        "authors": "Xin Feng, Wenjie Pei, Zihui Jia, Fanglin Chen, David Zhang, Guangming Lu",
+        "published": "2020-10-09",
+        "updated": "2021-04-12",
+        "primary_cat": "cs.CV",
+        "cats": [
+            "cs.CV"
+        ],
+        "label": "Related Work"
+    },
+    {
+        "url": "http://arxiv.org/abs/2111.14813v2",
+        "title": "TransWeather: Transformer-based Restoration of Images Degraded by Adverse Weather Conditions",
+        "abstract": "Removing adverse weather conditions like rain, fog, and snow from images is\nan important problem in many applications. Most methods proposed in the\nliterature have been designed to deal with just removing one type of\ndegradation. Recently, a CNN-based method using neural architecture search\n(All-in-One) was proposed to remove all the weather conditions at once.\nHowever, it has a large number of parameters as it uses multiple encoders to\ncater to each weather removal task and still has scope for improvement in its\nperformance. In this work, we focus on developing an efficient solution for the\nall adverse weather removal problem. To this end, we propose TransWeather, a\ntransformer-based end-to-end model with just a single encoder and a decoder\nthat can restore an image degraded by any weather condition. Specifically, we\nutilize a novel transformer encoder using intra-patch transformer blocks to\nenhance attention inside the patches to effectively remove smaller weather\ndegradations. We also introduce a transformer decoder with learnable weather\ntype embeddings to adjust to the weather degradation at hand. TransWeather\nachieves improvements across multiple test datasets over both All-in-One\nnetwork as well as methods fine-tuned for specific tasks. TransWeather is also\nvalidated on real world test images and found to be more effective than\nprevious methods. Implementation code can be accessed at\nhttps://github.com/jeya-maria-jose/TransWeather .",
+        "authors": "Jeya Maria Jose Valanarasu, Rajeev Yasarla, Vishal M. Patel",
+        "published": "2021-11-29",
+        "updated": "2022-06-17",
+        "primary_cat": "cs.CV",
+        "cats": [
+            "cs.CV"
+        ],
+        "label": "Related Work"
+    },
+    {
+        "url": "http://arxiv.org/abs/2206.13947v3",
+        "title": "Long Range Language Modeling via Gated State Spaces",
+        "abstract": "State space models have shown to be effective at modeling long range\ndependencies, specially on sequence classification tasks. In this work we focus\non autoregressive sequence modeling over English books, Github source code and\nArXiv mathematics articles. Based on recent developments around the\neffectiveness of gated activation functions, we propose a new layer named Gated\nState Space (GSS) and show that it trains significantly faster than the\ndiagonal version of S4 (i.e. DSS) on TPUs, is fairly competitive with several\nwell-tuned Transformer-based baselines and exhibits zero-shot generalization to\nlonger inputs while being straightforward to implement. Finally, we show that\nleveraging self-attention to model local dependencies improves the performance\nof GSS even further.",
+        "authors": "Harsh Mehta, Ankit Gupta, Ashok Cutkosky, Behnam Neyshabur",
+        "published": "2022-06-27",
+        "updated": "2022-07-02",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG",
+            "cs.CL"
+        ],
+        "label": "Related Work"
+    },
+    {
+        "url": "http://arxiv.org/abs/2208.04933v3",
+        "title": "Simplified State Space Layers for Sequence Modeling",
+        "abstract": "Models using structured state space sequence (S4) layers have achieved\nstate-of-the-art performance on long-range sequence modeling tasks. An S4 layer\ncombines linear state space models (SSMs), the HiPPO framework, and deep\nlearning to achieve high performance. We build on the design of the S4 layer\nand introduce a new state space layer, the S5 layer. Whereas an S4 layer uses\nmany independent single-input, single-output SSMs, the S5 layer uses one\nmulti-input, multi-output SSM. We establish a connection between S5 and S4, and\nuse this to develop the initialization and parameterization used by the S5\nmodel. The result is a state space layer that can leverage efficient and widely\nimplemented parallel scans, allowing S5 to match the computational efficiency\nof S4, while also achieving state-of-the-art performance on several long-range\nsequence modeling tasks. S5 averages 87.4% on the long range arena benchmark,\nand 98.5% on the most difficult Path-X task.",
+        "authors": "Jimmy T. H. Smith, Andrew Warrington, Scott W. Linderman",
+        "published": "2022-08-09",
+        "updated": "2023-03-03",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG"
+        ],
+        "label": "Related Work"
+    },
+    {
+        "url": "http://arxiv.org/abs/2105.05233v4",
+        "title": "Diffusion Models Beat GANs on Image Synthesis",
+        "abstract": "We show that diffusion models can achieve image sample quality superior to\nthe current state-of-the-art generative models. We achieve this on\nunconditional image synthesis by finding a better architecture through a series\nof ablations. For conditional image synthesis, we further improve sample\nquality with classifier guidance: a simple, compute-efficient method for\ntrading off diversity for fidelity using gradients from a classifier. We\nachieve an FID of 2.97 on ImageNet 128$\\times$128, 4.59 on ImageNet\n256$\\times$256, and 7.72 on ImageNet 512$\\times$512, and we match BigGAN-deep\neven with as few as 25 forward passes per sample, all while maintaining better\ncoverage of the distribution. Finally, we find that classifier guidance\ncombines well with upsampling diffusion models, further improving FID to 3.94\non ImageNet 256$\\times$256 and 3.85 on ImageNet 512$\\times$512. We release our\ncode at https://github.com/openai/guided-diffusion",
+        "authors": "Prafulla Dhariwal, Alex Nichol",
+        "published": "2021-05-11",
+        "updated": "2021-06-01",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG",
+            "cs.AI",
+            "cs.CV",
+            "stat.ML"
+        ],
+        "label": "Related Work"
+    },
+    {
+        "url": "http://arxiv.org/abs/2009.12664v1",
+        "title": "Multispectral Fusion for Object Detection with Cyclic Fuse-and-Refine Blocks",
+        "abstract": "Multispectral images (e.g. visible and infrared) may be particularly useful\nwhen detecting objects with the same model in different environments (e.g.\nday/night outdoor scenes). To effectively use the different spectra, the main\ntechnical problem resides in the information fusion process. In this paper, we\npropose a new halfway feature fusion method for neural networks that leverages\nthe complementary/consistency balance existing in multispectral features by\nadding to the network architecture, a particular module that cyclically fuses\nand refines each spectral feature. We evaluate the effectiveness of our fusion\nmethod on two challenging multispectral datasets for object detection. Our\nresults show that implementing our Cyclic Fuse-and-Refine module in any network\nimproves the performance on both datasets compared to other state-of-the-art\nmultispectral object detection methods.",
+        "authors": "Heng Zhang, Elisa Fromont, S\u00e9bastien Lefevre, Bruno Avignon",
+        "published": "2020-09-26",
+        "updated": "2020-09-26",
+        "primary_cat": "cs.CV",
+        "cats": [
+            "cs.CV"
+        ],
+        "label": "Related Work"
+    },
+    {
+        "url": "http://arxiv.org/abs/2211.04877v1",
+        "title": "Interactive Feature Embedding for Infrared and Visible Image Fusion",
+        "abstract": "General deep learning-based methods for infrared and visible image fusion\nrely on the unsupervised mechanism for vital information retention by utilizing\nelaborately designed loss functions. However, the unsupervised mechanism\ndepends on a well designed loss function, which cannot guarantee that all vital\ninformation of source images is sufficiently extracted. In this work, we\npropose a novel interactive feature embedding in self-supervised learning\nframework for infrared and visible image fusion, attempting to overcome the\nissue of vital information degradation. With the help of self-supervised\nlearning framework, hierarchical representations of source images can be\nefficiently extracted. In particular, interactive feature embedding models are\ntactfully designed to build a bridge between the self-supervised learning and\ninfrared and visible image fusion learning, achieving vital information\nretention. Qualitative and quantitative evaluations exhibit that the proposed\nmethod performs favorably against state-of-the-art methods.",
+        "authors": "Fan Zhao, Wenda Zhao, Huchuan Lu",
+        "published": "2022-11-09",
+        "updated": "2022-11-09",
+        "primary_cat": "cs.CV",
+        "cats": [
+            "cs.CV"
+        ],
+        "label": "Related Work"
+    },
+    {
+        "url": "http://arxiv.org/abs/1807.03744v2",
+        "title": "Enhanced Diffusivity in Perturbed Senile Reinforced Random Walk Models",
+        "abstract": "We consider diffusivity of random walks with transition probabilities\ndepending on the number of consecutive traversals of the last traversed edge,\nthe so called senile reinforced random walk (SeRW). In one dimension, the walk\nis known to be sub-diffusive with identity reinforcement function. We perturb\nthe model by introducing a small probability $\\delta$ of escaping the last\ntraversed edge at each step. The perturbed SeRW model is diffusive for any\n$\\delta >0 $, with enhanced diffusivity ($\\gg O(\\delta^2)$) in the small\n$\\delta$ regime. We further study stochastically perturbed SeRW models by\nhaving the last edge escape probability of the form $\\delta\\, \\xi_n$ with\n$\\xi_n$'s being independent random variables. Enhanced diffusivity in such\nmodels are logarithmically close to the so called residual diffusivity\n(positive in the zero $\\delta$ limit), with diffusivity between\n$O\\left(\\frac{1}{|\\log\\delta |}\\right)$ and\n$O\\left(\\frac{1}{\\log|\\log\\delta|}\\right)$. Finally, we generalize our results\nto higher dimensions where the unperturbed model is already diffusive. The\nenhanced diffusivity can be as much as $O(\\log^{-2}\\delta)$.",
+        "authors": "Thu Dinh, Jack Xin",
+        "published": "2018-07-10",
+        "updated": "2020-03-16",
+        "primary_cat": "math.PR",
+        "cats": [
+            "math.PR",
+            "60G50, 60H30, 58J37"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/1602.07007v1",
+        "title": "Distributional Behaviors of Time-averaged Observables in Langevin Equation with Fluctuating Diffusivity: Normal Diffusion but Anomalous Fluctuations",
+        "abstract": "We consider Langevin equation with dichotomously fluctuating diffusivity,\nwhere the diffusion coefficient changes dichotomously in time, in order to\nstudy fluctuations of time-averaged observables in temporary heterogeneous\ndiffusion process. We find that occupation time statistics is a powerful tool\nfor calculating the time-averaged mean square displacement in the model. We\nshow that the time-averaged diffusion coefficients are intrinsically random\nwhen the mean sojourn time for one of the states diverges. Our model provides\nanomalous fluctuations of time-averaged diffusivity, which have relevance to\nlarge fluctuations of the diffusion coefficient in single-particle-tracking\nexperiments.",
+        "authors": "Takuma Akimoto, Eiji Yamamoto",
+        "published": "2016-02-23",
+        "updated": "2016-02-23",
+        "primary_cat": "cond-mat.stat-mech",
+        "cats": [
+            "cond-mat.stat-mech",
+            "cond-mat.soft"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/2111.03914v2",
+        "title": "A systematic approach for modeling a nonlocal eddy diffusivity",
+        "abstract": "This study considers advective and diffusive transport of passive scalar\nfields by spatially-varying incompressible flows. Prior studies have shown that\nthe eddy diffusivities governing the mean field transport in such systems can\ngenerally be nonlocal in space and time. While for many flows nonlocal eddy\ndiffusivities are more accurate than commonly-used Boussinesq eddy\ndiffusivities, nonlocal eddy diffusivities are often computationally\ncost-prohibitive to obtain and difficult to implement in practice. We develop a\nsystematic and more cost-effective approach for modeling nonlocal eddy\ndiffusivities using matched moment inverse (MMI) operators. These operators are\nconstructed using only a few leading-order moments of the exact nonlocal eddy\ndiffusivity kernel, which can be easily computed using the inverse macroscopic\nforcing method (IMFM) (Mani and Park (2021)). The resulting reduced-order\nmodels for the mean fields that incorporate the modeled eddy diffusivities\noften improve Boussinesq-limit models since they capture leading-order nonlocal\neffects. But more importantly, these models can be expressed as partial\ndifferential equations that are readily solvable using existing computational\nfluid dynamics capabilities rather than as integro-partial differential\nequations.",
+        "authors": "Jessie Liu, Hannah Williams, Ali Mani",
+        "published": "2021-11-06",
+        "updated": "2023-06-28",
+        "primary_cat": "physics.flu-dyn",
+        "cats": [
+            "physics.flu-dyn"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/1709.05336v1",
+        "title": "Cs diffusion in SiC high-energy grain boundaries",
+        "abstract": "Cesium (Cs) is a radioactive fission product whose release is of concern for\nTristructural-Isotropic (TRISO) fuel particles. In this work, Cs diffusion\nthrough high energy grain boundaries (HEGBs) of cubic-SiC is studied using an\nab-initio based kinetic Monte Carlo (kMC) model. The HEGB environment was\nmodeled as an amorphous SiC (a-SiC), and Cs defect energies were calculated\nusing density functional theory (DFT). From defect energies, it was suggested\nthat the fastest diffusion mechanism as Cs interstitial in an amorphous SiC.\nThe diffusion of Cs interstitial was simulated using a kMC, based on the site\nand transition state energies sampled from the DFT. The Cs HEGB diffusion\nexhibited an Arrhenius type diffusion in the range of 1200-1600{\\deg}C. The\ncomparison between HEGB results and the other studies suggests not only that\nthe GB diffusion dominates the bulk diffusion, but also that the HEGB is one of\nthe fastest grain boundary paths for the Cs diffusion. The diffusion\ncoefficients in HEGB are clearly a few orders of magnitude lower than the\nreported diffusion coefficients from in- and out-of- pile samples, suggesting\nthat other contributions are responsible, such as a radiation enhanced\ndiffusion.",
+        "authors": "Hyunseok Ko, Izabela Szlufarska, Dane Morgan",
+        "published": "2017-09-11",
+        "updated": "2017-09-11",
+        "primary_cat": "cond-mat.mtrl-sci",
+        "cats": [
+            "cond-mat.mtrl-sci",
+            "nucl-th"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/2302.05737v2",
+        "title": "A Reparameterized Discrete Diffusion Model for Text Generation",
+        "abstract": "This work studies discrete diffusion probabilistic models with applications\nto natural language generation. We derive an alternative yet equivalent\nformulation of the sampling from discrete diffusion processes and leverage this\ninsight to develop a family of reparameterized discrete diffusion models. The\nderived generic framework is highly flexible, offers a fresh perspective of the\ngeneration process in discrete diffusion models, and features more effective\ntraining and decoding techniques. We conduct extensive experiments to evaluate\nthe text generation capability of our model, demonstrating significant\nimprovements over existing diffusion models.",
+        "authors": "Lin Zheng, Jianbo Yuan, Lei Yu, Lingpeng Kong",
+        "published": "2023-02-11",
+        "updated": "2024-02-03",
+        "primary_cat": "cs.CL",
+        "cats": [
+            "cs.CL",
+            "cs.LG"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/1210.5101v1",
+        "title": "Global well-posedness and zero-diffusion limit of classical solutions to the 3D conservation laws arising in chemotaxis",
+        "abstract": "In this paper, we study the relationship between a diffusive model and a\nnon-diffusive model which are both derived from the well-known Keller-Segel\nmodel, as a coefficient of diffusion $\\varepsilon$ goes to zero. First, we\nestablish the global well-posedness of classical solutions to the Cauchy\nproblem for the diffusive model with smooth initial data which is of small\n$L^2$ norm, together with some {\\it a priori} estimates uniform for $t$ and\n$\\varepsilon$. Then we investigate the zero-diffusion limit, and get the global\nwell-posedness of classical solutions to the Cauchy problem for the\nnon-diffusive model. Finally, we derive the convergence rate of the diffusive\nmodel toward the non-diffusive model. It is shown that the convergence rate in\n$L^\\infty$ norm is of the order $O(\\varepsilon^{1/2})$. It should be noted that\nthe initial data is small in $L^2$-norm but can be of large oscillations with\nconstant state at far field. As a byproduct, we improve the corresponding\nresult on the well-posedness of the non-difussive model which requires small\noscillations.",
+        "authors": "Hongyun Peng, Huanyao Wen, Changjiang Zhu",
+        "published": "2012-10-18",
+        "updated": "2012-10-18",
+        "primary_cat": "math.AP",
+        "cats": [
+            "math.AP"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/2305.10028v1",
+        "title": "Pyramid Diffusion Models For Low-light Image Enhancement",
+        "abstract": "Recovering noise-covered details from low-light images is challenging, and\nthe results given by previous methods leave room for improvement. Recent\ndiffusion models show realistic and detailed image generation through a\nsequence of denoising refinements and motivate us to introduce them to\nlow-light image enhancement for recovering realistic details. However, we found\ntwo problems when doing this, i.e., 1) diffusion models keep constant\nresolution in one reverse process, which limits the speed; 2) diffusion models\nsometimes result in global degradation (e.g., RGB shift). To address the above\nproblems, this paper proposes a Pyramid Diffusion model (PyDiff) for low-light\nimage enhancement. PyDiff uses a novel pyramid diffusion method to perform\nsampling in a pyramid resolution style (i.e., progressively increasing\nresolution in one reverse process). Pyramid diffusion makes PyDiff much faster\nthan vanilla diffusion models and introduces no performance degradation.\nFurthermore, PyDiff uses a global corrector to alleviate the global degradation\nthat may occur in the reverse process, significantly improving the performance\nand making the training of diffusion models easier with little additional\ncomputational consumption. Extensive experiments on popular benchmarks show\nthat PyDiff achieves superior performance and efficiency. Moreover, PyDiff can\ngeneralize well to unseen noise and illumination distributions.",
+        "authors": "Dewei Zhou, Zongxin Yang, Yi Yang",
+        "published": "2023-05-17",
+        "updated": "2023-05-17",
+        "primary_cat": "cs.CV",
+        "cats": [
+            "cs.CV"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/1708.06890v1",
+        "title": "Collaborative Inference of Coexisting Information Diffusions",
+        "abstract": "Recently, \\textit{diffusion history inference} has become an emerging\nresearch topic due to its great benefits for various applications, whose\npurpose is to reconstruct the missing histories of information diffusion traces\naccording to incomplete observations. The existing methods, however, often\nfocus only on single information diffusion trace, while in a real-world social\nnetwork, there often coexist multiple information diffusions over the same\nnetwork. In this paper, we propose a novel approach called Collaborative\nInference Model (CIM) for the problem of the inference of coexisting\ninformation diffusions. By exploiting the synergism between the coexisting\ninformation diffusions, CIM holistically models multiple information diffusions\nas a sparse 4th-order tensor called Coexisting Diffusions Tensor (CDT) without\nany prior assumption of diffusion models, and collaboratively infers the\nhistories of the coexisting information diffusions via a low-rank approximation\nof CDT with a fusion of heterogeneous constraints generated from additional\ndata sources. To improve the efficiency, we further propose an optimal\nalgorithm called Time Window based Parallel Decomposition Algorithm (TWPDA),\nwhich can speed up the inference without compromise on the accuracy by\nutilizing the temporal locality of information diffusions. The extensive\nexperiments conducted on real world datasets and synthetic datasets verify the\neffectiveness and efficiency of CIM and TWPDA.",
+        "authors": "Yanchao Sun, Cong Qian, Ning Yang, Philip S. Yu",
+        "published": "2017-08-23",
+        "updated": "2017-08-23",
+        "primary_cat": "cs.SI",
+        "cats": [
+            "cs.SI"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/1801.09352v1",
+        "title": "Distributed order Hausdorff derivative diffusion model to characterize non-Fickian diffusion in porous media",
+        "abstract": "Many theoretical and experimental results show that solute transport in\nheterogeneous porous media exhibits multi-scaling behaviors. To describe such\nnon-Fickian diffusions, this work provides a distributed order Hausdorff\ndiffusion model to describe the tracer transport in porous media. This model is\nproved to be equivalent with the diffusion equation model with a nonlinear time\ndependent diffusion coefficient. In conjunction with the structural derivative,\nits mean squared displacement (MSD) of the tracer particles is explicitly\nderived as a dilogarithm function when the weight function of the order\ndistribution is a linear function of the time derivative order. This model can\ncapture both accelerating and decelerating anomalous and ultraslow diffusions\nby varying the weight parameter c. In this study, the tracer transport in\nwater-filled pore spaces of two-dimensional Euclidean is demonstrated as a\ndecelerating sub-diffusion, and can well be described by the distributed order\nHausdorff diffusion model with c = 1.73. While the Hausdorff diffusion model\ncan accurately fit the sub-diffusion experimental data of the tracer transport\nin the pore-solid prefractal porous media.",
+        "authors": "Yingjie Liang, Wen Chen, Wei Xu, HongGuang Sun",
+        "published": "2018-01-29",
+        "updated": "2018-01-29",
+        "primary_cat": "physics.flu-dyn",
+        "cats": [
+            "physics.flu-dyn"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/0805.0647v1",
+        "title": "Scaling of Rough Surfaces: Effects of Surface Diffusion on Growth and Roughness Exponents",
+        "abstract": "Random deposition model with surface diffusion over several next nearest\nneighbours is studied. The results agree with the results obtained by Family\nfor the case of nearest neighbour diffusion [F. Family, J. Phys. A 19(8), L441,\n1986]. However for larger diffusion steps, the growth exponent and the\nroughness exponent show interesting dependence on diffusion length.",
+        "authors": "Baisakhi Mal, Subhankar Ray, J. Shamanna",
+        "published": "2008-05-06",
+        "updated": "2008-05-06",
+        "primary_cat": "cond-mat.soft",
+        "cats": [
+            "cond-mat.soft",
+            "cond-mat.stat-mech"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/2312.08873v1",
+        "title": "Diffusion Cocktail: Fused Generation from Diffusion Models",
+        "abstract": "Diffusion models excel at generating high-quality images and are easy to\nextend, making them extremely popular among active users who have created an\nextensive collection of diffusion models with various styles by fine-tuning\nbase models such as Stable Diffusion. Recent work has focused on uncovering\nsemantic and visual information encoded in various components of a diffusion\nmodel, enabling better generation quality and more fine-grained control.\nHowever, those methods target improving a single model and overlook the vastly\navailable collection of fine-tuned diffusion models. In this work, we study the\ncombinations of diffusion models. We propose Diffusion Cocktail (Ditail), a\ntraining-free method that can accurately transfer content information between\ntwo diffusion models. This allows us to perform diverse generations using a set\nof diffusion models, resulting in novel images that are unlikely to be obtained\nby a single model alone. We also explore utilizing Ditail for style transfer,\nwith the target style set by a diffusion model instead of an image. Ditail\noffers a more detailed manipulation of the diffusion generation, thereby\nenabling the vast community to integrate various styles and contents seamlessly\nand generate any content of any style.",
+        "authors": "Haoming Liu, Yuanhe Guo, Shengjie Wang, Hongyi Wen",
+        "published": "2023-12-12",
+        "updated": "2023-12-12",
+        "primary_cat": "cs.CV",
+        "cats": [
+            "cs.CV",
+            "cs.AI"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/2305.09605v1",
+        "title": "Expressiveness Remarks for Denoising Diffusion Models and Samplers",
+        "abstract": "Denoising diffusion models are a class of generative models which have\nrecently achieved state-of-the-art results across many domains. Gradual noise\nis added to the data using a diffusion process, which transforms the data\ndistribution into a Gaussian. Samples from the generative model are then\nobtained by simulating an approximation of the time reversal of this diffusion\ninitialized by Gaussian samples. Recent research has explored adapting\ndiffusion models for sampling and inference tasks. In this paper, we leverage\nknown connections to stochastic control akin to the F\\\"ollmer drift to extend\nestablished neural network approximation results for the F\\\"ollmer drift to\ndenoising diffusion models and samplers.",
+        "authors": "Francisco Vargas, Teodora Reu, Anna Kerekes",
+        "published": "2023-05-16",
+        "updated": "2023-05-16",
+        "primary_cat": "stat.ML",
+        "cats": [
+            "stat.ML",
+            "cs.LG"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/1906.02405v1",
+        "title": "Indirect interactions influence contact network structure and diffusion dynamics",
+        "abstract": "Interaction patterns at the individual level influence the behaviour of\ndiffusion over contact networks. Most of the current diffusion models only\nconsider direct interactions among individuals to build underlying infectious\nitems transmission networks. However, delayed indirect interactions, where a\nsusceptible individual interacts with infectious items after the infected\nindividual has left the interaction space, can also cause transmission events.\nWe define a diffusion model called the same place different time transmission\n(SPDT) based diffusion that considers transmission links for these indirect\ninteractions. Our SPDT model changes the network dynamics where the\nconnectivity among individuals varies with the decay rates of link infectivity.\nWe investigate SPDT diffusion behaviours by simulating airborne disease\nspreading on data-driven contact networks. The SPDT model significantly\nincreases diffusion dynamics (particularly for networks with low link densities\nwhere indirect interactions create new infection pathways) and is capable of\nproducing realistic disease reproduction number. Our results show that the SPDT\nmodel is significantly more likely to lead to outbreaks compared to current\ndiffusion models with direct interactions. We find that the diffusion dynamics\nwith including indirect links are not reproducible by the current models,\nhighlighting the importance of the indirect links for predicting outbreaks.",
+        "authors": "Md Shahzamal, Raja Jurdak, Bernard Mans, Frank de Hoog",
+        "published": "2019-06-06",
+        "updated": "2019-06-06",
+        "primary_cat": "cs.SI",
+        "cats": [
+            "cs.SI",
+            "physics.soc-ph"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/2012.06816v1",
+        "title": "Evaluation and Comparison of Diffusion Models with Motif Features",
+        "abstract": "Diffusion models simulate the propagation of influence in networks. The\ndesign and evaluation of diffusion models has been subjective and empirical.\nWhen being applied to a network represented by a graph, the diffusion model\ngenerates a sequence of edges on which the influence flows, such sequence forms\na temporal network. In most scenarios, the statistical properties or the\ncharacteristics of a network are inferred by analyzing the temporal networks\ngenerated by diffusion models. To analyze real temporal networks, the motif has\nbeen proposed as a reliable feature. However, it is unclear how the network\ntopology and the diffusion model affect the motif feature of a generated\ntemporal network. In this paper, we adopt the motif feature to evaluate the\ntemporal graph generated by a diffusion model, thence the diffusion model\nitself. Two benchmarks for quantitively evaluating diffusion models with motif,\nstability and separability, are proposed and measured on numerous diffusion\nmodels. One motif-based metric is proposed to measure the similarity between\ndiffusion models. The experiments suggest that the motif of a generated\ntemporal network is dominated by the diffusion model, while the network\ntopology is almost ignored. This result indicates that more practical and\nreliable diffusion models have to be designed with delicacy in order to capture\nthe propagation patterns of real temporal networks.",
+        "authors": "Fangqi Li",
+        "published": "2020-12-12",
+        "updated": "2020-12-12",
+        "primary_cat": "cs.SI",
+        "cats": [
+            "cs.SI",
+            "cs.NI"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/2401.06046v2",
+        "title": "Quantifying the contributions to diffusion in complex materials",
+        "abstract": "Using machine learning with a variational formula for diffusivity, we recast\ndiffusion as a sum of individual contributions to diffusion--called\n\"kinosons\"--and compute their statistical distribution to model a complex\nmulticomponent alloy. Calculating kinosons is orders of magnitude more\nefficient than computing whole trajectories, and elucidates kinetic mechanisms\nfor diffusion. The distribution of kinosons with temperature leads to new\naccurate analytic models for macroscale diffusivity. This combination of\nmachine learning with diffusion theory promises insight into other complex\nmaterials.",
+        "authors": "Soham Chattopadhyay, Dallas R. Trinkle",
+        "published": "2024-01-11",
+        "updated": "2024-03-14",
+        "primary_cat": "cond-mat.mtrl-sci",
+        "cats": [
+            "cond-mat.mtrl-sci"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/1404.3573v1",
+        "title": "\"Diffusing diffusivity\": A model for anomalous and \"anomalous yet Brownian\" diffusion",
+        "abstract": "Wang et al. [PNAS 106 (2009) 15160] have found that in several systems the\nlinear time dependence of the mean-square displacement (MSD) of diffusing\ncolloidal particles, typical of normal diffusion, is accompanied by a\nnon-Gaussian displacement distribution (DisD), with roughly exponential tails\nat short times, a situation they termed \"anomalous yet Brownian\" diffusion. The\ndiversity of systems in which this is observed calls for a generic model. We\npresent such a model where there is \"diffusivity memory\" but no \"direction\nmemory\" in the particle trajectory, and we show that it leads to both a linear\nMSD and a non-Gaussian DisD at short times. In our model, the diffusivity is\nundergoing a (perhaps biased) random walk, hence the expression \"diffusing\ndiffusivity\". The DisD is predicted to be exactly exponential at short times if\nthe distribution of diffusivities is itself exponential, but an exponential\nremains a good fit to the DisD for a variety of diffusivity distributions.\nMoreover, our generic model can be modified to produce subdiffusion.",
+        "authors": "Mykyta V. Chubynsky, Gary W. Slater",
+        "published": "2014-04-14",
+        "updated": "2014-04-14",
+        "primary_cat": "cond-mat.stat-mech",
+        "cats": [
+            "cond-mat.stat-mech",
+            "cond-mat.soft"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/2211.07804v3",
+        "title": "Diffusion Models for Medical Image Analysis: A Comprehensive Survey",
+        "abstract": "Denoising diffusion models, a class of generative models, have garnered\nimmense interest lately in various deep-learning problems. A diffusion\nprobabilistic model defines a forward diffusion stage where the input data is\ngradually perturbed over several steps by adding Gaussian noise and then learns\nto reverse the diffusion process to retrieve the desired noise-free data from\nnoisy data samples. Diffusion models are widely appreciated for their strong\nmode coverage and quality of the generated samples despite their known\ncomputational burdens. Capitalizing on the advances in computer vision, the\nfield of medical imaging has also observed a growing interest in diffusion\nmodels. To help the researcher navigate this profusion, this survey intends to\nprovide a comprehensive overview of diffusion models in the discipline of\nmedical image analysis. Specifically, we introduce the solid theoretical\nfoundation and fundamental concepts behind diffusion models and the three\ngeneric diffusion modelling frameworks: diffusion probabilistic models,\nnoise-conditioned score networks, and stochastic differential equations. Then,\nwe provide a systematic taxonomy of diffusion models in the medical domain and\npropose a multi-perspective categorization based on their application, imaging\nmodality, organ of interest, and algorithms. To this end, we cover extensive\napplications of diffusion models in the medical domain. Furthermore, we\nemphasize the practical use case of some selected approaches, and then we\ndiscuss the limitations of the diffusion models in the medical domain and\npropose several directions to fulfill the demands of this field. Finally, we\ngather the overviewed studies with their available open-source implementations\nat\nhttps://github.com/amirhossein-kz/Awesome-Diffusion-Models-in-Medical-Imaging.",
+        "authors": "Amirhossein Kazerouni, Ehsan Khodapanah Aghdam, Moein Heidari, Reza Azad, Mohsen Fayyaz, Ilker Hacihaliloglu, Dorit Merhof",
+        "published": "2022-11-14",
+        "updated": "2023-06-03",
+        "primary_cat": "eess.IV",
+        "cats": [
+            "eess.IV",
+            "cs.CV"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/2312.04410v1",
+        "title": "Smooth Diffusion: Crafting Smooth Latent Spaces in Diffusion Models",
+        "abstract": "Recently, diffusion models have made remarkable progress in text-to-image\n(T2I) generation, synthesizing images with high fidelity and diverse contents.\nDespite this advancement, latent space smoothness within diffusion models\nremains largely unexplored. Smooth latent spaces ensure that a perturbation on\nan input latent corresponds to a steady change in the output image. This\nproperty proves beneficial in downstream tasks, including image interpolation,\ninversion, and editing. In this work, we expose the non-smoothness of diffusion\nlatent spaces by observing noticeable visual fluctuations resulting from minor\nlatent variations. To tackle this issue, we propose Smooth Diffusion, a new\ncategory of diffusion models that can be simultaneously high-performing and\nsmooth. Specifically, we introduce Step-wise Variation Regularization to\nenforce the proportion between the variations of an arbitrary input latent and\nthat of the output image is a constant at any diffusion training step. In\naddition, we devise an interpolation standard deviation (ISTD) metric to\neffectively assess the latent space smoothness of a diffusion model. Extensive\nquantitative and qualitative experiments demonstrate that Smooth Diffusion\nstands out as a more desirable solution not only in T2I generation but also\nacross various downstream tasks. Smooth Diffusion is implemented as a\nplug-and-play Smooth-LoRA to work with various community models. Code is\navailable at https://github.com/SHI-Labs/Smooth-Diffusion.",
+        "authors": "Jiayi Guo, Xingqian Xu, Yifan Pu, Zanlin Ni, Chaofei Wang, Manushree Vasu, Shiji Song, Gao Huang, Humphrey Shi",
+        "published": "2023-12-07",
+        "updated": "2023-12-07",
+        "primary_cat": "cs.CV",
+        "cats": [
+            "cs.CV"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/2210.05559v2",
+        "title": "Unifying Diffusion Models' Latent Space, with Applications to CycleDiffusion and Guidance",
+        "abstract": "Diffusion models have achieved unprecedented performance in generative\nmodeling. The commonly-adopted formulation of the latent code of diffusion\nmodels is a sequence of gradually denoised samples, as opposed to the simpler\n(e.g., Gaussian) latent space of GANs, VAEs, and normalizing flows. This paper\nprovides an alternative, Gaussian formulation of the latent space of various\ndiffusion models, as well as an invertible DPM-Encoder that maps images into\nthe latent space. While our formulation is purely based on the definition of\ndiffusion models, we demonstrate several intriguing consequences. (1)\nEmpirically, we observe that a common latent space emerges from two diffusion\nmodels trained independently on related domains. In light of this finding, we\npropose CycleDiffusion, which uses DPM-Encoder for unpaired image-to-image\ntranslation. Furthermore, applying CycleDiffusion to text-to-image diffusion\nmodels, we show that large-scale text-to-image diffusion models can be used as\nzero-shot image-to-image editors. (2) One can guide pre-trained diffusion\nmodels and GANs by controlling the latent codes in a unified, plug-and-play\nformulation based on energy-based models. Using the CLIP model and a face\nrecognition model as guidance, we demonstrate that diffusion models have better\ncoverage of low-density sub-populations and individuals than GANs. The code is\npublicly available at https://github.com/ChenWu98/cycle-diffusion.",
+        "authors": "Chen Henry Wu, Fernando De la Torre",
+        "published": "2022-10-11",
+        "updated": "2022-12-07",
+        "primary_cat": "cs.CV",
+        "cats": [
+            "cs.CV",
+            "cs.GR",
+            "cs.LG"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/2210.07677v1",
+        "title": "TransFusion: Transcribing Speech with Multinomial Diffusion",
+        "abstract": "Diffusion models have shown exceptional scaling properties in the image\nsynthesis domain, and initial attempts have shown similar benefits for applying\ndiffusion to unconditional text synthesis. Denoising diffusion models attempt\nto iteratively refine a sampled noise signal until it resembles a coherent\nsignal (such as an image or written sentence). In this work we aim to see\nwhether the benefits of diffusion models can also be realized for speech\nrecognition. To this end, we propose a new way to perform speech recognition\nusing a diffusion model conditioned on pretrained speech features.\nSpecifically, we propose TransFusion: a transcribing diffusion model which\niteratively denoises a random character sequence into coherent text\ncorresponding to the transcript of a conditioning utterance. We demonstrate\ncomparable performance to existing high-performing contrastive models on the\nLibriSpeech speech recognition benchmark. To the best of our knowledge, we are\nthe first to apply denoising diffusion to speech recognition. We also propose\nnew techniques for effectively sampling and decoding multinomial diffusion\nmodels. These are required because traditional methods of sampling from\nacoustic models are not possible with our new discrete diffusion approach. Code\nand trained models are available: https://github.com/RF5/transfusion-asr",
+        "authors": "Matthew Baas, Kevin Eloff, Herman Kamper",
+        "published": "2022-10-14",
+        "updated": "2022-10-14",
+        "primary_cat": "eess.AS",
+        "cats": [
+            "eess.AS",
+            "cs.AI",
+            "cs.SD"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/2006.00003v1",
+        "title": "Coupling particle-based reaction-diffusion simulations with reservoirs mediated by reaction-diffusion PDEs",
+        "abstract": "Open biochemical systems of interacting molecules are ubiquitous in\nlife-related processes. However, established computational methodologies, like\nmolecular dynamics, are still mostly constrained to closed systems and\ntimescales too small to be relevant for life processes. Alternatively,\nparticle-based reaction-diffusion models are currently the most accurate and\ncomputationally feasible approach at these scales. Their efficiency lies in\nmodeling entire molecules as particles that can diffuse and interact with each\nother. In this work, we develop modeling and numerical schemes for\nparticle-based reaction-diffusion in an open setting, where the reservoirs are\nmediated by reaction-diffusion PDEs. We derive two important theoretical\nresults. The first one is the mean-field for open systems of diffusing\nparticles; the second one is the mean-field for a particle-based\nreaction-diffusion system with second-order reactions. We employ these two\nresults to develop a numerical scheme that consistently couples particle-based\nreaction-diffusion processes with reaction-diffusion PDEs. This allows modeling\nopen biochemical systems in contact with reservoirs that are time-dependent and\nspatially inhomogeneous, as in many relevant real-world applications.",
+        "authors": "Margarita Kostr\u00e9, Christof Sch\u00fctte, Frank No\u00e9, Mauricio J. del Razo",
+        "published": "2020-05-29",
+        "updated": "2020-05-29",
+        "primary_cat": "q-bio.QM",
+        "cats": [
+            "q-bio.QM",
+            "physics.chem-ph",
+            "physics.comp-ph",
+            "92C40, 92C45, 60J70, 60Gxx, 70Lxx"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/2306.03436v2",
+        "title": "Intellectual Property Protection of Diffusion Models via the Watermark Diffusion Process",
+        "abstract": "Diffusion models have rapidly become a vital part of deep generative\narchitectures, given today's increasing demands. Obtaining large,\nhigh-performance diffusion models demands significant resources, highlighting\ntheir importance as intellectual property worth protecting. However, existing\nwatermarking techniques for ownership verification are insufficient when\napplied to diffusion models. Very recent research in watermarking diffusion\nmodels either exposes watermarks during task generation, which harms the\nimperceptibility, or is developed for conditional diffusion models that require\nprompts to trigger the watermark. This paper introduces WDM, a novel\nwatermarking solution for diffusion models without imprinting the watermark\nduring task generation. It involves training a model to concurrently learn a\nWatermark Diffusion Process (WDP) for embedding watermarks alongside the\nstandard diffusion process for task generation. We provide a detailed\ntheoretical analysis of WDP training and sampling, relating it to a shifted\nGaussian diffusion process via the same reverse noise. Extensive experiments\nare conducted to validate the effectiveness and robustness of our approach in\nvarious trigger and watermark data configurations.",
+        "authors": "Sen Peng, Yufei Chen, Cong Wang, Xiaohua Jia",
+        "published": "2023-06-06",
+        "updated": "2023-11-29",
+        "primary_cat": "cs.CR",
+        "cats": [
+            "cs.CR",
+            "cs.LG"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/1906.02856v1",
+        "title": "Diffusion on dynamic contact networks with indirect transmission links",
+        "abstract": "Modelling diffusion processes on dynamic contact networks is an important\nresearch area for epidemiology, marketing, cybersecurity, and ecology. However,\ncurrent diffusion models cannot capture transmissions occurring for indirect\ninteractions. For example, an airborne infected individual releases infectious\nparticles at locations that can suspend in the air and infect susceptible\nindividuals arriving even after the infected individual left. Thus, current\ndiffusion models miss transmissions during indirect interactions. In this\nthesis, a novel diffusion model called the same place different time\ntransmission based diffusion (SPDT) is introduced to take into account the\ntransmissions through indirect interactions. The behaviour of SPDT diffusion is\nanalysed on real dynamic contact networks and a significant amplification in\ndiffusion dynamics is observed. The SPDT model also introduces some novel\nbehaviours different from current diffusion models. In this work, a new SPDT\ngraph model is also developed to generate synthetic traces to explore SPDT\ndiffusion in several scenarios. The analysis shows that the emergence of new\ndiffusion becomes common thanks to the inclusion of indirect transmissions\nwithin the SPDT model. This work finally investigates how diffusion can be\ncontrolled and develops new methods to hinder diffusion.",
+        "authors": "Md Shahzamal",
+        "published": "2019-06-07",
+        "updated": "2019-06-07",
+        "primary_cat": "cs.SI",
+        "cats": [
+            "cs.SI",
+            "physics.soc-ph"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/2303.09295v1",
+        "title": "DIRE for Diffusion-Generated Image Detection",
+        "abstract": "Diffusion models have shown remarkable success in visual synthesis, but have\nalso raised concerns about potential abuse for malicious purposes. In this\npaper, we seek to build a detector for telling apart real images from\ndiffusion-generated images. We find that existing detectors struggle to detect\nimages generated by diffusion models, even if we include generated images from\na specific diffusion model in their training data. To address this issue, we\npropose a novel image representation called DIffusion Reconstruction Error\n(DIRE), which measures the error between an input image and its reconstruction\ncounterpart by a pre-trained diffusion model. We observe that\ndiffusion-generated images can be approximately reconstructed by a diffusion\nmodel while real images cannot. It provides a hint that DIRE can serve as a\nbridge to distinguish generated and real images. DIRE provides an effective way\nto detect images generated by most diffusion models, and it is general for\ndetecting generated images from unseen diffusion models and robust to various\nperturbations. Furthermore, we establish a comprehensive diffusion-generated\nbenchmark including images generated by eight diffusion models to evaluate the\nperformance of diffusion-generated image detectors. Extensive experiments on\nour collected benchmark demonstrate that DIRE exhibits superiority over\nprevious generated-image detectors. The code and dataset are available at\nhttps://github.com/ZhendongWang6/DIRE.",
+        "authors": "Zhendong Wang, Jianmin Bao, Wengang Zhou, Weilun Wang, Hezhen Hu, Hong Chen, Houqiang Li",
+        "published": "2023-03-16",
+        "updated": "2023-03-16",
+        "primary_cat": "cs.CV",
+        "cats": [
+            "cs.CV"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/1701.00257v2",
+        "title": "Analyzing PFG anisotropic anomalous diffusions by instantaneous signal attenuation method",
+        "abstract": "Anomalous diffusion has been investigated in many systems. Pulsed field\ngradient (PFG) anomalous diffusion is much more complicated than PFG normal\ndiffusion. There have been many theoretical and experimental studies for PFG\nisotropic anomalous diffusion, but there are very few theoretical treatments\nreported for anisotropic anomalous diffusion. Currently, there is not a general\nPFG signal attenuation expression, which includes the finite gradient pulse\neffect and can treat all three types of anisotropic fractional diffusions:\ngeneral fractional diffusion, time fractional diffusion, and space-fractional\ndiffusion. In this paper, the recently developed instantaneous signal\nattenuation (ISA) method was applied to obtain PFG signal attenuation\nexpression for free and restricted anisotropic anomalous diffusion with two\nmodels: fractal derivative and fractional derivative models. The obtained PFG\nsignal attenuation expression for anisotropic anomalous diffusion can reduce to\nthe reported result for PFG anisotropic normal diffusion. The results can also\nreduce to reported PFG isotropic anomalous diffusion results obtained by\neffective phase shift diffusion equation method and instantaneous signal\nattenuation method. For anisotropic space-fractional diffusion, the obtained\nresult agrees with that obtained by the modified Bloch equation method.\nAdditionally, The PFG signal attenuation expressions for free and restricted\nanisotropic curvilinear diffusions were derived by the traditional method, the\nresults of which agree with the PFG anisotropic fractional diffusion results\nbased on the fractional derivative model. The powder pattern of PFG anisotropic\ndiffusion was also discussed. The results here improve our understanding of PFG\nanomalous diffusion, and provide new formalisms for PFG anisotropic anomalous\ndiffusion in NMR and MRI.",
+        "authors": "Guoxing Lin",
+        "published": "2017-01-01",
+        "updated": "2017-01-05",
+        "primary_cat": "physics.chem-ph",
+        "cats": [
+            "physics.chem-ph"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/2005.00562v1",
+        "title": "Unexpected crossovers in correlated random-diffusivity processes",
+        "abstract": "The passive and active motion of micron-sized tracer particles in crowded\nliquids and inside living biological cells is ubiquitously characterised by\n\"viscoelastic\" anomalous diffusion, in which the increments of the motion\nfeature long-ranged negative and positive correlations. While viscoelastic\nanomalous diffusion is typically modelled by a Gaussian process with correlated\nincrements, so-called fractional Gaussian noise, an increasing number of\nsystems are reported, in which viscoelastic anomalous diffusion is paired with\nnon-Gaussian displacement distributions. Following recent advances in Brownian\nyet non-Gaussian diffusion we here introduce and discuss several possible\nversions of random-diffusivity models with long-ranged correlations. While all\nthese models show a crossover from non-Gaussian to Gaussian distributions\nbeyond some correlation time, their mean squared displacements exhibit\nstrikingly different behaviours: depending on the model crossovers from\nanomalous to normal diffusion are observed, as well as unexpected dependencies\nof the effective diffusion coefficient on the correlation exponent. Our\nobservations of the strong non-universality of random-diffusivity viscoelastic\nanomalous diffusion are important for the analysis of experiments and a better\nunderstanding of the physical origins of \"viscoelastic yet non-Gaussian\"\ndiffusion.",
+        "authors": "Wei Wang, Flavio Seno, Igor M. Sokolov, Aleksei V. Chechkin, Ralf Metzler",
+        "published": "2020-05-01",
+        "updated": "2020-05-01",
+        "primary_cat": "cond-mat.stat-mech",
+        "cats": [
+            "cond-mat.stat-mech",
+            "physics.bio-ph"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/2209.05557v3",
+        "title": "Blurring Diffusion Models",
+        "abstract": "Recently, Rissanen et al., (2022) have presented a new type of diffusion\nprocess for generative modeling based on heat dissipation, or blurring, as an\nalternative to isotropic Gaussian diffusion. Here, we show that blurring can\nequivalently be defined through a Gaussian diffusion process with non-isotropic\nnoise. In making this connection, we bridge the gap between inverse heat\ndissipation and denoising diffusion, and we shed light on the inductive bias\nthat results from this modeling choice. Finally, we propose a generalized class\nof diffusion models that offers the best of both standard Gaussian denoising\ndiffusion and inverse heat dissipation, which we call Blurring Diffusion\nModels.",
+        "authors": "Emiel Hoogeboom, Tim Salimans",
+        "published": "2022-09-12",
+        "updated": "2024-05-01",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG",
+            "cs.CV",
+            "stat.ML"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/2301.00527v1",
+        "title": "Diffusion Probabilistic Models for Scene-Scale 3D Categorical Data",
+        "abstract": "In this paper, we learn a diffusion model to generate 3D data on a\nscene-scale. Specifically, our model crafts a 3D scene consisting of multiple\nobjects, while recent diffusion research has focused on a single object. To\nrealize our goal, we represent a scene with discrete class labels, i.e.,\ncategorical distribution, to assign multiple objects into semantic categories.\nThus, we extend discrete diffusion models to learn scene-scale categorical\ndistributions. In addition, we validate that a latent diffusion model can\nreduce computation costs for training and deploying. To the best of our\nknowledge, our work is the first to apply discrete and latent diffusion for 3D\ncategorical data on a scene-scale. We further propose to perform semantic scene\ncompletion (SSC) by learning a conditional distribution using our diffusion\nmodel, where the condition is a partial observation in a sparse point cloud. In\nexperiments, we empirically show that our diffusion models not only generate\nreasonable scenes, but also perform the scene completion task better than a\ndiscriminative model. Our code and models are available at\nhttps://github.com/zoomin-lee/scene-scale-diffusion",
+        "authors": "Jumin Lee, Woobin Im, Sebin Lee, Sung-Eui Yoon",
+        "published": "2023-01-02",
+        "updated": "2023-01-02",
+        "primary_cat": "cs.CV",
+        "cats": [
+            "cs.CV"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/2305.08379v2",
+        "title": "TESS: Text-to-Text Self-Conditioned Simplex Diffusion",
+        "abstract": "Diffusion models have emerged as a powerful paradigm for generation,\nobtaining strong performance in various continuous domains. However, applying\ncontinuous diffusion models to natural language remains challenging due to its\ndiscrete nature and the need for a large number of diffusion steps to generate\ntext, making diffusion-based generation expensive. In this work, we propose\nText-to-text Self-conditioned Simplex Diffusion (TESS), a text diffusion model\nthat is fully non-autoregressive, employs a new form of self-conditioning, and\napplies the diffusion process on the logit simplex space rather than the\nlearned embedding space. Through extensive experiments on natural language\nunderstanding and generation tasks including summarization, text\nsimplification, paraphrase generation, and question generation, we demonstrate\nthat TESS outperforms state-of-the-art non-autoregressive models, requires\nfewer diffusion steps with minimal drop in performance, and is competitive with\npretrained autoregressive sequence-to-sequence models. We publicly release our\ncodebase at https://github.com/allenai/tess-diffusion.",
+        "authors": "Rabeeh Karimi Mahabadi, Hamish Ivison, Jaesung Tae, James Henderson, Iz Beltagy, Matthew E. Peters, Arman Cohan",
+        "published": "2023-05-15",
+        "updated": "2024-02-21",
+        "primary_cat": "cs.CL",
+        "cats": [
+            "cs.CL",
+            "cs.LG"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/2307.13949v1",
+        "title": "How Does Diffusion Influence Pretrained Language Models on Out-of-Distribution Data?",
+        "abstract": "Transformer-based pretrained language models (PLMs) have achieved great\nsuccess in modern NLP. An important advantage of PLMs is good\nout-of-distribution (OOD) robustness. Recently, diffusion models have attracted\na lot of work to apply diffusion to PLMs. It remains under-explored how\ndiffusion influences PLMs on OOD data. The core of diffusion models is a\nforward diffusion process which gradually applies Gaussian noise to inputs, and\na reverse denoising process which removes noise. The noised input\nreconstruction is a fundamental ability of diffusion models. We directly\nanalyze OOD robustness by measuring the reconstruction loss, including testing\nthe abilities to reconstruct OOD data, and to detect OOD samples. Experiments\nare conducted by analyzing different training parameters and data statistical\nfeatures on eight datasets. It shows that finetuning PLMs with diffusion\ndegrades the reconstruction ability on OOD data. The comparison also shows that\ndiffusion models can effectively detect OOD samples, achieving state-of-the-art\nperformance in most of the datasets with an absolute accuracy improvement up to\n18%. These results indicate that diffusion reduces OOD robustness of PLMs.",
+        "authors": "Huazheng Wang, Daixuan Cheng, Haifeng Sun, Jingyu Wang, Qi Qi, Jianxin Liao, Jing Wang, Cong Liu",
+        "published": "2023-07-26",
+        "updated": "2023-07-26",
+        "primary_cat": "cs.CL",
+        "cats": [
+            "cs.CL",
+            "cs.AI"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/1603.05605v1",
+        "title": "Multiscale modeling of diffusion in a crowded environment",
+        "abstract": "We present a multiscale approach to model diffusion in a crowded environment\nand its effect on the reaction rates. Diffusion in biological systems is often\nmodeled by a discrete space jump process in order to capture the inherent noise\nof biological systems, which becomes important in the low copy number regime.\nTo model diffusion in the crowded cell environment efficiently, we compute the\njump rates in this mesoscopic model from local first exit times, which account\nfor the microscopic positions of the crowding molecules, while the diffusing\nmolecules jump on a coarser Cartesian grid. We then extract a macroscopic\ndescription from the resulting jump rates, where the excluded volume effect is\nmodeled by a diffusion equation with space dependent diffusion coefficient. The\ncrowding molecules can be of arbitrary shape and size and numerical experiments\ndemonstrate that those factors together with the size of the diffusing molecule\nplay a crucial role on the magnitude of the decrease in diffusive motion. When\ncorrecting the reaction rates for the altered diffusion we can show that\nmolecular crowding either enhances or inhibits chemical reactions depending on\nlocal fluctuations of the obstacle density.",
+        "authors": "Lina Meinecke",
+        "published": "2016-03-12",
+        "updated": "2016-03-12",
+        "primary_cat": "q-bio.SC",
+        "cats": [
+            "q-bio.SC",
+            "math.NA",
+            "92-08"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/2305.16269v1",
+        "title": "UDPM: Upsampling Diffusion Probabilistic Models",
+        "abstract": "In recent years, Denoising Diffusion Probabilistic Models (DDPM) have caught\nsignificant attention. By composing a Markovian process that starts in the data\ndomain and then gradually adds noise until reaching pure white noise, they\nachieve superior performance in learning data distributions. Yet, these models\nrequire a large number of diffusion steps to produce aesthetically pleasing\nsamples, which is inefficient. In addition, unlike common generative\nadversarial networks, the latent space of diffusion models is not\ninterpretable. In this work, we propose to generalize the denoising diffusion\nprocess into an Upsampling Diffusion Probabilistic Model (UDPM), in which we\nreduce the latent variable dimension in addition to the traditional noise level\naddition. As a result, we are able to sample images of size $256\\times 256$\nwith only 7 diffusion steps, which is less than two orders of magnitude\ncompared to standard DDPMs. We formally develop the Markovian diffusion\nprocesses of the UDPM, and demonstrate its generation capabilities on the\npopular FFHQ, LSUN horses, ImageNet, and AFHQv2 datasets. Another favorable\nproperty of UDPM is that it is very easy to interpolate its latent space, which\nis not the case with standard diffusion models. Our code is available online\n\\url{https://github.com/shadyabh/UDPM}",
+        "authors": "Shady Abu-Hussein, Raja Giryes",
+        "published": "2023-05-25",
+        "updated": "2023-05-25",
+        "primary_cat": "cs.CV",
+        "cats": [
+            "cs.CV",
+            "cs.LG",
+            "eess.IV"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/0801.3436v1",
+        "title": "Model for Diffusion-Induced Ramsey Narrowing",
+        "abstract": "Diffusion-induced Ramsey narrowing that appears when atoms can leave the\ninteraction region and repeatedly return without lost of coherence is\ninvestigated using strong collisions approximation. The effective diffusion\nequation is obtained and solved for low-dimensional model configurations and\nthree-dimensional real one.",
+        "authors": "Alexander Romanenko, Leonid Yatsenko",
+        "published": "2008-01-22",
+        "updated": "2008-01-22",
+        "primary_cat": "quant-ph",
+        "cats": [
+            "quant-ph"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/1609.04658v1",
+        "title": "Analyzing Signal Attenuation in PFG Anomalous Diffusion via a Modified Gaussian Phase Distribution Approximation Based on Fractal Derivative Model",
+        "abstract": "Pulsed field gradient (PFG) has been increasingly employed to study anomalous\ndiffusions in Nuclear Magnetic Resonance (NMR) and Magnetic Resonance Imaging\n(MRI). However, the analysis of PFG anomalous diffusion is complicated. In this\npaper, a fractal derivative model based modified Gaussian phase distribution\nmethod is proposed to describe PFG anomalous diffusion. By using the phase\ndistribution obtained from the effective phase shift diffusion method based on\nfractal derivatives, and employing some of the traditional Gaussian phase\ndistribution approximation techniques, a general signal attenuation expression\nfor free fractional diffusion is derived. This expression describes a stretched\nexponential function based attenuation, which is distinct from both the\nexponential attenuation for normal diffusion obtained from conventional\nGaussian phase distribution approximation, and the Mittag-Leffler function\nbased attenuation for anomalous diffusion obtained from fractional derivative.\nThe obtained signal attenuation expression can analyze the finite gradient\npulse width (FGPW) effect. Additionally, it can generally be applied to all\nthree types of PFG fractional diffusions classified based on time derivative\norder alpha and space derivative order beta. These three types of fractional\ndiffusions include time-fractional diffusion, space-fractional diffusion, and\ngeneral fractional diffusion. The results in this paper are consistent with\nreported results based on effective phase shift diffusion equation method and\ninstantaneous signal attenuation method. This method provides a new, convenient\napproximation formalism for analyzing PFG anomalous diffusion experiments.",
+        "authors": "Guoxing Lin",
+        "published": "2016-09-15",
+        "updated": "2016-09-15",
+        "primary_cat": "physics.chem-ph",
+        "cats": [
+            "physics.chem-ph"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/2305.13122v1",
+        "title": "Policy Representation via Diffusion Probability Model for Reinforcement Learning",
+        "abstract": "Popular reinforcement learning (RL) algorithms tend to produce a unimodal\npolicy distribution, which weakens the expressiveness of complicated policy and\ndecays the ability of exploration. The diffusion probability model is powerful\nto learn complicated multimodal distributions, which has shown promising and\npotential applications to RL. In this paper, we formally build a theoretical\nfoundation of policy representation via the diffusion probability model and\nprovide practical implementations of diffusion policy for online model-free RL.\nConcretely, we character diffusion policy as a stochastic process, which is a\nnew approach to representing a policy. Then we present a convergence guarantee\nfor diffusion policy, which provides a theory to understand the multimodality\nof diffusion policy. Furthermore, we propose the DIPO which is an\nimplementation for model-free online RL with DIffusion POlicy. To the best of\nour knowledge, DIPO is the first algorithm to solve model-free online RL\nproblems with the diffusion model. Finally, extensive empirical results show\nthe effectiveness and superiority of DIPO on the standard continuous control\nMujoco benchmark.",
+        "authors": "Long Yang, Zhixiong Huang, Fenghao Lei, Yucun Zhong, Yiming Yang, Cong Fang, Shiting Wen, Binbin Zhou, Zhouchen Lin",
+        "published": "2023-05-22",
+        "updated": "2023-05-22",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/astro-ph/0012545v1",
+        "title": "Diffusion and the occurrence of hydrogen shell flashes in helium white dwarf stars",
+        "abstract": "We investigate the effects of element diffusion on the structure and\nevolution of low-mass helium white dwarfs (WD). Attention is focused on the\noccurrence of hydrogen shell flashes induced by diffusion processes during\ncooling phases. Initial models from 0.406 to 0.161 solar masses are constructed\nby applying mass loss rates at different stages of the RGB evolution of a solar\nmodel. The multicomponent flow equations describing gravitational settling, and\nchemical and thermal diffusion are solved and the diffusion calculations are\ncoupled to an evolutionary code. In addition, the same sequences are computed\nbut neglecting diffusion. We find that element diffusion strongly affects the\nstructure and cooling history of helium WD. In particular, diffusion induces\nthe occurrence of hydrogen shell flashes in models with masses ranging from\n0.18 to 0.41 solar masses, which is in sharp contrast from the situation when\ndiffusion is neglected. In connection with the further evolution, these\ndiffusion-induced flashes lead to much thinner hydrogen envelopes, preventing\nstable nuclear burning from being an appreciable energy source at advanced\nstages of evolution. This implies much shorter cooling ages than in the case\nwhen diffusion is neglected. These new WD models are discussed in light of\nrecent observational data of some millisecond pulsar systems with WD\ncompanions. We find that age discrepancies between the predictions of standard\nevolutionary models and such observations appear to be the result of ignoring\nelement diffusion in such models. Indeed, such discrepancies vanish when\naccount is made of diffusion.",
+        "authors": "L. G. Althaus, A. M. Serenelli, O. G. Benvenuto",
+        "published": "2000-12-29",
+        "updated": "2000-12-29",
+        "primary_cat": "astro-ph",
+        "cats": [
+            "astro-ph"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/1812.07249v1",
+        "title": "A unifying approach to first-passage time distributions in diffusing diffusivity and switching diffusion models",
+        "abstract": "We propose a unifying theoretical framework for the analysis of first-passage\ntime distributions in two important classes of stochastic processes in which\nthe diffusivity of a particle evolves randomly in time. In the first class of\n\"diffusing diffusivity\" models, the diffusivity changes continuously via a\nprescribed stochastic equation. In turn, the diffusivity switches randomly\nbetween discrete values in the second class of \"switching diffusion\" models.\nFor both cases, we quantify the impact of the diffusivity dynamics onto the\nfirst-passage time distribution of a particle via the moment-generating\nfunction of the integrated diffusivity. We provide general formulas and some\nexplicit solutions for some particular cases of practical interest.",
+        "authors": "D. S. Grebenkov",
+        "published": "2018-12-18",
+        "updated": "2018-12-18",
+        "primary_cat": "cond-mat.stat-mech",
+        "cats": [
+            "cond-mat.stat-mech",
+            "physics.bio-ph",
+            "physics.chem-ph"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/2302.07261v2",
+        "title": "Where to Diffuse, How to Diffuse, and How to Get Back: Automated Learning for Multivariate Diffusions",
+        "abstract": "Diffusion-based generative models (DBGMs) perturb data to a target noise\ndistribution and reverse this process to generate samples. The choice of\nnoising process, or inference diffusion process, affects both likelihoods and\nsample quality. For example, extending the inference process with auxiliary\nvariables leads to improved sample quality. While there are many such\nmultivariate diffusions to explore, each new one requires significant\nmodel-specific analysis, hindering rapid prototyping and evaluation. In this\nwork, we study Multivariate Diffusion Models (MDMs). For any number of\nauxiliary variables, we provide a recipe for maximizing a lower-bound on the\nMDMs likelihood without requiring any model-specific analysis. We then\ndemonstrate how to parameterize the diffusion for a specified target noise\ndistribution; these two points together enable optimizing the inference\ndiffusion process. Optimizing the diffusion expands easy experimentation from\njust a few well-known processes to an automatic search over all linear\ndiffusions. To demonstrate these ideas, we introduce two new specific\ndiffusions as well as learn a diffusion process on the MNIST, CIFAR10, and\nImageNet32 datasets. We show learned MDMs match or surpass bits-per-dims (BPDs)\nrelative to fixed choices of diffusions for a given dataset and model\narchitecture.",
+        "authors": "Raghav Singhal, Mark Goldstein, Rajesh Ranganath",
+        "published": "2023-02-14",
+        "updated": "2023-03-03",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG",
+            "stat.ML"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/1308.3393v2",
+        "title": "Cosmology with matter diffusion",
+        "abstract": "We construct a viable cosmological model based on velocity diffusion of\nmatter particles. In order to ensure the conservation of the total\nenergy-momentum tensor in the presence of diffusion, we include a cosmological\nscalar field $\\phi$ which we identify with the dark energy component of the\nUniverse. The model is characterized by only one new degree of freedom, the\ndiffusion parameter $\\sigma$. The standard $\\Lambda$CDM model can be recovered\nby setting $\\sigma=0$. If diffusion takes place ($\\sigma >0$) the dynamics of\nthe matter and of the dark energy fields are coupled. We argue that the\nexistence of a diffusion mechanism in the Universe can serve as a theoretical\nmotivation for interacting models. We constrain the background dynamics of the\ndiffusion model with Supernovae, H(z) and BAO data. We also perform a\nperturbative analysis of this model in order to understand structure formation\nin the Universe. We calculate the impact of diffusion both on the CMB spectrum,\nwith particular attention to the integrated Sachs-Wolfe signal, and on the\nmatter power spectrum $P(k)$. The latter analysis places strong constraints on\nthe magnitude of the diffusion mechanism but does not rule out the model.",
+        "authors": "Simone Calogero, Hermano Velten",
+        "published": "2013-08-15",
+        "updated": "2013-10-29",
+        "primary_cat": "astro-ph.CO",
+        "cats": [
+            "astro-ph.CO"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/1907.09989v1",
+        "title": "Rogue Heat and Diffusion Waves",
+        "abstract": "In this paper, we numerically show and discuss the existence and\ncharacteristics of rogue heat and diffusion waves. More specifically, we use\ntwo different nonlinear heat (diffusion) models and show that modulation\ninstability leads to the generation of unexpected and large fluctuations in the\nframe of these models. These fluctuations can be named as rogue heat\n(diffusion) waves. We discuss the properties and statistics of such rogue\nwaves. Our results can find many important applications in many branches such\nas the nonlinear heat transfer, turbulence, financial mathematics, chemical or\nbiological diffusion, nuclear reactions, subsurface water infiltration, and\npore water pressure diffusion modeled in the frame of nonlinear Terzaghi\nconsolidation models, just to name a few.",
+        "authors": "Cihan Bayindir",
+        "published": "2019-07-18",
+        "updated": "2019-07-18",
+        "primary_cat": "nlin.PS",
+        "cats": [
+            "nlin.PS",
+            "physics.flu-dyn"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/1711.09967v2",
+        "title": "CO diffusion and desorption kinetics in CO$_2$ ices",
+        "abstract": "Diffusion of species in icy dust grain mantles is a fundamental process that\nshapes the chemistry of interstellar regions; yet measurements of diffusion in\ninterstellar ice analogs are scarce. Here we present measurements of CO\ndiffusion into CO$_2$ ice at low temperatures (T=11--23~K) using CO$_2$\nlongitudinal optical (LO) phonon modes to monitor the level of mixing of\ninitially layered ices. We model the diffusion kinetics using Fick's second law\nand find the temperature dependent diffusion coefficients are well fit by an\nArrhenius equation giving a diffusion barrier of 300 $\\pm$ 40 K. The low\nbarrier along with the diffusion kinetics through isotopically labeled layers\nsuggest that CO diffuses through CO$_2$ along pore surfaces rather than through\nbulk diffusion. In complementary experiments, we measure the desorption energy\nof CO from CO$_2$ ices deposited at 11-50 K by temperature-programmed\ndesorption (TPD) and find that the desorption barrier ranges from 1240 $\\pm$ 90\nK to 1410 $\\pm$ 70 K depending on the CO$_2$ deposition temperature and\nresultant ice porosity. The measured CO-CO$_2$ desorption barriers demonstrate\nthat CO binds equally well to CO$_2$ and H$_2$O ices when both are compact. The\nCO-CO$_2$ diffusion-desorption barrier ratio ranges from 0.21-0.24 dependent on\nthe binding environment during diffusion. The diffusion-desorption ratio is\nconsistent with the above hypothesis that the observed diffusion is a surface\nprocess and adds to previous experimental evidence on diffusion in water ice\nthat suggests surface diffusion is important to the mobility of molecules\nwithin interstellar ices.",
+        "authors": "Ilsa R. Cooke, Karin I. \u00d6berg, Edith C. Fayolle, Zoe Peeler, Jennifer B. Bergner",
+        "published": "2017-11-27",
+        "updated": "2017-12-18",
+        "primary_cat": "astro-ph.GA",
+        "cats": [
+            "astro-ph.GA"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/2207.09786v1",
+        "title": "Non-Uniform Diffusion Models",
+        "abstract": "Diffusion models have emerged as one of the most promising frameworks for\ndeep generative modeling. In this work, we explore the potential of non-uniform\ndiffusion models. We show that non-uniform diffusion leads to multi-scale\ndiffusion models which have similar structure to this of multi-scale\nnormalizing flows. We experimentally find that in the same or less training\ntime, the multi-scale diffusion model achieves better FID score than the\nstandard uniform diffusion model. More importantly, it generates samples $4.4$\ntimes faster in $128\\times 128$ resolution. The speed-up is expected to be\nhigher in higher resolutions where more scales are used. Moreover, we show that\nnon-uniform diffusion leads to a novel estimator for the conditional score\nfunction which achieves on par performance with the state-of-the-art\nconditional denoising estimator. Our theoretical and experimental findings are\naccompanied by an open source library MSDiff which can facilitate further\nresearch of non-uniform diffusion models.",
+        "authors": "Georgios Batzolis, Jan Stanczuk, Carola-Bibiane Sch\u00f6nlieb, Christian Etmann",
+        "published": "2022-07-20",
+        "updated": "2022-07-20",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/1705.01542v2",
+        "title": "A Spatial Structural Derivative Model for Ultraslow Diffusion",
+        "abstract": "This study investigates the ultraslow diffusion by a spatial structural\nderivative, in which the exponential function exp(x)is selected as the\nstructural function to construct the local structural derivative diffusion\nequation model. The analytical solution of the diffusion equation is a form of\nBiexponential distribution. Its corresponding mean squared displacement is\nnumerically calculated, and increases more slowly than the logarithmic function\nof time. The local structural derivative diffusion equation with the structural\nfunction exp(x)in space is an alternative physical and mathematical modeling\nmodel to characterize a kind of ultraslow diffusion.",
+        "authors": "Wei Xu, Wen Chen, Yingjie Liang, Jose Weberszpil",
+        "published": "2017-05-03",
+        "updated": "2017-06-13",
+        "primary_cat": "cond-mat.stat-mech",
+        "cats": [
+            "cond-mat.stat-mech"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/2403.01742v2",
+        "title": "Diffusion-TS: Interpretable Diffusion for General Time Series Generation",
+        "abstract": "Denoising diffusion probabilistic models (DDPMs) are becoming the leading\nparadigm for generative models. It has recently shown breakthroughs in audio\nsynthesis, time series imputation and forecasting. In this paper, we propose\nDiffusion-TS, a novel diffusion-based framework that generates multivariate\ntime series samples of high quality by using an encoder-decoder transformer\nwith disentangled temporal representations, in which the decomposition\ntechnique guides Diffusion-TS to capture the semantic meaning of time series\nwhile transformers mine detailed sequential information from the noisy model\ninput. Different from existing diffusion-based approaches, we train the model\nto directly reconstruct the sample instead of the noise in each diffusion step,\ncombining a Fourier-based loss term. Diffusion-TS is expected to generate time\nseries satisfying both interpretablity and realness. In addition, it is shown\nthat the proposed Diffusion-TS can be easily extended to conditional generation\ntasks, such as forecasting and imputation, without any model changes. This also\nmotivates us to further explore the performance of Diffusion-TS under irregular\nsettings. Finally, through qualitative and quantitative experiments, results\nshow that Diffusion-TS achieves the state-of-the-art results on various\nrealistic analyses of time series.",
+        "authors": "Xinyu Yuan, Yan Qiao",
+        "published": "2024-03-04",
+        "updated": "2024-03-14",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG",
+            "cs.AI"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/1911.11645v1",
+        "title": "Effects of different discretisations of the Laplacian upon stochastic simulations of reaction-diffusion systems on both static and growing domains",
+        "abstract": "By discretising space into compartments and letting system dynamics be\ngoverned by the reaction-diffusion master equation, it is possible to derive\nand simulate a stochastic model of reaction and diffusion on an arbitrary\ndomain. However, there are many implementation choices involved in this\nprocess, such as the choice of discretisation and method of derivation of the\ndiffusive jump rates, and it is not clear a priori how these affect model\npredictions. To shed light on this issue, in this work we explore how a variety\nof discretisations and method for derivation of the diffusive jump rates affect\nthe outputs of stochastic simulations of reaction-diffusion models, in\nparticular using Turing's model of pattern formation as a key example. We\nconsider both static and uniformly growing domains and demonstrate that, while\nonly minor differences are observed for simple reaction-diffusion systems,\nthere can be vast differences in model predictions for systems that include\ncomplicated reaction kinetics, such as Turing's model of pattern formation. Our\nwork highlights that care must be taken in using the reaction-diffusion master\nequation to make predictions as to the dynamics of stochastic\nreaction-diffusion systems.",
+        "authors": "Bartosz J. Bartmanski, Ruth E. Baker",
+        "published": "2019-11-26",
+        "updated": "2019-11-26",
+        "primary_cat": "physics.comp-ph",
+        "cats": [
+            "physics.comp-ph"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/0907.0417v1",
+        "title": "Microscopic origin of the jump diffusion model",
+        "abstract": "The present paper is aimed at studying the microscopic origin of the jump\ndiffusion. Starting from the $N$-body Liouville equation and making only the\nassumption that molecular reorientation is overdamped, we derive and solve the\nnew (hereafter generalized diffusion) equation. This is the most general\nequation which governs orientational relaxation of an equilibrium molecular\nensemble in the hindered rotation limit and in the long time limit. The\ngeneralized diffusion equation is an extension of the small-angle diffusion\nequation beyond the impact approximation. We establish the conditions under\nwhich the generalized diffusion equation can be identified with the jump\ndiffusion equation, and also discuss the similarities and differences between\nthe two approaches.",
+        "authors": "M. F. Gelin, D. S. Kosov",
+        "published": "2009-07-02",
+        "updated": "2009-07-02",
+        "primary_cat": "cond-mat.stat-mech",
+        "cats": [
+            "cond-mat.stat-mech"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/2312.14589v1",
+        "title": "Non-Denoising Forward-Time Diffusions",
+        "abstract": "The scope of this paper is generative modeling through diffusion processes.\nAn approach falling within this paradigm is the work of Song et al. (2021),\nwhich relies on a time-reversal argument to construct a diffusion process\ntargeting the desired data distribution. We show that the time-reversal\nargument, common to all denoising diffusion probabilistic modeling proposals,\nis not necessary. We obtain diffusion processes targeting the desired data\ndistribution by taking appropriate mixtures of diffusion bridges. The resulting\ntransport is exact by construction, allows for greater flexibility in choosing\nthe dynamics of the underlying diffusion, and can be approximated by means of a\nneural network via novel training objectives. We develop a unifying view of the\ndrift adjustments corresponding to our and to time-reversal approaches and make\nuse of this representation to inspect the inner workings of diffusion-based\ngenerative models. Finally, we leverage on scalable simulation and inference\ntechniques common in spatial statistics to move beyond fully factorial\ndistributions in the underlying diffusion dynamics. The methodological advances\ncontained in this work contribute toward establishing a general framework for\ngenerative modeling based on diffusion processes.",
+        "authors": "Stefano Peluchetti",
+        "published": "2023-12-22",
+        "updated": "2023-12-22",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG",
+            "stat.ML"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/2304.05060v2",
+        "title": "SPIRiT-Diffusion: Self-Consistency Driven Diffusion Model for Accelerated MRI",
+        "abstract": "Diffusion models have emerged as a leading methodology for image generation\nand have proven successful in the realm of magnetic resonance imaging (MRI)\nreconstruction. However, existing reconstruction methods based on diffusion\nmodels are primarily formulated in the image domain, making the reconstruction\nquality susceptible to inaccuracies in coil sensitivity maps (CSMs). k-space\ninterpolation methods can effectively address this issue but conventional\ndiffusion models are not readily applicable in k-space interpolation. To\novercome this challenge, we introduce a novel approach called SPIRiT-Diffusion,\nwhich is a diffusion model for k-space interpolation inspired by the iterative\nself-consistent SPIRiT method. Specifically, we utilize the iterative solver of\nthe self-consistent term (i.e., k-space physical prior) in SPIRiT to formulate\na novel stochastic differential equation (SDE) governing the diffusion process.\nSubsequently, k-space data can be interpolated by executing the diffusion\nprocess. This innovative approach highlights the optimization model's role in\ndesigning the SDE in diffusion models, enabling the diffusion process to align\nclosely with the physics inherent in the optimization model, a concept referred\nto as model-driven diffusion. We evaluated the proposed SPIRiT-Diffusion method\nusing a 3D joint intracranial and carotid vessel wall imaging dataset. The\nresults convincingly demonstrate its superiority over image-domain\nreconstruction methods, achieving high reconstruction quality even at a\nsubstantial acceleration rate of 10.",
+        "authors": "Zhuo-Xu Cui, Chentao Cao, Yue Wang, Sen Jia, Jing Cheng, Xin Liu, Hairong Zheng, Dong Liang, Yanjie Zhu",
+        "published": "2023-04-11",
+        "updated": "2024-04-20",
+        "primary_cat": "cs.CV",
+        "cats": [
+            "cs.CV"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/cond-mat/0210703v1",
+        "title": "Membrane bound protein diffusion viewed by fluorescence recovery after bleaching experiments : models analysis",
+        "abstract": "Diffusion processes in biological membranes are of interest to understand the\nmacromolecular organisation and function of several molecules. Fluorescence\nRecovery After Photobleaching (FRAP) has been widely used as a method to\nanalyse this processes using classical Brownian diffusion model. In the first\npart of this work, the analytical expression of the fluorescence recovery as a\nfunction of time has been established for anomalous diffusion due to long\nwaiting times. Then, experimental fluorescence recoveries recorded in living\ncells on a membrane-bound protein have been analysed using three different\nmodels : normal Brownian diffusion, Brownian diffusion with an immobile\nfraction and anomalous diffusion due to long waiting times.",
+        "authors": "C. Favard, N. Olivi-Tran, J. -L. Meunier",
+        "published": "2002-10-31",
+        "updated": "2002-10-31",
+        "primary_cat": "cond-mat.stat-mech",
+        "cats": [
+            "cond-mat.stat-mech",
+            "physics.bio-ph",
+            "q-bio.BM"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/2307.06272v1",
+        "title": "Exposing the Fake: Effective Diffusion-Generated Images Detection",
+        "abstract": "Image synthesis has seen significant advancements with the advent of\ndiffusion-based generative models like Denoising Diffusion Probabilistic Models\n(DDPM) and text-to-image diffusion models. Despite their efficacy, there is a\ndearth of research dedicated to detecting diffusion-generated images, which\ncould pose potential security and privacy risks. This paper addresses this gap\nby proposing a novel detection method called Stepwise Error for\nDiffusion-generated Image Detection (SeDID). Comprising statistical-based\n$\\text{SeDID}_{\\text{Stat}}$ and neural network-based\n$\\text{SeDID}_{\\text{NNs}}$, SeDID exploits the unique attributes of diffusion\nmodels, namely deterministic reverse and deterministic denoising computation\nerrors. Our evaluations demonstrate SeDID's superior performance over existing\nmethods when applied to diffusion models. Thus, our work makes a pivotal\ncontribution to distinguishing diffusion model-generated images, marking a\nsignificant step in the domain of artificial intelligence security.",
+        "authors": "Ruipeng Ma, Jinhao Duan, Fei Kong, Xiaoshuang Shi, Kaidi Xu",
+        "published": "2023-07-12",
+        "updated": "2023-07-12",
+        "primary_cat": "cs.CV",
+        "cats": [
+            "cs.CV",
+            "cs.CR",
+            "cs.LG"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/1506.05574v1",
+        "title": "Information Diffusion issues",
+        "abstract": "In this report there will be a discussion for Information Diffusion. There\nwill be discussions on what information diffusion is, its key characteristics\nand on several other aspects of these kinds of networks. This report will focus\non peer to peer models in information diffusion. There will be discussions on\nepidemic model, OSN and other details related to information diffusion.",
+        "authors": "Jonathan Helmigh",
+        "published": "2015-06-18",
+        "updated": "2015-06-18",
+        "primary_cat": "cs.SI",
+        "cats": [
+            "cs.SI"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/nlin/0212039v2",
+        "title": "Front dynamics in reaction-diffusion systems with Levy flights: a fractional diffusion approach",
+        "abstract": "The use of reaction-diffusion models rests on the key assumption that the\nunderlying diffusive process is Gaussian. However, a growing number of studies\nhave pointed out the prevalence of anomalous diffusion, and there is a need to\nunderstand the dynamics of reactive systems in the presence of this type of\nnon-Gaussian diffusion. Here we present a study of front dynamics in\nreaction-diffusion systems where anomalous diffusion is due to the presence of\nasymmetric Levy flights. Our approach consists of replacing the Laplacian\ndiffusion operator by a fractional diffusion operator, whose fundamental\nsolutions are Levy $\\alpha$-stable distributions. Numerical simulation of the\nfractional Fisher-Kolmogorov equation, and analytical arguments show that\nanomalous diffusion leads to the exponential acceleration of fronts and a\nuniversal power law decay, $x^{-\\alpha}$, of the tail, where $\\alpha$, the\nindex of the Levy distribution, is the order of the fractional derivative.",
+        "authors": "D. del-Castillo-Negrete, B. A. Carreras, V. E. Lynch",
+        "published": "2002-12-17",
+        "updated": "2003-06-30",
+        "primary_cat": "nlin.PS",
+        "cats": [
+            "nlin.PS",
+            "nlin.CD"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/2303.16203v3",
+        "title": "Your Diffusion Model is Secretly a Zero-Shot Classifier",
+        "abstract": "The recent wave of large-scale text-to-image diffusion models has\ndramatically increased our text-based image generation abilities. These models\ncan generate realistic images for a staggering variety of prompts and exhibit\nimpressive compositional generalization abilities. Almost all use cases thus\nfar have solely focused on sampling; however, diffusion models can also provide\nconditional density estimates, which are useful for tasks beyond image\ngeneration. In this paper, we show that the density estimates from large-scale\ntext-to-image diffusion models like Stable Diffusion can be leveraged to\nperform zero-shot classification without any additional training. Our\ngenerative approach to classification, which we call Diffusion Classifier,\nattains strong results on a variety of benchmarks and outperforms alternative\nmethods of extracting knowledge from diffusion models. Although a gap remains\nbetween generative and discriminative approaches on zero-shot recognition\ntasks, our diffusion-based approach has significantly stronger multimodal\ncompositional reasoning ability than competing discriminative approaches.\nFinally, we use Diffusion Classifier to extract standard classifiers from\nclass-conditional diffusion models trained on ImageNet. Our models achieve\nstrong classification performance using only weak augmentations and exhibit\nqualitatively better \"effective robustness\" to distribution shift. Overall, our\nresults are a step toward using generative over discriminative models for\ndownstream tasks. Results and visualizations at\nhttps://diffusion-classifier.github.io/",
+        "authors": "Alexander C. Li, Mihir Prabhudesai, Shivam Duggal, Ellis Brown, Deepak Pathak",
+        "published": "2023-03-28",
+        "updated": "2023-09-13",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG",
+            "cs.AI",
+            "cs.CV",
+            "cs.NE",
+            "cs.RO"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/math/0204289v1",
+        "title": "On diffusion approximation with discontinuous coefficients",
+        "abstract": "Convergence of stochastic processes with jumps to diffusion processes is\ninvestigated in the case when the limit process has discontinuous coefficients.\n  An example is given in which the diffusion approximation of a queueing model\nyields a diffusion process with discontinuous diffusion and drift coefficients.",
+        "authors": "N. V. Krylov, R. Liptser",
+        "published": "2002-04-24",
+        "updated": "2002-04-24",
+        "primary_cat": "math.PR",
+        "cats": [
+            "math.PR",
+            "math.SG",
+            "60B10; 60K25}"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/1908.03076v3",
+        "title": "The strategy of survival for a competition between normal and anomalous diffusion",
+        "abstract": "In this paper, we study the competition of two diffusion processes for\nachieving the maximum possible diffusion in an area. This competition, however,\ndoes not occur in the same circumstance; one of these processes is a normal\ndiffusion with a higher growth rate, and another one is an anomalous diffusion\nwith a lower growth rate. The trivial solution of the proposed model suggests\nthat the winner is the one with the higher growth rate. But, the question is:\nwhat characteristics and strategies should the second diffusion include to\nprolong the survival in such a competition? The studied diffusion equations\ncorrespond to the SI model such that the anomalous diffusion has memory\ndescribed by a fractional order derivative. The strategy promise that anomalous\ndiffusion reaches maximum survival in case of forgetting some parts of the\nmemory. This model can represent some of real phenomena, such as the contest of\ntwo companies in a market share, the spreading of two epidemic diseases, the\ndiffusion of two species, or any reaction-diffusion related to real-world\ncompetition.",
+        "authors": "Moein Khalighi, Jamshid Ardalankia, Abbas Karimi Rizi, Haleh Ebadi, Gholamreza Jafari",
+        "published": "2019-08-07",
+        "updated": "2020-10-18",
+        "primary_cat": "physics.soc-ph",
+        "cats": [
+            "physics.soc-ph"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/2305.12377v1",
+        "title": "The vanishing diffusion limit for an Oldroyd-B model in $\\mathbb{R}^2_+$",
+        "abstract": "We consider the initial-boundary value problem for an incompressible\nOldroyd-B model with stress diffusion in two-dimensional upper half plane which\ndescribes the motion of viscoelastic polymeric fluids. From the physical point\nof view, the diffusive coefficient is several orders of magnitude smaller than\nother parameters in the model, and is usually assumed to be zero. However, the\nlink between the diffusive model and the standard one (zero diffusion) via\nvanishing diffusion limit is still unknown from the mathematical point of view,\nin particular for the problem with boundary. Some numerical results [13]\nsuggest that this should be true. In this work, we provide a rigorous\njustification for the vanishing diffusion in $L^\\infty$-norm.",
+        "authors": "Yinghui Wang, Huanyao Wen",
+        "published": "2023-05-21",
+        "updated": "2023-05-21",
+        "primary_cat": "math.AP",
+        "cats": [
+            "math.AP",
+            "35Q35, 76A10, 76D10"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/1409.3132v1",
+        "title": "Front propagation in reaction-diffusion systems with anomalous diffusion",
+        "abstract": "A numerical study of the role of anomalous diffusion in front propagation in\nreaction-diffusion systems is presented. Three models of anomalous diffusion\nare considered: fractional diffusion, tempered fractional diffusion, and a\nmodel that combines fractional diffusion and regular diffusion. The reaction\nkinetics corresponds to a Fisher-Kolmogorov nonlinearity. The numerical method\nis based on a finite-difference operator splitting algorithm with an explicit\nEuler step for the time advance of the reaction kinetics, and a Crank-Nicholson\nsemi-implicit time step for the transport operator. The anomalous diffusion\noperators are discretized using an upwind, flux-conserving, Grunwald-Letnikov\nfinite-difference scheme applied to the regularized fractional derivatives.\nWith fractional diffusion of order $\\alpha$, fronts exhibit exponential\nacceleration, $a_L(t) \\sim e^{\\gamma t/\\alpha}$, and develop algebraic decaying\ntails, $\\phi \\sim 1/x^{\\alpha}$. In the case of tempered fractional diffusion,\nthis phenomenology prevails in the intermediate asymptotic regime\n  $\\left(\\chi t \\right)^{1/\\alpha} \\ll x \\ll 1/\\lambda$, where $1/\\lambda$ is\nthe scale of the tempering. Outside this regime, i.e. for $x > 1/\\lambda$, the\ntail exhibits the tempered decay $\\phi \\sim e^{-\\lambda x}/x^{\\alpha+1}$, and\nthe front velocity approaches the terminal speed $v_*=\n\\left(\\gamma-\\lambda^\\alpha \\chi\\right)/ \\lambda$. Of particular interest is\nthe study of the interplay of regular and fractional diffusion. It is shown\nthat the main role of regular diffusion is to delay the onset of front\nacceleration. In particular, the crossover time, $t_c$, to transition to the\naccelerated fractional regime exhibits a logarithmic scaling of the form $t_c\n\\sim \\log \\left(\\chi_d/\\chi_f\\right)$ where $\\chi_d$ and $\\chi_f$ are the\nregular and fractional diffusivities.",
+        "authors": "D. del-Castillo-Negrete",
+        "published": "2014-09-10",
+        "updated": "2014-09-10",
+        "primary_cat": "nlin.PS",
+        "cats": [
+            "nlin.PS",
+            "cond-mat.stat-mech"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/1905.04004v2",
+        "title": "Well-posedness of a cross-diffusion population model with nonlocal diffusion",
+        "abstract": "We prove the existence and uniqueness of solution of a nonlocal\ncross-diffusion competitive population model for two species. The model may be\nconsidered as a version, or even an approximation, of the paradigmatic\nShigesada-Kawasaki-Teramoto cross-diffusion model, in which the usual diffusion\ndifferential operator is replaced by an integral diffusion operator. The proof\nof existence of solutions is based on a compactness argument, while the\nuniqueness of solution is achieved through a duality technique.",
+        "authors": "Gonzalo Galiano, Juli\u00e1n Velasco",
+        "published": "2019-05-10",
+        "updated": "2024-01-24",
+        "primary_cat": "math.AP",
+        "cats": [
+            "math.AP"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/2202.05830v1",
+        "title": "Learning Fast Samplers for Diffusion Models by Differentiating Through Sample Quality",
+        "abstract": "Diffusion models have emerged as an expressive family of generative models\nrivaling GANs in sample quality and autoregressive models in likelihood scores.\nStandard diffusion models typically require hundreds of forward passes through\nthe model to generate a single high-fidelity sample. We introduce\nDifferentiable Diffusion Sampler Search (DDSS): a method that optimizes fast\nsamplers for any pre-trained diffusion model by differentiating through sample\nquality scores. We also present Generalized Gaussian Diffusion Models (GGDM), a\nfamily of flexible non-Markovian samplers for diffusion models. We show that\noptimizing the degrees of freedom of GGDM samplers by maximizing sample quality\nscores via gradient descent leads to improved sample quality. Our optimization\nprocedure backpropagates through the sampling process using the\nreparametrization trick and gradient rematerialization. DDSS achieves strong\nresults on unconditional image generation across various datasets (e.g., FID\nscores on LSUN church 128x128 of 11.6 with only 10 inference steps, and 4.82\nwith 20 steps, compared to 51.1 and 14.9 with strongest DDPM/DDIM baselines).\nOur method is compatible with any pre-trained diffusion model without\nfine-tuning or re-training required.",
+        "authors": "Daniel Watson, William Chan, Jonathan Ho, Mohammad Norouzi",
+        "published": "2022-02-11",
+        "updated": "2022-02-11",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/1304.0925v1",
+        "title": "A new approach to multi-modal diffusions with applications to protein folding",
+        "abstract": "This article demonstrates that flexible and statistically tractable\nmulti-modal diffusion models can be attained by transformation of simple\nwell-known diffusion models such as the Ornstein-Uhlenbeck model, or more\ngenerally a Pearson diffusion. The transformed diffusion inherits many\nproperties of the underlying simple diffusion including its mixing rates and\ndistributions of first passage times. Likelihood inference and martingale\nestimating functions are considered in the case of a discretely observed\nbimodal diffusion. It is further demonstrated that model parameters can be\nidentified and estimated when the diffusion is observed with additional\nmeasurement error. The new approach is applied to molecular dynamics data in\nform of a reaction coordinate of the small Trp-zipper protein, for which the\nfolding and unfolding rates are estimated. The new models provide a better fit\nto this type of protein folding data than previous models because the diffusion\ncoefficient is state-dependent.",
+        "authors": "Julie Forman, Michael S\u00f8rensen",
+        "published": "2013-04-03",
+        "updated": "2013-04-03",
+        "primary_cat": "stat.ME",
+        "cats": [
+            "stat.ME"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/2304.01565v1",
+        "title": "A Survey on Graph Diffusion Models: Generative AI in Science for Molecule, Protein and Material",
+        "abstract": "Diffusion models have become a new SOTA generative modeling method in various\nfields, for which there are multiple survey works that provide an overall\nsurvey. With the number of articles on diffusion models increasing\nexponentially in the past few years, there is an increasing need for surveys of\ndiffusion models on specific fields. In this work, we are committed to\nconducting a survey on the graph diffusion models. Even though our focus is to\ncover the progress of diffusion models in graphs, we first briefly summarize\nhow other generative modeling methods are used for graphs. After that, we\nintroduce the mechanism of diffusion models in various forms, which facilitates\nthe discussion on the graph diffusion models. The applications of graph\ndiffusion models mainly fall into the category of AI-generated content (AIGC)\nin science, for which we mainly focus on how graph diffusion models are\nutilized for generating molecules and proteins but also cover other cases,\nincluding materials design. Moreover, we discuss the issue of evaluating\ndiffusion models in the graph domain and the existing challenges.",
+        "authors": "Mengchun Zhang, Maryam Qamar, Taegoo Kang, Yuna Jung, Chenshuang Zhang, Sung-Ho Bae, Chaoning Zhang",
+        "published": "2023-04-04",
+        "updated": "2023-04-04",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG",
+            "cs.CV"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/2305.14671v2",
+        "title": "A Survey of Diffusion Models in Natural Language Processing",
+        "abstract": "This survey paper provides a comprehensive review of the use of diffusion\nmodels in natural language processing (NLP). Diffusion models are a class of\nmathematical models that aim to capture the diffusion of information or signals\nacross a network or manifold. In NLP, diffusion models have been used in a\nvariety of applications, such as natural language generation, sentiment\nanalysis, topic modeling, and machine translation. This paper discusses the\ndifferent formulations of diffusion models used in NLP, their strengths and\nlimitations, and their applications. We also perform a thorough comparison\nbetween diffusion models and alternative generative models, specifically\nhighlighting the autoregressive (AR) models, while also examining how diverse\narchitectures incorporate the Transformer in conjunction with diffusion models.\nCompared to AR models, diffusion models have significant advantages for\nparallel generation, text interpolation, token-level controls such as syntactic\nstructures and semantic contents, and robustness. Exploring further\npermutations of integrating Transformers into diffusion models would be a\nvaluable pursuit. Also, the development of multimodal diffusion models and\nlarge-scale diffusion language models with notable capabilities for few-shot\nlearning would be important directions for the future advance of diffusion\nmodels in NLP.",
+        "authors": "Hao Zou, Zae Myung Kim, Dongyeop Kang",
+        "published": "2023-05-24",
+        "updated": "2023-06-14",
+        "primary_cat": "cs.CL",
+        "cats": [
+            "cs.CL"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/1712.02290v2",
+        "title": "Effects of nongaussian diffusion on \"isotropic diffusion measurements'': an ex-vivo microimaging and simulation study",
+        "abstract": "Designing novel diffusion-weighted pulse sequences to probe tissue\nmicrostructure beyond the conventional Stejskal-Tanner family is currently of\nbroad interest. One such technique, multidimensional diffusion MRI, has been\nrecently proposed to afford model-free decomposition of diffusion signal\nkurtosis into terms originating from either ensemble variance of isotropic\ndiffusivity or microscopic diffusion anisotropy. This ability rests on the\nassumption that diffusion can be described as a sum of multiple Gaussian\ncompartments, but this is often not strictly fulfilled. The effects of\nnongaussian diffusion on single shot isotropic diffusion sequences were first\nconsidered in detail by de Swiet and Mitra in 1996. They showed theoretically\nthat anisotropic compartments lead to anisotropic time dependence of the\ndiffusion tensors, which causes the measured isotropic diffusivity to depend on\ngradient frame orientation. Here we show how such deviations from the multiple\nGaussian compartments assumption conflates orientation dispersion with ensemble\nvariance in isotropic diffusivity. Second, we consider additional contributions\nto the apparent variance in isotropic diffusivity arising due to\nintracompartmental kurtosis. These will likewise depend on gradient frame\norientation. We illustrate the potential importance of these confounds with\nanalytical expressions, numerical simulations in simple model geometries, and\nmicroimaging experiments in fixed spinal cord using isotropic diffusion\nencoding waveforms with 7.5 ms duration and 3000 mT/m maximum amplitude.",
+        "authors": "Sune N\u00f8rh\u00f8j Jespersen, Jonas Lynge Olesen, Andrada Ianu\u015f, Noam Shemesh",
+        "published": "2017-12-06",
+        "updated": "2019-02-04",
+        "primary_cat": "physics.bio-ph",
+        "cats": [
+            "physics.bio-ph"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/2402.13144v1",
+        "title": "Neural Network Diffusion",
+        "abstract": "Diffusion models have achieved remarkable success in image and video\ngeneration. In this work, we demonstrate that diffusion models can also\n\\textit{generate high-performing neural network parameters}. Our approach is\nsimple, utilizing an autoencoder and a standard latent diffusion model. The\nautoencoder extracts latent representations of a subset of the trained network\nparameters. A diffusion model is then trained to synthesize these latent\nparameter representations from random noise. It then generates new\nrepresentations that are passed through the autoencoder's decoder, whose\noutputs are ready to use as new subsets of network parameters. Across various\narchitectures and datasets, our diffusion process consistently generates models\nof comparable or improved performance over trained networks, with minimal\nadditional cost. Notably, we empirically find that the generated models perform\ndifferently with the trained networks. Our results encourage more exploration\non the versatile use of diffusion models.",
+        "authors": "Kai Wang, Zhaopan Xu, Yukun Zhou, Zelin Zang, Trevor Darrell, Zhuang Liu, Yang You",
+        "published": "2024-02-20",
+        "updated": "2024-02-20",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG",
+            "cs.CV"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/1609.09697v1",
+        "title": "Anomalous diffusion in time-fluctuating non-stationary diffusivity landscapes",
+        "abstract": "We investigate the ensemble and time averaged mean squared displacements for\nparticle diffusion in a simple model for disordered media by assuming that the\nlocal diffusivity is both fluctuating in time and has a deterministic average\ngrowth or decay in time. In this study we compare computer simulations of the\nstochastic Langevin equation for this random diffusion process with analytical\nresults. We explore the regimes of normal Brownian motion as well as anomalous\ndiffusion in the sub- and superdiffusive regimes. We also consider effects of\nthe inertial term on the particle motion. The investigation of the resulting\ndiffusion is performed for unconfined and confined motion.",
+        "authors": "A. G. Cherstvy, R. Metzler",
+        "published": "2016-09-30",
+        "updated": "2016-09-30",
+        "primary_cat": "cond-mat.stat-mech",
+        "cats": [
+            "cond-mat.stat-mech"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/2402.01965v2",
+        "title": "Analyzing Neural Network-Based Generative Diffusion Models through Convex Optimization",
+        "abstract": "Diffusion models are becoming widely used in state-of-the-art image, video\nand audio generation. Score-based diffusion models stand out among these\nmethods, necessitating the estimation of score function of the input data\ndistribution. In this study, we present a theoretical framework to analyze\ntwo-layer neural network-based diffusion models by reframing score matching and\ndenoising score matching as convex optimization. Though existing diffusion\ntheory is mainly asymptotic, we characterize the exact predicted score function\nand establish the convergence result for neural network-based diffusion models\nwith finite data. This work contributes to understanding what neural\nnetwork-based diffusion model learns in non-asymptotic settings.",
+        "authors": "Fangzhao Zhang, Mert Pilanci",
+        "published": "2024-02-03",
+        "updated": "2024-02-06",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG",
+            "math.OC"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/2305.01115v2",
+        "title": "In-Context Learning Unlocked for Diffusion Models",
+        "abstract": "We present Prompt Diffusion, a framework for enabling in-context learning in\ndiffusion-based generative models. Given a pair of task-specific example\nimages, such as depth from/to image and scribble from/to image, and a text\nguidance, our model automatically understands the underlying task and performs\nthe same task on a new query image following the text guidance. To achieve\nthis, we propose a vision-language prompt that can model a wide range of\nvision-language tasks and a diffusion model that takes it as input. The\ndiffusion model is trained jointly over six different tasks using these\nprompts. The resulting Prompt Diffusion model is the first diffusion-based\nvision-language foundation model capable of in-context learning. It\ndemonstrates high-quality in-context generation on the trained tasks and\ngeneralizes effectively to new, unseen vision tasks with their respective\nprompts. Our model also shows compelling text-guided image editing results. Our\nframework aims to facilitate research into in-context learning for computer\nvision. We share our code and pre-trained models at\nhttps://github.com/Zhendong-Wang/Prompt-Diffusion.",
+        "authors": "Zhendong Wang, Yifan Jiang, Yadong Lu, Yelong Shen, Pengcheng He, Weizhu Chen, Zhangyang Wang, Mingyuan Zhou",
+        "published": "2023-05-01",
+        "updated": "2023-10-18",
+        "primary_cat": "cs.CV",
+        "cats": [
+            "cs.CV"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/1009.5965v1",
+        "title": "Sensitivity of a Babcock-Leighton Flux-Transport Dynamo to Magnetic Diffusivity Profiles",
+        "abstract": "We study the influence of various magnetic diffusivity profiles on the\nevolution of the poloidal and toroidal magnetic fields in a kinematic flux\ntransport dynamo model for the Sun. The diffusivity is a poorly understood\ningredient in solar dynamo models. We mathematically construct various\ntheoretical profiles of the depth-dependent diffusivity, based on constraints\nfrom mixing length theory and turbulence, and on comparisons of poloidal field\nevolution on the Sun with that from the flux-transport dynamo model.\n  We then study the effect of each diffusivity profile in the cyclic evolution\nof the magnetic fields in the Sun, by solving the mean-field dynamo equations.\nWe investigate effects on the solar cycle periods, the maximum tachocline field\nstrengths, and the evolution of the toroidal and poloidal field structures\ninside the convection zone, due to different diffusivity profiles.\n  We conduct three experiments: (I) comparing very different magnetic\ndiffusivity profiles; (II) comparing different locations of diffusivity\ngradient near the tachocline for the optimal profile; and (III) comparing\ndifferent slopes of diffusivity gradient for an optimal profile.\n  Based on these simulations, we discuss which aspects of depth-dependent\ndiffusivity profiles may be most relevant for magnetic flux evolution in the\nSun, and how certain observations could help improve knowledge of this dynamo\ningredient.",
+        "authors": "E. J. Zita",
+        "published": "2010-09-29",
+        "updated": "2010-09-29",
+        "primary_cat": "astro-ph.SR",
+        "cats": [
+            "astro-ph.SR",
+            "physics.flu-dyn"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/2306.07491v2",
+        "title": "Exact sharp-fronted solutions for nonlinear diffusion on evolving domains",
+        "abstract": "Models of diffusive processes that occur on evolving domains are frequently\nemployed to describe biological and physical phenomena, such as diffusion\nwithin expanding tissues or substrates. Previous investigations into these\nmodels either report numerical solutions or require an assumption of linear\ndiffusion to determine exact solutions. Unfortunately, numerical solutions do\nnot reveal the relationship between the model parameters and the solution\nfeatures. Additionally, experimental observations typically report the presence\nof sharp fronts, which are not captured by linear diffusion. Here we address\nboth limitations by presenting exact sharp-fronted solutions to a model of\ndegenerate nonlinear diffusion on a growing domain. We obtain the solution by\nidentifying a series of transformations that converts the model of a nonlinear\ndiffusive process on an evolving domain to a nonlinear diffusion equation on a\nfixed domain, which admits known exact solutions for certain choices of\ndiffusivity functions. We determine expressions for critical time scales and\ndomain growth rates such that the diffusive population never reaches the domain\nboundaries and hence the solution remains valid.",
+        "authors": "Stuart T. Johnston, Matthew J. Simpson",
+        "published": "2023-06-13",
+        "updated": "2023-10-06",
+        "primary_cat": "q-bio.PE",
+        "cats": [
+            "q-bio.PE"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/2002.02101v1",
+        "title": "Trace of anomalous diffusion in a biased quenched trap model",
+        "abstract": "Diffusion on a quenched heterogeneous environment in the presence of bias is\nconsidered analytically. The first-passage-time statistics can be applied to\nobtain the drift and the diffusion coefficient in periodic quenched\nenvironments. We show several transition points at which sample-to-sample\nfluctuations of the drift or the diffusion coefficient remain large even when\nthe system size becomes large, i.e., non-self-averaging. Moreover, we find that\nthe disorder average of the diffusion coefficient diverges or becomes zero when\nthe corresponding annealed model generates superdiffusion or subdiffusion,\nrespectively. This result implies that anomalous diffusion in an annealed model\nis traced by anomaly of the diffusion coefficients in the corresponding\nquenched model.",
+        "authors": "Takuma Akimoto, Keiji Saito",
+        "published": "2020-02-06",
+        "updated": "2020-02-06",
+        "primary_cat": "cond-mat.stat-mech",
+        "cats": [
+            "cond-mat.stat-mech"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/2401.17181v1",
+        "title": "Transfer Learning for Text Diffusion Models",
+        "abstract": "In this report, we explore the potential for text diffusion to replace\nautoregressive (AR) decoding for the training and deployment of large language\nmodels (LLMs). We are particularly interested to see whether pretrained AR\nmodels can be transformed into text diffusion models through a lightweight\nadaptation procedure we call ``AR2Diff''. We begin by establishing a strong\nbaseline setup for training text diffusion models. Comparing across multiple\narchitectures and pretraining objectives, we find that training a decoder-only\nmodel with a prefix LM objective is best or near-best across several tasks.\nBuilding on this finding, we test various transfer learning setups for text\ndiffusion models. On machine translation, we find that text diffusion\nunderperforms the standard AR approach. However, on code synthesis and\nextractive QA, we find diffusion models trained from scratch outperform AR\nmodels in many cases. We also observe quality gains from AR2Diff -- adapting AR\nmodels to use diffusion decoding. These results are promising given that text\ndiffusion is relatively underexplored and can be significantly faster than AR\ndecoding for long text generation.",
+        "authors": "Kehang Han, Kathleen Kenealy, Aditya Barua, Noah Fiedel, Noah Constant",
+        "published": "2024-01-30",
+        "updated": "2024-01-30",
+        "primary_cat": "cs.CL",
+        "cats": [
+            "cs.CL"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/2301.00059v2",
+        "title": "Describing NMR chemical exchange by effective phase diffusion approach",
+        "abstract": "This paper proposes an effective phase diffusion method to analyze chemical\nexchange in nuclear magnetic resonance (NMR). The chemical exchange involves\nspin jumps around different sites where the spin angular frequencies vary,\nwhich leads to a random phase walk viewed from the rotating frame reference.\nTherefore, the random walk in phase space can be treated by the effective phase\ndiffusion method. Both the coupled and uncoupled phase diffusions are\nconsidered; additionally, it includes normal diffusion as well as fractional\ndiffusion. Based on these phase diffusion equations, the line shape of NMR\nexchange spectrum can be analyzed. By comparing these theoretical results with\nthe conventional theory, this phase diffusion approach works for fast exchange,\nranging from slightly faster than intermediate exchange to very fast exchange.\nFor normal diffusion models, the theoretically predicted curves agree with\nthose predicted from traditional models in the literature, and the\ncharacteristic exchange time obtained from phase diffusion with a fixed jump\ntime is the same as that obtained from the conventional model. However, the\nphase diffusion with a monoexponential time distribution gives a characteristic\nexchange time constant which is half of that obtained from the traditional\nmodel. Additionally, the fractional diffusion obtains a significantly different\nline shape than that predicted based on normal diffusion.",
+        "authors": "Guoxing Lin",
+        "published": "2022-12-30",
+        "updated": "2023-05-17",
+        "primary_cat": "physics.chem-ph",
+        "cats": [
+            "physics.chem-ph",
+            "cond-mat.stat-mech"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/1202.6521v1",
+        "title": "Coherence transition in degenerate diffusion equations with mean field coupling",
+        "abstract": "We introduce non-linear diffusion in a classical diffusion advection model\nwith non local aggregative coupling on the circle, that exhibits a transition\nfrom an uncoherent state to a coherent one when the coupling strength is\nincreased. We show first that all solutions of the equation converge to the set\nof equilibria, second that the set of equilibria undergoes a bifurcation\nrepresenting the transition to coherence when the coupling strength is\nincreased. These two properties are similar to the situation with linear\ndiffusion. Nevertheless nonlinear diffusion alters the transition scenari,\nwhich are different when the diffusion is sub-quadratic and when the diffusion\nis super-quadratic. When the diffusion is super-quadratic, it results in a\nmultistability region that preceeds the pitchfork bifurcation at which the\nuncoherent equilibrium looses stability. When the diffusion is quadratic the\npitchfork bifurcation at the onset of coherence is infinitely degenerate and a\ndisk of equilibria exist for the critical value of the coupling strength.\nAnother impact of nonlinear diffusion is that coherent equilibria become\nlocalized when advection is strong enough, a phenomenon that is preculded when\nthe diffusion is linear.",
+        "authors": "Khashayar Pakdaman, Xavier Pellegrin",
+        "published": "2012-02-29",
+        "updated": "2012-02-29",
+        "primary_cat": "nlin.AO",
+        "cats": [
+            "nlin.AO",
+            "37N25, 92B25, 35Q35, 35K55, 37B25, 82C26"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/2310.05264v3",
+        "title": "The Emergence of Reproducibility and Consistency in Diffusion Models",
+        "abstract": "In this work, we investigate an intriguing and prevalent phenomenon of\ndiffusion models which we term as \"consistent model reproducibility\": given the\nsame starting noise input and a deterministic sampler, different diffusion\nmodels often yield remarkably similar outputs. We confirm this phenomenon\nthrough comprehensive experiments, implying that different diffusion models\nconsistently reach the same data distribution and scoring function regardless\nof diffusion model frameworks, model architectures, or training procedures.\nMore strikingly, our further investigation implies that diffusion models are\nlearning distinct distributions affected by the training data size. This is\nsupported by the fact that the model reproducibility manifests in two distinct\ntraining regimes: (i) \"memorization regime\", where the diffusion model overfits\nto the training data distribution, and (ii) \"generalization regime\", where the\nmodel learns the underlying data distribution. Our study also finds that this\nvaluable property generalizes to many variants of diffusion models, including\nthose for conditional use, solving inverse problems, and model fine-tuning.\nFinally, our work raises numerous intriguing theoretical questions for future\ninvestigation and highlights practical implications regarding training\nefficiency, model privacy, and the controlled generation of diffusion models.",
+        "authors": "Huijie Zhang, Jinfan Zhou, Yifu Lu, Minzhe Guo, Peng Wang, Liyue Shen, Qing Qu",
+        "published": "2023-10-08",
+        "updated": "2024-02-21",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG",
+            "cs.CV"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/2010.02514v1",
+        "title": "Diffusion model and analysis of diffusion process at lagrangian method",
+        "abstract": "Based on Fick's 2nd law the development of moving particle semi-implicit\nmethod for predicting diffusion process is proposed in this study",
+        "authors": "Ziqi Zhou",
+        "published": "2020-10-06",
+        "updated": "2020-10-06",
+        "primary_cat": "physics.flu-dyn",
+        "cats": [
+            "physics.flu-dyn"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/0910.2253v1",
+        "title": "Linearized Kompaneetz equation as a relativistic diffusion",
+        "abstract": "We show that Kompaneetz equation describing photon diffusion in an\nenvironment of an electron gas, when linearized around its equilibrium\ndistribution, coincides with the relativistic diffusion discussed in recent\npublications. The model of the relativistic diffusion is related to soluble\nmodels of imaginary time quantum mechanics. We suggest some non-linear\ngeneralizations of the relativistic diffusion equation and their astrophysical\napplications (in particular to the Sunyaev-Zeldovich effect).",
+        "authors": "Z. Haba",
+        "published": "2009-10-12",
+        "updated": "2009-10-12",
+        "primary_cat": "astro-ph.CO",
+        "cats": [
+            "astro-ph.CO"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/2104.13565v2",
+        "title": "Generalisation of continuous time random walk to anomalous diffusion MRI models with an age-related evaluation of human corpus callosum",
+        "abstract": "Diffusion MRI measures of the human brain provide key insight into\nmicrostructural variations across individuals and into the impact of central\nnervous system diseases and disorders. One approach to extract information from\ndiffusion signals has been to use biologically relevant analytical models to\nlink millimetre scale diffusion MRI measures with microscale influences. The\nother approach has been to represent diffusion as an anomalous transport\nprocess and infer microstructural information from the different anomalous\ndiffusion equation parameters. In this study, we investigated how parameters of\nvarious anomalous diffusion models vary with age in the human brain white\nmatter, particularly focusing on the corpus callosum. We first unified several\nestablished anomalous diffusion models (the super-diffusion, sub-diffusion,\nquasi-diffusion and fractional Bloch-Torrey models) under the continuous time\nrandom walk modelling framework. This unification allows a consistent parameter\nfitting strategy to be applied from which meaningful model parameter\ncomparisons can be made. We then provided a novel way to derive the diffusional\nkurtosis imaging (DKI) model, which is shown to be a degree two approximation\nof the sub-diffusion model. This link between the DKI and sub-diffusion models\nled to a new robust technique for generating maps of kurtosis and diffusivity\nusing the sub-diffusion parameters \\b{eta}_SUB and D_SUB. Superior tissue\ncontrast is achieved in kurtosis maps based on the sub-diffusion model. 7T\ndiffusion weighted MRI data for 65 healthy participants in the age range 19-78\nyears was used in this study. Results revealed that anomalous diffusion model\nparameters {\\alpha} and \\b{eta} have shown consistent positive correlation with\nage in the corpus callosum, indicating {\\alpha} and \\b{eta} are sensitive to\ntissue microstructural changes in aging.",
+        "authors": "Qianqian Yang, David C. Reutens, Viktor Vegh",
+        "published": "2021-04-28",
+        "updated": "2022-01-17",
+        "primary_cat": "physics.med-ph",
+        "cats": [
+            "physics.med-ph"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/physics/0403039v1",
+        "title": "Non-diffusive transport in plasma turbulence: a fractional diffusion approach",
+        "abstract": "Numerical evidence of non-diffusive transport in three-dimensional, resistive\npressure-gradient-driven plasma turbulence is presented. It is shown that the\nprobability density function (pdf) of test particles' radial displacements is\nstrongly non-Gaussian and exhibits algebraic decaying tails. To model these\nresults we propose a macroscopic transport model for the pdf based on the use\nof fractional derivatives in space and time, that incorporate in a unified way\nspace-time non-locality (non-Fickian transport), non-Gaussianity, and\nnon-diffusive scaling. The fractional diffusion model reproduces the shape, and\nspace-time scaling of the non-Gaussian pdf of turbulent transport calculations.\nThe model also reproduces the observed super-diffusive scaling.",
+        "authors": "D. del-Castillo-Negrete, B. A. Carreras, V. E. Lynch",
+        "published": "2004-03-04",
+        "updated": "2004-03-04",
+        "primary_cat": "physics.plasm-ph",
+        "cats": [
+            "physics.plasm-ph"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/0912.3770v1",
+        "title": "SLE(6) and the geometry of diffusion fronts",
+        "abstract": "We study the diffusion front for a natural two-dimensional model where many\nparticles starting at the origin diffuse independently. It turns out that this\nmodel can be described using properties of near-critical percolation, and\nprovides a natural example where critical fractal geometries spontaneously\narise.",
+        "authors": "Pierre Nolin",
+        "published": "2009-12-18",
+        "updated": "2009-12-18",
+        "primary_cat": "math.PR",
+        "cats": [
+            "math.PR"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/2404.07771v1",
+        "title": "An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimization",
+        "abstract": "Diffusion models, a powerful and universal generative AI technology, have\nachieved tremendous success in computer vision, audio, reinforcement learning,\nand computational biology. In these applications, diffusion models provide\nflexible high-dimensional data modeling, and act as a sampler for generating\nnew samples under active guidance towards task-desired properties. Despite the\nsignificant empirical success, theory of diffusion models is very limited,\npotentially slowing down principled methodological innovations for further\nharnessing and improving diffusion models. In this paper, we review emerging\napplications of diffusion models, understanding their sample generation under\nvarious controls. Next, we overview the existing theories of diffusion models,\ncovering their statistical properties and sampling capabilities. We adopt a\nprogressive routine, beginning with unconditional diffusion models and\nconnecting to conditional counterparts. Further, we review a new avenue in\nhigh-dimensional structured optimization through conditional diffusion models,\nwhere searching for solutions is reformulated as a conditional sampling problem\nand solved by diffusion models. Lastly, we discuss future directions about\ndiffusion models. The purpose of this paper is to provide a well-rounded\ntheoretical exposure for stimulating forward-looking theories and methods of\ndiffusion models.",
+        "authors": "Minshuo Chen, Song Mei, Jianqing Fan, Mengdi Wang",
+        "published": "2024-04-11",
+        "updated": "2024-04-11",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG",
+            "math.ST",
+            "stat.ML",
+            "stat.TH"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/2310.01221v2",
+        "title": "Nonlocal diffusion model with maximum principle",
+        "abstract": "In this paper, we propose nonlocal diffusion models with Dirichlet boundary.\nThese nonlocal diffusion models preserve the maximum principle and also have\ncorresponding variational form. With these good properties, It is relatively\neasy to prove the well-posedness and the vanishing nonlocality convergence.\nFurthermore, by specifically designed weight function, we can get a nonlocal\ndiffusion model with second order convergence which is optimal for nonlocal\ndiffusion models.",
+        "authors": "Zuoqiang Shi",
+        "published": "2023-10-02",
+        "updated": "2023-10-12",
+        "primary_cat": "math.AP",
+        "cats": [
+            "math.AP",
+            "cs.NA",
+            "math.NA"
+        ],
+        "category": "Diffusion AND Model"
+    },
+    {
+        "url": "http://arxiv.org/abs/1212.2829v1",
+        "title": "Spin diffusion in one-dimensional classical Heisenberg mode",
+        "abstract": "The problem of spin diffusion is studied numerically in one-dimensional\nclassical Heisenberg model using a deterministic odd even spin precession\ndynamics. We demonstrate that spin diffusion in this model, like energy\ndiffusion, is normal and one obtains a long time diffusive tail in the decay of\nautocorrelation function (ACF). Some variations of the model with different\ncoupling schemes and with anisotropy are also studied and we find normal\ndiffusion in all of them. A systematic finite size analysis of the Heisenberg\nmodel also suggests diffusive spreading of fluctuation, contrary to previous\nclaims of anomalous diffusion.",
+        "authors": "Debarshee Bagchi",
+        "published": "2012-12-12",
+        "updated": "2012-12-12",
+        "primary_cat": "cond-mat.stat-mech",
+        "cats": [
+            "cond-mat.stat-mech"
+        ],
+        "category": "Diffusion AND Model"
+    }
+]
\ No newline at end of file