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Multistep DPM-Solver

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# 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

< >

( 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 )

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++. 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++ 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.

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).

~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

< >

( 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

< >

( model_output: FloatTensor timestep: int prev_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.
• 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

< >

( 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 second-order multistep DPM-Solver.

#### multistep_dpm_solver_third_order_update

< >

( 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

< >

( 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

< >

( num_inference_steps: int 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

< >

( model_output: FloatTensor timestep: int sample: FloatTensor 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.