# Copied from https://github.com/huggingface/diffusers/blob/main/src/diffusers/schedulers/scheduling_dpmsolver_multistep.py
# Convert dpm solver for flow matching
# Copyright 2024-2025 The Alibaba Wan Team Authors. All rights reserved.
import inspect
import math
from typing import List, Optional, Tuple, Union
import numpy as np
import torch
from diffusers.configuration_utils import ConfigMixin, register_to_config
from diffusers.schedulers.scheduling_utils import (KarrasDiffusionSchedulers,
SchedulerMixin,
SchedulerOutput)
from diffusers.utils import deprecate, is_scipy_available
from diffusers.utils.torch_utils import randn_tensor
if is_scipy_available():
pass
def get_sampling_sigmas(sampling_steps, shift):
sigma = np.linspace(1, 0, sampling_steps + 1)[:sampling_steps]
sigma = (shift * sigma / (1 + (shift - 1) * sigma))
return sigma
def retrieve_timesteps(
scheduler,
num_inference_steps=None,
device=None,
timesteps=None,
sigmas=None,
**kwargs,
):
if timesteps is not None and sigmas is not None:
raise ValueError(
"Only one of `timesteps` or `sigmas` can be passed. Please choose one to set custom values"
)
if timesteps is not None:
accepts_timesteps = "timesteps" in set(
inspect.signature(scheduler.set_timesteps).parameters.keys())
if not accepts_timesteps:
raise ValueError(
f"The current scheduler class {scheduler.__class__}'s `set_timesteps` does not support custom"
f" timestep schedules. Please check whether you are using the correct scheduler."
)
scheduler.set_timesteps(timesteps=timesteps, device=device, **kwargs)
timesteps = scheduler.timesteps
num_inference_steps = len(timesteps)
elif sigmas is not None:
accept_sigmas = "sigmas" in set(
inspect.signature(scheduler.set_timesteps).parameters.keys())
if not accept_sigmas:
raise ValueError(
f"The current scheduler class {scheduler.__class__}'s `set_timesteps` does not support custom"
f" sigmas schedules. Please check whether you are using the correct scheduler."
)
scheduler.set_timesteps(sigmas=sigmas, device=device, **kwargs)
timesteps = scheduler.timesteps
num_inference_steps = len(timesteps)
else:
scheduler.set_timesteps(num_inference_steps, device=device, **kwargs)
timesteps = scheduler.timesteps
return timesteps, num_inference_steps
class FlowDPMSolverMultistepScheduler(SchedulerMixin, ConfigMixin):
"""
`FlowDPMSolverMultistepScheduler` is a fast dedicated high-order solver for diffusion ODEs.
This model inherits from [`SchedulerMixin`] and [`ConfigMixin`]. Check the superclass documentation for the generic
methods the library implements for all schedulers such as loading and saving.
Args:
num_train_timesteps (`int`, defaults to 1000):
The number of diffusion steps to train the model. This determines the resolution of the diffusion process.
solver_order (`int`, defaults to 2):
The DPMSolver order which can be `1`, `2`, or `3`. It is recommended to use `solver_order=2` for guided
sampling, and `solver_order=3` for unconditional sampling. This affects the number of model outputs stored
and used in multistep updates.
prediction_type (`str`, defaults to "flow_prediction"):
Prediction type of the scheduler function; must be `flow_prediction` for this scheduler, which predicts
the flow of the diffusion process.
shift (`float`, *optional*, defaults to 1.0):
A factor used to adjust the sigmas in the noise schedule. It modifies the step sizes during the sampling
process.
use_dynamic_shifting (`bool`, defaults to `False`):
Whether to apply dynamic shifting to the timesteps based on image resolution. If `True`, the shifting is
applied on the fly.
thresholding (`bool`, defaults to `False`):
Whether to use the "dynamic thresholding" method. This method adjusts the predicted sample to prevent
saturation and improve photorealism.
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`, `dpmsolver++`, `sde-dpmsolver` or `sde-dpmsolver++`. The
`dpmsolver` type implements the algorithms in the [DPMSolver](https://huggingface.co/papers/2206.00927)
paper, and 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`, *optional*, 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.
lambda_min_clipped (`float`, defaults to `-inf`):
Clipping threshold for the minimum value of `lambda(t)` for numerical stability. This is critical for the
cosine (`squaredcos_cap_v2`) noise schedule.
variance_type (`str`, *optional*):
Set to "learned" or "learned_range" for diffusion models that predict variance. If set, the model's output
contains the predicted Gaussian variance.
"""
_compatibles = [e.name for e in KarrasDiffusionSchedulers]
order = 1
@register_to_config
def __init__(
self,
num_train_timesteps: int = 1000,
solver_order: int = 2,
prediction_type: str = "flow_prediction",
shift: Optional[float] = 1.0,
use_dynamic_shifting=False,
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,
euler_at_final: bool = False,
final_sigmas_type: Optional[str] = "zero", # "zero", "sigma_min"
lambda_min_clipped: float = -float("inf"),
variance_type: Optional[str] = None,
invert_sigmas: bool = False,
):
if algorithm_type in ["dpmsolver", "sde-dpmsolver"]:
deprecation_message = f"algorithm_type {algorithm_type} is deprecated and will be removed in a future version. Choose from `dpmsolver++` or `sde-dpmsolver++` instead"
deprecate("algorithm_types dpmsolver and sde-dpmsolver", "1.0.0",
deprecation_message)
# settings for DPM-Solver
if algorithm_type not in [
"dpmsolver", "dpmsolver++", "sde-dpmsolver", "sde-dpmsolver++"
]:
if algorithm_type == "deis":
self.register_to_config(algorithm_type="dpmsolver++")
else:
raise NotImplementedError(
f"{algorithm_type} is not implemented for {self.__class__}")
if solver_type not in ["midpoint", "heun"]:
if solver_type in ["logrho", "bh1", "bh2"]:
self.register_to_config(solver_type="midpoint")
else:
raise NotImplementedError(
f"{solver_type} is not implemented for {self.__class__}")
if algorithm_type not in ["dpmsolver++", "sde-dpmsolver++"
] and final_sigmas_type == "zero":
raise ValueError(
f"`final_sigmas_type` {final_sigmas_type} is not supported for `algorithm_type` {algorithm_type}. Please choose `sigma_min` instead."
)
# setable values
self.num_inference_steps = None
alphas = np.linspace(1, 1 / num_train_timesteps,
num_train_timesteps)[::-1].copy()
sigmas = 1.0 - alphas
sigmas = torch.from_numpy(sigmas).to(dtype=torch.float32)
if not use_dynamic_shifting:
# when use_dynamic_shifting is True, we apply the timestep shifting on the fly based on the image resolution
sigmas = shift * sigmas / (1 +
(shift - 1) * sigmas) # pyright: ignore
self.sigmas = sigmas
self.timesteps = sigmas * num_train_timesteps
self.model_outputs = [None] * solver_order
self.lower_order_nums = 0
self._step_index = None
self._begin_index = None
# self.sigmas = self.sigmas.to(
# "cpu") # to avoid too much CPU/GPU communication
self.sigma_min = self.sigmas[-1].item()
self.sigma_max = self.sigmas[0].item()
@property
def step_index(self):
"""
The index counter for current timestep. It will increase 1 after each scheduler step.
"""
return self._step_index
@property
def begin_index(self):
"""
The index for the first timestep. It should be set from pipeline with `set_begin_index` method.
"""
return self._begin_index
# Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.set_begin_index
def set_begin_index(self, begin_index: int = 0):
"""
Sets the begin index for the scheduler. This function should be run from pipeline before the inference.
Args:
begin_index (`int`):
The begin index for the scheduler.
"""
self._begin_index = begin_index
# Modified from diffusers.schedulers.scheduling_flow_match_euler_discrete.FlowMatchEulerDiscreteScheduler.set_timesteps
def set_timesteps(
self,
num_inference_steps: Union[int, None] = None,
device: Union[str, torch.device] = None,
sigmas: Optional[List[float]] = None,
mu: Optional[Union[float, None]] = None,
shift: Optional[Union[float, None]] = None,
):
"""
Sets the discrete timesteps used for the diffusion chain (to be run before inference).
Args:
num_inference_steps (`int`):
Total number of the spacing of the time steps.
device (`str` or `torch.device`, *optional*):
The device to which the timesteps should be moved to. If `None`, the timesteps are not moved.
"""
if self.config.use_dynamic_shifting and mu is None:
raise ValueError(
" you have to pass a value for `mu` when `use_dynamic_shifting` is set to be `True`"
)
if sigmas is None:
sigmas = np.linspace(self.sigma_max, self.sigma_min,
num_inference_steps +
1).copy()[:-1] # pyright: ignore
if self.config.use_dynamic_shifting:
sigmas = self.time_shift(mu, 1.0, sigmas) # pyright: ignore
else:
if shift is None:
shift = self.config.shift
sigmas = shift * sigmas / (1 +
(shift - 1) * sigmas) # pyright: ignore
if self.config.final_sigmas_type == "sigma_min":
sigma_last = ((1 - self.alphas_cumprod[0]) /
self.alphas_cumprod[0])**0.5
elif self.config.final_sigmas_type == "zero":
sigma_last = 0
else:
raise ValueError(
f"`final_sigmas_type` must be one of 'zero', or 'sigma_min', but got {self.config.final_sigmas_type}"
)
timesteps = sigmas * self.config.num_train_timesteps
sigmas = np.concatenate([sigmas, [sigma_last]
]).astype(np.float32) # pyright: ignore
self.sigmas = torch.from_numpy(sigmas)
self.timesteps = torch.from_numpy(timesteps).to(
device=device, dtype=torch.int64)
self.num_inference_steps = len(timesteps)
self.model_outputs = [
None,
] * self.config.solver_order
self.lower_order_nums = 0
self._step_index = None
self._begin_index = None
# self.sigmas = self.sigmas.to(
# "cpu") # to avoid too much CPU/GPU communication
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMScheduler._threshold_sample
def _threshold_sample(self, sample: torch.Tensor) -> torch.Tensor:
"""
"Dynamic thresholding: At each sampling step we set s to a certain percentile absolute pixel value in xt0 (the
prediction of x_0 at timestep t), and if s > 1, then we threshold xt0 to the range [-s, s] and then divide by
s. Dynamic thresholding pushes saturated pixels (those near -1 and 1) inwards, thereby actively preventing
pixels from saturation at each step. We find that dynamic thresholding results in significantly better
photorealism as well as better image-text alignment, especially when using very large guidance weights."
https://arxiv.org/abs/2205.11487
"""
dtype = sample.dtype
batch_size, channels, *remaining_dims = sample.shape
if dtype not in (torch.float32, torch.float64):
sample = sample.float(
) # upcast for quantile calculation, and clamp not implemented for cpu half
# Flatten sample for doing quantile calculation along each image
sample = sample.reshape(batch_size, channels * np.prod(remaining_dims))
abs_sample = sample.abs() # "a certain percentile absolute pixel value"
s = torch.quantile(
abs_sample, self.config.dynamic_thresholding_ratio, dim=1)
s = torch.clamp(
s, min=1, max=self.config.sample_max_value
) # When clamped to min=1, equivalent to standard clipping to [-1, 1]
s = s.unsqueeze(
1) # (batch_size, 1) because clamp will broadcast along dim=0
sample = torch.clamp(
sample, -s, s
) / s # "we threshold xt0 to the range [-s, s] and then divide by s"
sample = sample.reshape(batch_size, channels, *remaining_dims)
sample = sample.to(dtype)
return sample
# Copied from diffusers.schedulers.scheduling_flow_match_euler_discrete.FlowMatchEulerDiscreteScheduler._sigma_to_t
def _sigma_to_t(self, sigma):
return sigma * self.config.num_train_timesteps
def _sigma_to_alpha_sigma_t(self, sigma):
return 1 - sigma, sigma
# Copied from diffusers.schedulers.scheduling_flow_match_euler_discrete.set_timesteps
def time_shift(self, mu: float, sigma: float, t: torch.Tensor):
return math.exp(mu) / (math.exp(mu) + (1 / t - 1)**sigma)
# Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.convert_model_output
def convert_model_output(
self,
model_output: torch.Tensor,
*args,
sample: torch.Tensor = None,
**kwargs,
) -> torch.Tensor:
"""
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.
</Tip>
Args:
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.
Returns:
`torch.Tensor`:
The converted model output.
"""
timestep = args[0] if len(args) > 0 else kwargs.pop("timestep", None)
if sample is None:
if len(args) > 1:
sample = args[1]
else:
raise ValueError(
"missing `sample` as a required keyward argument")
if timestep is not None:
deprecate(
"timesteps",
"1.0.0",
"Passing `timesteps` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`",
)
# DPM-Solver++ needs to solve an integral of the data prediction model.
if self.config.algorithm_type in ["dpmsolver++", "sde-dpmsolver++"]:
if self.config.prediction_type == "flow_prediction":
sigma_t = self.sigmas[self.step_index]
x0_pred = sample - sigma_t * model_output
else:
raise ValueError(
f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`,"
" `v_prediction`, or `flow_prediction` for the FlowDPMSolverMultistepScheduler."
)
if self.config.thresholding:
x0_pred = self._threshold_sample(x0_pred)
return x0_pred
# DPM-Solver needs to solve an integral of the noise prediction model.
elif self.config.algorithm_type in ["dpmsolver", "sde-dpmsolver"]:
if self.config.prediction_type == "flow_prediction":
sigma_t = self.sigmas[self.step_index]
epsilon = sample - (1 - sigma_t) * model_output
else:
raise ValueError(
f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`,"
" `v_prediction` or `flow_prediction` for the FlowDPMSolverMultistepScheduler."
)
if self.config.thresholding:
sigma_t = self.sigmas[self.step_index]
x0_pred = sample - sigma_t * model_output
x0_pred = self._threshold_sample(x0_pred)
epsilon = model_output + x0_pred
return epsilon
# Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.dpm_solver_first_order_update
def dpm_solver_first_order_update(
self,
model_output: torch.Tensor,
*args,
sample: torch.Tensor = None,
noise: Optional[torch.Tensor] = None,
**kwargs,
) -> torch.Tensor:
"""
One step for the first-order DPMSolver (equivalent to DDIM).
Args:
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.
Returns:
`torch.Tensor`:
The sample tensor at the previous timestep.
"""
timestep = args[0] if len(args) > 0 else kwargs.pop("timestep", None)
prev_timestep = args[1] if len(args) > 1 else kwargs.pop(
"prev_timestep", None)
if sample is None:
if len(args) > 2:
sample = args[2]
else:
raise ValueError(
" missing `sample` as a required keyward argument")
if timestep is not None:
deprecate(
"timesteps",
"1.0.0",
"Passing `timesteps` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`",
)
if prev_timestep is not None:
deprecate(
"prev_timestep",
"1.0.0",
"Passing `prev_timestep` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`",
)
sigma_t, sigma_s = self.sigmas[self.step_index + 1], self.sigmas[
self.step_index] # pyright: ignore
alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma_t)
alpha_s, sigma_s = self._sigma_to_alpha_sigma_t(sigma_s)
lambda_t = torch.log(alpha_t) - torch.log(sigma_t)
lambda_s = torch.log(alpha_s) - torch.log(sigma_s)
h = lambda_t - lambda_s
if self.config.algorithm_type == "dpmsolver++":
x_t = (sigma_t /
sigma_s) * sample - (alpha_t *
(torch.exp(-h) - 1.0)) * model_output
elif self.config.algorithm_type == "dpmsolver":
x_t = (alpha_t /
alpha_s) * sample - (sigma_t *
(torch.exp(h) - 1.0)) * model_output
elif self.config.algorithm_type == "sde-dpmsolver++":
assert noise is not None
x_t = ((sigma_t / sigma_s * torch.exp(-h)) * sample +
(alpha_t * (1 - torch.exp(-2.0 * h))) * model_output +
sigma_t * torch.sqrt(1.0 - torch.exp(-2 * h)) * noise)
elif self.config.algorithm_type == "sde-dpmsolver":
assert noise is not None
x_t = ((alpha_t / alpha_s) * sample - 2.0 *
(sigma_t * (torch.exp(h) - 1.0)) * model_output +
sigma_t * torch.sqrt(torch.exp(2 * h) - 1.0) * noise)
return x_t # pyright: ignore
# Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.multistep_dpm_solver_second_order_update
def multistep_dpm_solver_second_order_update(
self,
model_output_list: List[torch.Tensor],
*args,
sample: torch.Tensor = None,
noise: Optional[torch.Tensor] = None,
**kwargs,
) -> torch.Tensor:
"""
One step for the second-order multistep DPMSolver.
Args:
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.
Returns:
`torch.Tensor`:
The sample tensor at the previous timestep.
"""
timestep_list = args[0] if len(args) > 0 else kwargs.pop(
"timestep_list", None)
prev_timestep = args[1] if len(args) > 1 else kwargs.pop(
"prev_timestep", None)
if sample is None:
if len(args) > 2:
sample = args[2]
else:
raise ValueError(
" missing `sample` as a required keyward argument")
if timestep_list is not None:
deprecate(
"timestep_list",
"1.0.0",
"Passing `timestep_list` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`",
)
if prev_timestep is not None:
deprecate(
"prev_timestep",
"1.0.0",
"Passing `prev_timestep` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`",
)
sigma_t, sigma_s0, sigma_s1 = (
self.sigmas[self.step_index + 1], # pyright: ignore
self.sigmas[self.step_index],
self.sigmas[self.step_index - 1], # pyright: ignore
)
alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma_t)
alpha_s0, sigma_s0 = self._sigma_to_alpha_sigma_t(sigma_s0)
alpha_s1, sigma_s1 = self._sigma_to_alpha_sigma_t(sigma_s1)
lambda_t = torch.log(alpha_t) - torch.log(sigma_t)
lambda_s0 = torch.log(alpha_s0) - torch.log(sigma_s0)
lambda_s1 = torch.log(alpha_s1) - torch.log(sigma_s1)
m0, m1 = model_output_list[-1], model_output_list[-2]
h, h_0 = lambda_t - lambda_s0, lambda_s0 - lambda_s1
r0 = h_0 / h
D0, D1 = m0, (1.0 / r0) * (m0 - m1)
if self.config.algorithm_type == "dpmsolver++":
# See https://arxiv.org/abs/2211.01095 for detailed derivations
if self.config.solver_type == "midpoint":
x_t = ((sigma_t / sigma_s0) * sample -
(alpha_t * (torch.exp(-h) - 1.0)) * D0 - 0.5 *
(alpha_t * (torch.exp(-h) - 1.0)) * D1)
elif self.config.solver_type == "heun":
x_t = ((sigma_t / sigma_s0) * sample -
(alpha_t * (torch.exp(-h) - 1.0)) * D0 +
(alpha_t * ((torch.exp(-h) - 1.0) / h + 1.0)) * D1)
elif self.config.algorithm_type == "dpmsolver":
# See https://arxiv.org/abs/2206.00927 for detailed derivations
if self.config.solver_type == "midpoint":
x_t = ((alpha_t / alpha_s0) * sample -
(sigma_t * (torch.exp(h) - 1.0)) * D0 - 0.5 *
(sigma_t * (torch.exp(h) - 1.0)) * D1)
elif self.config.solver_type == "heun":
x_t = ((alpha_t / alpha_s0) * sample -
(sigma_t * (torch.exp(h) - 1.0)) * D0 -
(sigma_t * ((torch.exp(h) - 1.0) / h - 1.0)) * D1)
elif self.config.algorithm_type == "sde-dpmsolver++":
assert noise is not None
if self.config.solver_type == "midpoint":
x_t = ((sigma_t / sigma_s0 * torch.exp(-h)) * sample +
(alpha_t * (1 - torch.exp(-2.0 * h))) * D0 + 0.5 *
(alpha_t * (1 - torch.exp(-2.0 * h))) * D1 +
sigma_t * torch.sqrt(1.0 - torch.exp(-2 * h)) * noise)
elif self.config.solver_type == "heun":
x_t = ((sigma_t / sigma_s0 * torch.exp(-h)) * sample +
(alpha_t * (1 - torch.exp(-2.0 * h))) * D0 +
(alpha_t * ((1.0 - torch.exp(-2.0 * h)) /
(-2.0 * h) + 1.0)) * D1 +
sigma_t * torch.sqrt(1.0 - torch.exp(-2 * h)) * noise)
elif self.config.algorithm_type == "sde-dpmsolver":
assert noise is not None
if self.config.solver_type == "midpoint":
x_t = ((alpha_t / alpha_s0) * sample - 2.0 *
(sigma_t * (torch.exp(h) - 1.0)) * D0 -
(sigma_t * (torch.exp(h) - 1.0)) * D1 +
sigma_t * torch.sqrt(torch.exp(2 * h) - 1.0) * noise)
elif self.config.solver_type == "heun":
x_t = ((alpha_t / alpha_s0) * sample - 2.0 *
(sigma_t * (torch.exp(h) - 1.0)) * D0 - 2.0 *
(sigma_t * ((torch.exp(h) - 1.0) / h - 1.0)) * D1 +
sigma_t * torch.sqrt(torch.exp(2 * h) - 1.0) * noise)
return x_t # pyright: ignore
# Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.multistep_dpm_solver_third_order_update
def multistep_dpm_solver_third_order_update(
self,
model_output_list: List[torch.Tensor],
*args,
sample: torch.Tensor = None,
**kwargs,
) -> torch.Tensor:
"""
One step for the third-order multistep DPMSolver.
Args:
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.
Returns:
`torch.Tensor`:
The sample tensor at the previous timestep.
"""
timestep_list = args[0] if len(args) > 0 else kwargs.pop(
"timestep_list", None)
prev_timestep = args[1] if len(args) > 1 else kwargs.pop(
"prev_timestep", None)
if sample is None:
if len(args) > 2:
sample = args[2]
else:
raise ValueError(
" missing`sample` as a required keyward argument")
if timestep_list is not None:
deprecate(
"timestep_list",
"1.0.0",
"Passing `timestep_list` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`",
)
if prev_timestep is not None:
deprecate(
"prev_timestep",
"1.0.0",
"Passing `prev_timestep` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`",
)
sigma_t, sigma_s0, sigma_s1, sigma_s2 = (
self.sigmas[self.step_index + 1], # pyright: ignore
self.sigmas[self.step_index],
self.sigmas[self.step_index - 1], # pyright: ignore
self.sigmas[self.step_index - 2], # pyright: ignore
)
alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma_t)
alpha_s0, sigma_s0 = self._sigma_to_alpha_sigma_t(sigma_s0)
alpha_s1, sigma_s1 = self._sigma_to_alpha_sigma_t(sigma_s1)
alpha_s2, sigma_s2 = self._sigma_to_alpha_sigma_t(sigma_s2)
lambda_t = torch.log(alpha_t) - torch.log(sigma_t)
lambda_s0 = torch.log(alpha_s0) - torch.log(sigma_s0)
lambda_s1 = torch.log(alpha_s1) - torch.log(sigma_s1)
lambda_s2 = torch.log(alpha_s2) - torch.log(sigma_s2)
m0, m1, m2 = model_output_list[-1], model_output_list[
-2], model_output_list[-3]
h, h_0, h_1 = lambda_t - lambda_s0, lambda_s0 - lambda_s1, lambda_s1 - lambda_s2
r0, r1 = h_0 / h, h_1 / h
D0 = m0
D1_0, D1_1 = (1.0 / r0) * (m0 - m1), (1.0 / r1) * (m1 - m2)
D1 = D1_0 + (r0 / (r0 + r1)) * (D1_0 - D1_1)
D2 = (1.0 / (r0 + r1)) * (D1_0 - D1_1)
if self.config.algorithm_type == "dpmsolver++":
# See https://arxiv.org/abs/2206.00927 for detailed derivations
x_t = ((sigma_t / sigma_s0) * sample -
(alpha_t * (torch.exp(-h) - 1.0)) * D0 +
(alpha_t * ((torch.exp(-h) - 1.0) / h + 1.0)) * D1 -
(alpha_t * ((torch.exp(-h) - 1.0 + h) / h**2 - 0.5)) * D2)
elif self.config.algorithm_type == "dpmsolver":
# See https://arxiv.org/abs/2206.00927 for detailed derivations
x_t = ((alpha_t / alpha_s0) * sample - (sigma_t *
(torch.exp(h) - 1.0)) * D0 -
(sigma_t * ((torch.exp(h) - 1.0) / h - 1.0)) * D1 -
(sigma_t * ((torch.exp(h) - 1.0 - h) / h**2 - 0.5)) * D2)
return x_t # pyright: ignore
def index_for_timestep(self, timestep, schedule_timesteps=None):
if schedule_timesteps is None:
schedule_timesteps = self.timesteps
indices = (schedule_timesteps == timestep).nonzero()
# The sigma index that is taken for the **very** first `step`
# is always the second index (or the last index if there is only 1)
# This way we can ensure we don't accidentally skip a sigma in
# case we start in the middle of the denoising schedule (e.g. for image-to-image)
pos = 1 if len(indices) > 1 else 0
return indices[pos].item()
def _init_step_index(self, timestep):
"""
Initialize the step_index counter for the scheduler.
"""
if self.begin_index is None:
if isinstance(timestep, torch.Tensor):
timestep = timestep.to(self.timesteps.device)
self._step_index = self.index_for_timestep(timestep)
else:
self._step_index = self._begin_index
# Modified from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.step
def step(
self,
model_output: torch.Tensor,
timestep: Union[int, torch.Tensor],
sample: torch.Tensor,
generator=None,
variance_noise: Optional[torch.Tensor] = None,
return_dict: bool = True,
) -> Union[SchedulerOutput, Tuple]:
"""
Predict the sample from the previous timestep by reversing the SDE. This function propagates the sample with
the multistep DPMSolver.
Args:
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.
variance_noise (`torch.Tensor`):
Alternative to generating noise with `generator` by directly providing the noise for the variance
itself. Useful for methods such as [`LEdits++`].
return_dict (`bool`):
Whether or not to return a [`~schedulers.scheduling_utils.SchedulerOutput`] or `tuple`.
Returns:
[`~schedulers.scheduling_utils.SchedulerOutput`] or `tuple`:
If return_dict is `True`, [`~schedulers.scheduling_utils.SchedulerOutput`] is returned, otherwise a
tuple is returned where the first element is the sample tensor.
"""
if self.num_inference_steps is None:
raise ValueError(
"Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler"
)
if self.step_index is None:
self._init_step_index(timestep)
# Improve numerical stability for small number of steps
lower_order_final = (self.step_index == len(self.timesteps) - 1) and (
self.config.euler_at_final or
(self.config.lower_order_final and len(self.timesteps) < 15) or
self.config.final_sigmas_type == "zero")
lower_order_second = ((self.step_index == len(self.timesteps) - 2) and
self.config.lower_order_final and
len(self.timesteps) < 15)
model_output = self.convert_model_output(model_output, sample=sample)
for i in range(self.config.solver_order - 1):
self.model_outputs[i] = self.model_outputs[i + 1]
self.model_outputs[-1] = model_output
# Upcast to avoid precision issues when computing prev_sample
sample = sample.to(torch.float32)
if self.config.algorithm_type in ["sde-dpmsolver", "sde-dpmsolver++"
] and variance_noise is None:
noise = randn_tensor(
model_output.shape,
generator=generator,
device=model_output.device,
dtype=torch.float32)
elif self.config.algorithm_type in ["sde-dpmsolver", "sde-dpmsolver++"]:
noise = variance_noise.to(
device=model_output.device,
dtype=torch.float32) # pyright: ignore
else:
noise = None
if self.config.solver_order == 1 or self.lower_order_nums < 1 or lower_order_final:
prev_sample = self.dpm_solver_first_order_update(
model_output, sample=sample, noise=noise)
elif self.config.solver_order == 2 or self.lower_order_nums < 2 or lower_order_second:
prev_sample = self.multistep_dpm_solver_second_order_update(
self.model_outputs, sample=sample, noise=noise)
else:
prev_sample = self.multistep_dpm_solver_third_order_update(
self.model_outputs, sample=sample)
if self.lower_order_nums < self.config.solver_order:
self.lower_order_nums += 1
# Cast sample back to expected dtype
prev_sample = prev_sample.to(model_output.dtype)
# upon completion increase step index by one
self._step_index += 1 # pyright: ignore
if not return_dict:
return (prev_sample,)
return SchedulerOutput(prev_sample=prev_sample)
# Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.scale_model_input
def scale_model_input(self, sample: torch.Tensor, *args,
**kwargs) -> torch.Tensor:
"""
Ensures interchangeability with schedulers that need to scale the denoising model input depending on the
current timestep.
Args:
sample (`torch.Tensor`):
The input sample.
Returns:
`torch.Tensor`:
A scaled input sample.
"""
return sample
# Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.scale_model_input
def add_noise(
self,
original_samples: torch.Tensor,
noise: torch.Tensor,
timesteps: torch.IntTensor,
) -> torch.Tensor:
# Make sure sigmas and timesteps have the same device and dtype as original_samples
sigmas = self.sigmas.to(
device=original_samples.device, dtype=original_samples.dtype)
if original_samples.device.type == "mps" and torch.is_floating_point(
timesteps):
# mps does not support float64
schedule_timesteps = self.timesteps.to(
original_samples.device, dtype=torch.float32)
timesteps = timesteps.to(
original_samples.device, dtype=torch.float32)
else:
schedule_timesteps = self.timesteps.to(original_samples.device)
timesteps = timesteps.to(original_samples.device)
# begin_index is None when the scheduler is used for training or pipeline does not implement set_begin_index
if self.begin_index is None:
step_indices = [
self.index_for_timestep(t, schedule_timesteps)
for t in timesteps
]
elif self.step_index is not None:
# add_noise is called after first denoising step (for inpainting)
step_indices = [self.step_index] * timesteps.shape[0]
else:
# add noise is called before first denoising step to create initial latent(img2img)
step_indices = [self.begin_index] * timesteps.shape[0]
sigma = sigmas[step_indices].flatten()
while len(sigma.shape) < len(original_samples.shape):
sigma = sigma.unsqueeze(-1)
alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
noisy_samples = alpha_t * original_samples + sigma_t * noise
return noisy_samples
def __len__(self):
return self.config.num_train_timesteps