  Continuous Conditional Generative Modeling (CCGM) aims to estimate the
distribution of high-dimensional data, typically images, conditioned on scalar
continuous variables known as regression labels. While Continuous conditional
Generative Adversarial Networks (CcGANs) were initially designed for this task,
their adversarial training mechanism remains vulnerable to extremely sparse or
imbalanced data, resulting in suboptimal outcomes. To enhance the quality of
generated images, a promising alternative is to replace CcGANs with Conditional
Diffusion Models (CDMs), renowned for their stable training process and ability
to produce more realistic images. However, existing CDMs encounter challenges
when applied to CCGM tasks due to several limitations such as inadequate U-Net
architectures and deficient model fitting mechanisms for handling regression
labels. In this paper, we introduce Continuous Conditional Diffusion Models
(CCDMs), the first CDM designed specifically for the CCGM task. CCDMs address
the limitations of existing CDMs by introducing specially designed conditional
diffusion processes, a modified denoising U-Net with a custom-made conditioning
mechanism, a novel hard vicinal loss for model fitting, and an efficient
conditional sampling procedure. With comprehensive experiments on four datasets
with varying resolutions ranging from 64x64 to 192x192, we demonstrate the
superiority of the proposed CCDM over state-of-the-art CCGM models,
establishing new benchmarks in CCGM. Extensive ablation studies validate the
model design and implementation configuration of the proposed CCDM. Our code is
publicly available at https://github.com/UBCDingXin/CCDM.
