# EDMDPMSolverMultistepScheduler

`EDMDPMSolverMultistepScheduler` is a [Karras formulation](https://huggingface.co/papers/2206.00364) of `DPMSolverMultistepScheduler`, a multistep scheduler from [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://huggingface.co/papers/2206.00927) and [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://huggingface.co/papers/2211.01095) by Cheng Lu, Yuhao Zhou, Fan Bao, Jianfei Chen, Chongxuan Li, and Jun Zhu.

DPMSolver (and the improved version DPMSolver++) is a fast dedicated high-order solver for diffusion ODEs with convergence order guarantee. Empirically, DPMSolver sampling with only 20 steps can generate high-quality
samples, and it can generate quite good samples even in 10 steps.

## EDMDPMSolverMultistepScheduler[[diffusers.EDMDPMSolverMultistepScheduler]]
<div class="docstring border-l-2 border-t-2 pl-4 pt-3.5 border-gray-100 rounded-tl-xl mb-6 mt-8">


<docstring><name>class diffusers.EDMDPMSolverMultistepScheduler</name><anchor>diffusers.EDMDPMSolverMultistepScheduler</anchor><source>https://github.com/huggingface/diffusers/blob/main/src/diffusers/schedulers/scheduling_edm_dpmsolver_multistep.py#L28</source><parameters>[{"name": "sigma_min", "val": ": float = 0.002"}, {"name": "sigma_max", "val": ": float = 80.0"}, {"name": "sigma_data", "val": ": float = 0.5"}, {"name": "sigma_schedule", "val": ": str = 'karras'"}, {"name": "num_train_timesteps", "val": ": int = 1000"}, {"name": "prediction_type", "val": ": str = 'epsilon'"}, {"name": "rho", "val": ": float = 7.0"}, {"name": "solver_order", "val": ": int = 2"}, {"name": "thresholding", "val": ": bool = False"}, {"name": "dynamic_thresholding_ratio", "val": ": float = 0.995"}, {"name": "sample_max_value", "val": ": float = 1.0"}, {"name": "algorithm_type", "val": ": str = 'dpmsolver++'"}, {"name": "solver_type", "val": ": str = 'midpoint'"}, {"name": "lower_order_final", "val": ": bool = True"}, {"name": "euler_at_final", "val": ": bool = False"}, {"name": "final_sigmas_type", "val": ": typing.Optional[str] = 'zero'"}]</parameters><paramsdesc>- **sigma_min** (`float`, *optional*, defaults to 0.002) --
  Minimum noise magnitude in the sigma schedule. This was set to 0.002 in the EDM paper [1]; a reasonable
  range is [0, 10].
- **sigma_max** (`float`, *optional*, defaults to 80.0) --
  Maximum noise magnitude in the sigma schedule. This was set to 80.0 in the EDM paper [1]; a reasonable
  range is [0.2, 80.0].
- **sigma_data** (`float`, *optional*, defaults to 0.5) --
  The standard deviation of the data distribution. This is set to 0.5 in the EDM paper [1].
- **sigma_schedule** (`str`, *optional*, defaults to `karras`) --
  Sigma schedule to compute the `sigmas`. By default, we the schedule introduced in the EDM paper
  (https://huggingface.co/papers/2206.00364). Other acceptable value is "exponential". The exponential
  schedule was incorporated in this model: https://huggingface.co/stabilityai/cosxl.
- **num_train_timesteps** (`int`, defaults to 1000) --
  The number of diffusion steps to train the model.
- **solver_order** (`int`, defaults to 2) --
  The DPMSolver order which can be `1` or `2` or `3`. It is recommended to use `solver_order=2` for guided
  sampling, and `solver_order=3` for unconditional sampling.
- **prediction_type** (`str`, defaults to `epsilon`, *optional*) --
  Prediction type of the scheduler function; can be `epsilon` (predicts the noise of the diffusion process),
  `sample` (directly predicts the noisy sample`) or `v_prediction` (see section 2.4 of [Imagen
  Video](https://imagen.research.google/video/paper.pdf) paper).
- **thresholding** (`bool`, defaults to `False`) --
  Whether to use the "dynamic thresholding" method. This is unsuitable for latent-space diffusion models such
  as Stable Diffusion.
- **dynamic_thresholding_ratio** (`float`, defaults to 0.995) --
  The ratio for the dynamic thresholding method. Valid only when `thresholding=True`.
- **sample_max_value** (`float`, defaults to 1.0) --
  The threshold value for dynamic thresholding. Valid only when `thresholding=True` and
  `algorithm_type="dpmsolver++"`.
- **algorithm_type** (`str`, defaults to `dpmsolver++`) --
  Algorithm type for the solver; can be `dpmsolver++` or `sde-dpmsolver++`. The `dpmsolver++` type implements
  the algorithms in the [DPMSolver++](https://huggingface.co/papers/2211.01095) paper. It is recommended to
  use `dpmsolver++` or `sde-dpmsolver++` with `solver_order=2` for guided sampling like in Stable Diffusion.
- **solver_type** (`str`, defaults to `midpoint`) --
  Solver type for the second-order solver; can be `midpoint` or `heun`. The solver type slightly affects the
  sample quality, especially for a small number of steps. It is recommended to use `midpoint` solvers.
- **lower_order_final** (`bool`, defaults to `True`) --
  Whether to use lower-order solvers in the final steps. Only valid for < 15 inference steps. This can
  stabilize the sampling of DPMSolver for steps < 15, especially for steps <= 10.
- **euler_at_final** (`bool`, defaults to `False`) --
  Whether to use Euler's method in the final step. It is a trade-off between numerical stability and detail
  richness. This can stabilize the sampling of the SDE variant of DPMSolver for small number of inference
  steps, but sometimes may result in blurring.
- **final_sigmas_type** (`str`, defaults to `"zero"`) --
  The final `sigma` value for the noise schedule during the sampling process. If `"sigma_min"`, the final
  sigma is the same as the last sigma in the training schedule. If `zero`, the final sigma is set to 0.</paramsdesc><paramgroups>0</paramgroups></docstring>

Implements DPMSolverMultistepScheduler in EDM formulation as presented in Karras et al. 2022 [1].
`EDMDPMSolverMultistepScheduler` is a fast dedicated high-order solver for diffusion ODEs.

[1] Karras, Tero, et al. "Elucidating the Design Space of Diffusion-Based Generative Models."
https://huggingface.co/papers/2206.00364

This model inherits from [SchedulerMixin](/docs/diffusers/main/en/api/schedulers/overview#diffusers.SchedulerMixin) and [ConfigMixin](/docs/diffusers/main/en/api/configuration#diffusers.ConfigMixin). Check the superclass documentation for the generic
methods the library implements for all schedulers such as loading and saving.





<div class="docstring border-l-2 border-t-2 pl-4 pt-3.5 border-gray-100 rounded-tl-xl mb-6 mt-8">


<docstring><name>convert_model_output</name><anchor>diffusers.EDMDPMSolverMultistepScheduler.convert_model_output</anchor><source>https://github.com/huggingface/diffusers/blob/main/src/diffusers/schedulers/scheduling_edm_dpmsolver_multistep.py#L363</source><parameters>[{"name": "model_output", "val": ": Tensor"}, {"name": "sample", "val": ": Tensor = None"}]</parameters><paramsdesc>- **model_output** (`torch.Tensor`) --
  The direct output from the learned diffusion model.
- **sample** (`torch.Tensor`) --
  A current instance of a sample created by the diffusion process.</paramsdesc><paramgroups>0</paramgroups><rettype>`torch.Tensor`</rettype><retdesc>The converted model output.</retdesc></docstring>

Convert the model output to the corresponding type the DPMSolver/DPMSolver++ algorithm needs. DPM-Solver is
designed to discretize an integral of the noise prediction model, and DPM-Solver++ is designed to discretize an
integral of the data prediction model.

> [!TIP] > The algorithm and model type are decoupled. You can use either DPMSolver or DPMSolver++ for both
noise > prediction and data prediction models.








</div>
<div class="docstring border-l-2 border-t-2 pl-4 pt-3.5 border-gray-100 rounded-tl-xl mb-6 mt-8">


<docstring><name>dpm_solver_first_order_update</name><anchor>diffusers.EDMDPMSolverMultistepScheduler.dpm_solver_first_order_update</anchor><source>https://github.com/huggingface/diffusers/blob/main/src/diffusers/schedulers/scheduling_edm_dpmsolver_multistep.py#L394</source><parameters>[{"name": "model_output", "val": ": Tensor"}, {"name": "sample", "val": ": Tensor = None"}, {"name": "noise", "val": ": typing.Optional[torch.Tensor] = None"}]</parameters><paramsdesc>- **model_output** (`torch.Tensor`) --
  The direct output from the learned diffusion model.
- **sample** (`torch.Tensor`) --
  A current instance of a sample created by the diffusion process.</paramsdesc><paramgroups>0</paramgroups><rettype>`torch.Tensor`</rettype><retdesc>The sample tensor at the previous timestep.</retdesc></docstring>

One step for the first-order DPMSolver (equivalent to DDIM).








</div>
<div class="docstring border-l-2 border-t-2 pl-4 pt-3.5 border-gray-100 rounded-tl-xl mb-6 mt-8">


<docstring><name>multistep_dpm_solver_second_order_update</name><anchor>diffusers.EDMDPMSolverMultistepScheduler.multistep_dpm_solver_second_order_update</anchor><source>https://github.com/huggingface/diffusers/blob/main/src/diffusers/schedulers/scheduling_edm_dpmsolver_multistep.py#L432</source><parameters>[{"name": "model_output_list", "val": ": typing.List[torch.Tensor]"}, {"name": "sample", "val": ": Tensor = None"}, {"name": "noise", "val": ": typing.Optional[torch.Tensor] = None"}]</parameters><paramsdesc>- **model_output_list** (`List[torch.Tensor]`) --
  The direct outputs from learned diffusion model at current and latter timesteps.
- **sample** (`torch.Tensor`) --
  A current instance of a sample created by the diffusion process.</paramsdesc><paramgroups>0</paramgroups><rettype>`torch.Tensor`</rettype><retdesc>The sample tensor at the previous timestep.</retdesc></docstring>

One step for the second-order multistep DPMSolver.








</div>
<div class="docstring border-l-2 border-t-2 pl-4 pt-3.5 border-gray-100 rounded-tl-xl mb-6 mt-8">


<docstring><name>multistep_dpm_solver_third_order_update</name><anchor>diffusers.EDMDPMSolverMultistepScheduler.multistep_dpm_solver_third_order_update</anchor><source>https://github.com/huggingface/diffusers/blob/main/src/diffusers/schedulers/scheduling_edm_dpmsolver_multistep.py#L503</source><parameters>[{"name": "model_output_list", "val": ": typing.List[torch.Tensor]"}, {"name": "sample", "val": ": Tensor = None"}]</parameters><paramsdesc>- **model_output_list** (`List[torch.Tensor]`) --
  The direct outputs from learned diffusion model at current and latter timesteps.
- **sample** (`torch.Tensor`) --
  A current instance of a sample created by diffusion process.</paramsdesc><paramgroups>0</paramgroups><rettype>`torch.Tensor`</rettype><retdesc>The sample tensor at the previous timestep.</retdesc></docstring>

One step for the third-order multistep DPMSolver.








</div>
<div class="docstring border-l-2 border-t-2 pl-4 pt-3.5 border-gray-100 rounded-tl-xl mb-6 mt-8">


<docstring><name>scale_model_input</name><anchor>diffusers.EDMDPMSolverMultistepScheduler.scale_model_input</anchor><source>https://github.com/huggingface/diffusers/blob/main/src/diffusers/schedulers/scheduling_edm_dpmsolver_multistep.py#L209</source><parameters>[{"name": "sample", "val": ": Tensor"}, {"name": "timestep", "val": ": typing.Union[float, torch.Tensor]"}]</parameters><paramsdesc>- **sample** (`torch.Tensor`) --
  The input sample.
- **timestep** (`int`, *optional*) --
  The current timestep in the diffusion chain.</paramsdesc><paramgroups>0</paramgroups><rettype>`torch.Tensor`</rettype><retdesc>A scaled input sample.</retdesc></docstring>

Ensures interchangeability with schedulers that need to scale the denoising model input depending on the
current timestep. Scales the denoising model input by `(sigma**2 + 1) ** 0.5` to match the Euler algorithm.








</div>
<div class="docstring border-l-2 border-t-2 pl-4 pt-3.5 border-gray-100 rounded-tl-xl mb-6 mt-8">


<docstring><name>set_begin_index</name><anchor>diffusers.EDMDPMSolverMultistepScheduler.set_begin_index</anchor><source>https://github.com/huggingface/diffusers/blob/main/src/diffusers/schedulers/scheduling_edm_dpmsolver_multistep.py#L167</source><parameters>[{"name": "begin_index", "val": ": int = 0"}]</parameters><paramsdesc>- **begin_index** (`int`) --
  The begin index for the scheduler.</paramsdesc><paramgroups>0</paramgroups></docstring>

Sets the begin index for the scheduler. This function should be run from pipeline before the inference.




</div>
<div class="docstring border-l-2 border-t-2 pl-4 pt-3.5 border-gray-100 rounded-tl-xl mb-6 mt-8">


<docstring><name>set_timesteps</name><anchor>diffusers.EDMDPMSolverMultistepScheduler.set_timesteps</anchor><source>https://github.com/huggingface/diffusers/blob/main/src/diffusers/schedulers/scheduling_edm_dpmsolver_multistep.py#L233</source><parameters>[{"name": "num_inference_steps", "val": ": int = None"}, {"name": "device", "val": ": typing.Union[str, torch.device] = None"}]</parameters><paramsdesc>- **num_inference_steps** (`int`) --
  The number of diffusion steps used when generating samples with a pre-trained model.
- **device** (`str` or `torch.device`, *optional*) --
  The device to which the timesteps should be moved to. If `None`, the timesteps are not moved.</paramsdesc><paramgroups>0</paramgroups></docstring>

Sets the discrete timesteps used for the diffusion chain (to be run before inference).




</div>
<div class="docstring border-l-2 border-t-2 pl-4 pt-3.5 border-gray-100 rounded-tl-xl mb-6 mt-8">


<docstring><name>step</name><anchor>diffusers.EDMDPMSolverMultistepScheduler.step</anchor><source>https://github.com/huggingface/diffusers/blob/main/src/diffusers/schedulers/scheduling_edm_dpmsolver_multistep.py#L590</source><parameters>[{"name": "model_output", "val": ": Tensor"}, {"name": "timestep", "val": ": typing.Union[int, torch.Tensor]"}, {"name": "sample", "val": ": Tensor"}, {"name": "generator", "val": " = None"}, {"name": "return_dict", "val": ": bool = True"}]</parameters><paramsdesc>- **model_output** (`torch.Tensor`) --
  The direct output from learned diffusion model.
- **timestep** (`int`) --
  The current discrete timestep in the diffusion chain.
- **sample** (`torch.Tensor`) --
  A current instance of a sample created by the diffusion process.
- **generator** (`torch.Generator`, *optional*) --
  A random number generator.
- **return_dict** (`bool`) --
  Whether or not to return a [SchedulerOutput](/docs/diffusers/main/en/api/schedulers/edm_multistep_dpm_solver#diffusers.schedulers.scheduling_utils.SchedulerOutput) or `tuple`.</paramsdesc><paramgroups>0</paramgroups><rettype>[SchedulerOutput](/docs/diffusers/main/en/api/schedulers/edm_multistep_dpm_solver#diffusers.schedulers.scheduling_utils.SchedulerOutput) or `tuple`</rettype><retdesc>If return_dict is `True`, [SchedulerOutput](/docs/diffusers/main/en/api/schedulers/edm_multistep_dpm_solver#diffusers.schedulers.scheduling_utils.SchedulerOutput) is returned, otherwise a
tuple is returned where the first element is the sample tensor.</retdesc></docstring>

Predict the sample from the previous timestep by reversing the SDE. This function propagates the sample with
the multistep DPMSolver.








</div></div>

## SchedulerOutput[[diffusers.schedulers.scheduling_utils.SchedulerOutput]]
<div class="docstring border-l-2 border-t-2 pl-4 pt-3.5 border-gray-100 rounded-tl-xl mb-6 mt-8">


<docstring><name>class diffusers.schedulers.scheduling_utils.SchedulerOutput</name><anchor>diffusers.schedulers.scheduling_utils.SchedulerOutput</anchor><source>https://github.com/huggingface/diffusers/blob/main/src/diffusers/schedulers/scheduling_utils.py#L62</source><parameters>[{"name": "prev_sample", "val": ": Tensor"}]</parameters><paramsdesc>- **prev_sample** (`torch.Tensor` of shape `(batch_size, num_channels, height, width)` for images) --
  Computed sample `(x_{t-1})` of previous timestep. `prev_sample` should be used as next model input in the
  denoising loop.</paramsdesc><paramgroups>0</paramgroups></docstring>

Base class for the output of a scheduler's `step` function.




</div>

<EditOnGithub source="https://github.com/huggingface/diffusers/blob/main/docs/source/en/api/schedulers/edm_multistep_dpm_solver.md" />