#
Multistep DPM-Solver

##
Overview

Original paper can be found here and the improved version. The original implementation can be found here.

##
DPMSolverMultistepScheduler

###
class diffusers.DPMSolverMultistepScheduler

< source >

( num_train_timesteps: int = 1000 beta_start: float = 0.0001 beta_end: float = 0.02 beta_schedule: str = 'linear' trained_betas: typing.Union[numpy.ndarray, typing.List[float], NoneType] = None solver_order: int = 2 prediction_type: str = 'epsilon' thresholding: bool = False dynamic_thresholding_ratio: float = 0.995 sample_max_value: float = 1.0 algorithm_type: str = 'dpmsolver++' solver_type: str = 'midpoint' lower_order_final: bool = True use_karras_sigmas: typing.Optional[bool] = False lambda_min_clipped: float = -inf variance_type: typing.Optional[str] = None timestep_spacing: str = 'linspace' steps_offset: int = 0 )

Parameters

- num_train_timesteps (`int`) — number of diffusion steps used to train the model.
- beta_start (`float`) — the starting `beta` value of inference.
- beta_end (`float`) — the final `beta` value.
- beta_schedule (`str`) — the beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Choose from `linear`, `scaled_linear`, or `squaredcos_cap_v2`.
- trained_betas (`np.ndarray`, optional) — option to pass an array of betas directly to the constructor to bypass `beta_start`, `beta_end` etc.
- solver_order (`int`, default `2`) — the order of DPM-Solver; can be `1` or `2` or `3`. We recommend to use `solver_order=2` for guided sampling, and `solver_order=3` for unconditional sampling.
- prediction_type (`str`, default `epsilon`, optional) — prediction type of the scheduler function, one of `epsilon` (predicting the noise of the diffusion process), `sample` (directly predicting the noisy sample`) or` v_prediction` (see section 2.4 https://imagen.research.google/video/paper.pdf)
- thresholding (`bool`, default `False`) — whether to use the “dynamic thresholding” method (introduced by Imagen, https://arxiv.org/abs/2205.11487). For pixel-space diffusion models, you can set both `algorithm_type=dpmsolver++` and `thresholding=True` to use the dynamic thresholding. Note that the thresholding method is unsuitable for latent-space diffusion models (such as stable-diffusion).
- dynamic_thresholding_ratio (`float`, default `0.995`) — the ratio for the dynamic thresholding method. Default is `0.995`, the same as Imagen (https://arxiv.org/abs/2205.11487).
- sample_max_value (`float`, default `1.0`) — the threshold value for dynamic thresholding. Valid only when `thresholding=True` and `algorithm_type="dpmsolver++`.
- algorithm_type (`str`, default `dpmsolver++`) — the algorithm type for the solver. Either `dpmsolver` or `dpmsolver++` or `sde-dpmsolver` or `sde-dpmsolver++`. The `dpmsolver` type implements the algorithms in https://arxiv.org/abs/2206.00927, and the `dpmsolver++` type implements the algorithms in https://arxiv.org/abs/2211.01095. We recommend to use `dpmsolver++` or `sde-dpmsolver++` with `solver_order=2` for guided sampling (e.g. stable-diffusion).
- solver_type (`str`, default `midpoint`) — the solver type for the second-order solver. Either `midpoint` or `heun`. The solver type slightly affects the sample quality, especially for small number of steps. We empirically find that `midpoint` solvers are slightly better, so we recommend to use the `midpoint` type.
- lower_order_final (`bool`, default `True`) — whether to use lower-order solvers in the final steps. Only valid for < 15 inference steps. We empirically find this trick can stabilize the sampling of DPM-Solver for steps < 15, especially for steps <= 10.
- use_karras_sigmas (`bool`, optional, defaults to `False`) — This parameter controls whether to use Karras sigmas (Karras et al. (2022) scheme) for step sizes in the noise schedule during the sampling process. If True, the sigmas will be determined according to a sequence of noise levels {σi} as defined in Equation (5) of the paper https://arxiv.org/pdf/2206.00364.pdf.
- lambda_min_clipped (`float`, default `-inf`) — the clipping threshold for the minimum value of lambda(t) for numerical stability. This is critical for cosine (squaredcos_cap_v2) noise schedule.
- variance_type (`str`, optional) — Set to “learned” or “learned_range” for diffusion models that predict variance. For example, OpenAI’s guided-diffusion (https://github.com/openai/guided-diffusion) predicts both mean and variance of the Gaussian distribution in the model’s output. DPM-Solver only needs the “mean” output because it is based on diffusion ODEs. whether the model’s output contains the predicted Gaussian variance. For example, OpenAI’s guided-diffusion (https://github.com/openai/guided-diffusion) predicts both mean and variance of the Gaussian distribution in the model’s output. DPM-Solver only needs the “mean” output because it is based on diffusion ODEs.
- timestep_spacing (`str`, default `"linspace"`) — The way the timesteps should be scaled. Refer to Table 2. of Common Diffusion Noise Schedules and Sample Steps are Flawed for more information.
- steps_offset (`int`, default `0`) — an offset added to the inference steps. You can use a combination of `offset=1` and `set_alpha_to_one=False`, to make the last step use step 0 for the previous alpha product, as done in stable diffusion.

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

For more details, see the original paper: https://arxiv.org/abs/2206.00927 and https://arxiv.org/abs/2211.01095

Currently, we support the multistep DPM-Solver for both noise prediction models and data prediction models. We recommend to use `solver_order=2` for guided sampling, and `solver_order=3` for unconditional sampling.

We also support the “dynamic thresholding” method in Imagen (https://arxiv.org/abs/2205.11487). For pixel-space diffusion models, you can set both `algorithm_type="dpmsolver++"` and `thresholding=True` to use the dynamic thresholding. Note that the thresholding method is unsuitable for latent-space diffusion models (such as stable-diffusion).

We also support the SDE variant of DPM-Solver and DPM-Solver++, which is a fast SDE solver for the reverse diffusion SDE. Currently we only support the first-order and second-order solvers. We recommend using the second-order `sde-dpmsolver++`.

~ConfigMixin takes care of storing all config attributes that are passed in the scheduler’s `__init__` function, such as `num_train_timesteps`. They can be accessed via `scheduler.config.num_train_timesteps`. SchedulerMixin provides general loading and saving functionality via the SchedulerMixin.save_pretrained() and from_pretrained() functions.

####
convert_model_output

< source >

( model_output: FloatTensor timestep: int sample: FloatTensor ) → `torch.FloatTensor`

Parameters

- model_output (`torch.FloatTensor`) — direct output from learned diffusion model.
- timestep (`int`) — current discrete timestep in the diffusion chain.
- sample (`torch.FloatTensor`) — current instance of sample being created by diffusion process.

Returns

`torch.FloatTensor`

the converted model output.

Convert the model output to the corresponding type that the algorithm (DPM-Solver / DPM-Solver++) 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. So we need to first convert the model output to the corresponding type to match the algorithm.

Note that the algorithm type and the model type is decoupled. That is to say, we can use either DPM-Solver or DPM-Solver++ for both noise prediction model and data prediction model.

####
dpm_solver_first_order_update

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( model_output: FloatTensor timestep: int prev_timestep: int sample: FloatTensor noise: typing.Optional[torch.FloatTensor] = None ) → `torch.FloatTensor`

Parameters

- model_output (`torch.FloatTensor`) — direct output from learned diffusion model.
- timestep (`int`) — current discrete timestep in the diffusion chain.
- prev_timestep (`int`) — previous discrete timestep in the diffusion chain.
- sample (`torch.FloatTensor`) — current instance of sample being created by diffusion process.

Returns

`torch.FloatTensor`

the sample tensor at the previous timestep.

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

See https://arxiv.org/abs/2206.00927 for the detailed derivation.

####
multistep_dpm_solver_second_order_update

< source >

( model_output_list: typing.List[torch.FloatTensor] timestep_list: typing.List[int] prev_timestep: int sample: FloatTensor noise: typing.Optional[torch.FloatTensor] = None ) → `torch.FloatTensor`

Parameters

- model_output_list (`List[torch.FloatTensor]`) — direct outputs from learned diffusion model at current and latter timesteps.
- timestep (`int`) — current and latter discrete timestep in the diffusion chain.
- prev_timestep (`int`) — previous discrete timestep in the diffusion chain.
- sample (`torch.FloatTensor`) — current instance of sample being created by diffusion process.

Returns

`torch.FloatTensor`

the sample tensor at the previous timestep.

One step for the second-order multistep DPM-Solver.

####
multistep_dpm_solver_third_order_update

< source >

( model_output_list: typing.List[torch.FloatTensor] timestep_list: typing.List[int] prev_timestep: int sample: FloatTensor ) → `torch.FloatTensor`

Parameters

- model_output_list (`List[torch.FloatTensor]`) — direct outputs from learned diffusion model at current and latter timesteps.
- timestep (`int`) — current and latter discrete timestep in the diffusion chain.
- prev_timestep (`int`) — previous discrete timestep in the diffusion chain.
- sample (`torch.FloatTensor`) — current instance of sample being created by diffusion process.

Returns

`torch.FloatTensor`

the sample tensor at the previous timestep.

One step for the third-order multistep DPM-Solver.

####
scale_model_input

< source >

( sample: FloatTensor *args **kwargs ) → `torch.FloatTensor`

Parameters

- sample (`torch.FloatTensor`) — input sample

Returns

`torch.FloatTensor`

scaled input sample

Ensures interchangeability with schedulers that need to scale the denoising model input depending on the current timestep.

####
set_timesteps

< source >

( num_inference_steps: int = None device: typing.Union[str, torch.device] = None )

Parameters

- 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.

Sets the timesteps used for the diffusion chain. Supporting function to be run before inference.

####
step

< source >

( model_output: FloatTensor timestep: int sample: FloatTensor generator = None return_dict: bool = True ) → `~scheduling_utils.SchedulerOutput` or `tuple`

Parameters

- model_output (`torch.FloatTensor`) — direct output from learned diffusion model.
- timestep (`int`) — current discrete timestep in the diffusion chain.
- sample (`torch.FloatTensor`) — current instance of sample being created by diffusion process.
- return_dict (`bool`) — option for returning tuple rather than SchedulerOutput class

Returns

`~scheduling_utils.SchedulerOutput` or `tuple`

`~scheduling_utils.SchedulerOutput` if `return_dict` is True, otherwise a `tuple`. When returning a tuple, the first element is the sample tensor.

Step function propagating the sample with the multistep DPM-Solver.