# Copyright 2023 TSAIL Team and The HuggingFace Team. All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# DISCLAIMER: This file is strongly influenced by https://github.com/LuChengTHU/dpm-solver
import math
from typing import List, Optional, Tuple, Union
import numpy as np
import torch
from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import deprecate
from ..utils.torch_utils import randn_tensor
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput
# Copied from diffusers.schedulers.scheduling_ddpm.betas_for_alpha_bar
def betas_for_alpha_bar(
num_diffusion_timesteps,
max_beta=0.999,
alpha_transform_type="cosine",
):
"""
Create a beta schedule that discretizes the given alpha_t_bar function, which defines the cumulative product of
(1-beta) over time from t = [0,1].
Contains a function alpha_bar that takes an argument t and transforms it to the cumulative product of (1-beta) up
to that part of the diffusion process.
Args:
num_diffusion_timesteps (`int`): the number of betas to produce.
max_beta (`float`): the maximum beta to use; use values lower than 1 to
prevent singularities.
alpha_transform_type (`str`, *optional*, default to `cosine`): the type of noise schedule for alpha_bar.
Choose from `cosine` or `exp`
Returns:
betas (`np.ndarray`): the betas used by the scheduler to step the model outputs
"""
if alpha_transform_type == "cosine":
def alpha_bar_fn(t):
return math.cos((t + 0.008) / 1.008 * math.pi / 2) ** 2
elif alpha_transform_type == "exp":
def alpha_bar_fn(t):
return math.exp(t * -12.0)
else:
raise ValueError(f"Unsupported alpha_tranform_type: {alpha_transform_type}")
betas = []
for i in range(num_diffusion_timesteps):
t1 = i / num_diffusion_timesteps
t2 = (i + 1) / num_diffusion_timesteps
betas.append(min(1 - alpha_bar_fn(t2) / alpha_bar_fn(t1), max_beta))
return torch.tensor(betas, dtype=torch.float32)
class DPMSolverMultistepScheduler(SchedulerMixin, ConfigMixin):
"""
`DPMSolverMultistepScheduler` 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.
beta_start (`float`, defaults to 0.0001):
The starting `beta` value of inference.
beta_end (`float`, defaults to 0.02):
The final `beta` value.
beta_schedule (`str`, defaults to `"linear"`):
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*):
Pass an array of betas directly to the constructor to bypass `beta_start` and `beta_end`.
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`, `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.
use_karras_sigmas (`bool`, *optional*, defaults to `False`):
Whether to use Karras sigmas for step sizes in the noise schedule during the sampling process. If `True`,
the sigmas are determined according to a sequence of noise levels {σi}.
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.
timestep_spacing (`str`, defaults to `"linspace"`):
The way the timesteps should be scaled. Refer to Table 2 of the [Common Diffusion Noise Schedules and
Sample Steps are Flawed](https://huggingface.co/papers/2305.08891) for more information.
steps_offset (`int`, defaults to 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 like in Stable
Diffusion.
"""
_compatibles = [e.name for e in KarrasDiffusionSchedulers]
order = 1
@register_to_config
def __init__(
self,
num_train_timesteps: int = 1000,
beta_start: float = 0.0001,
beta_end: float = 0.02,
beta_schedule: str = "linear",
trained_betas: Optional[Union[np.ndarray, List[float]]] = 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: Optional[bool] = False,
lambda_min_clipped: float = -float("inf"),
variance_type: Optional[str] = None,
timestep_spacing: str = "linspace",
steps_offset: int = 0,
):
if trained_betas is not None:
self.betas = torch.tensor(trained_betas, dtype=torch.float32)
elif beta_schedule == "linear":
self.betas = torch.linspace(beta_start, beta_end, num_train_timesteps, dtype=torch.float32)
elif beta_schedule == "scaled_linear":
# this schedule is very specific to the latent diffusion model.
self.betas = (
torch.linspace(beta_start**0.5, beta_end**0.5, num_train_timesteps, dtype=torch.float32) ** 2
)
elif beta_schedule == "squaredcos_cap_v2":
# Glide cosine schedule
self.betas = betas_for_alpha_bar(num_train_timesteps)
else:
raise NotImplementedError(f"{beta_schedule} does is not implemented for {self.__class__}")
self.alphas = 1.0 - self.betas
self.alphas_cumprod = torch.cumprod(self.alphas, dim=0)
# Currently we only support VP-type noise schedule
self.alpha_t = torch.sqrt(self.alphas_cumprod)
self.sigma_t = torch.sqrt(1 - self.alphas_cumprod)
self.lambda_t = torch.log(self.alpha_t) - torch.log(self.sigma_t)
# standard deviation of the initial noise distribution
self.init_noise_sigma = 1.0
# 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} does 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} does is not implemented for {self.__class__}")
# setable values
self.num_inference_steps = None
timesteps = np.linspace(0, num_train_timesteps - 1, num_train_timesteps, dtype=np.float32)[::-1].copy()
self.timesteps = torch.from_numpy(timesteps)
self.model_outputs = [None] * solver_order
self.lower_order_nums = 0
self._step_index = None
@property
def step_index(self):
"""
The index counter for current timestep. It will increae 1 after each scheduler step.
"""
return self._step_index
def set_timesteps(self, num_inference_steps: int = None, device: Union[str, torch.device] = None):
"""
Sets the discrete timesteps used for the diffusion chain (to be run before inference).
Args:
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.
"""
# Clipping the minimum of all lambda(t) for numerical stability.
# This is critical for cosine (squaredcos_cap_v2) noise schedule.
clipped_idx = torch.searchsorted(torch.flip(self.lambda_t, [0]), self.config.lambda_min_clipped)
last_timestep = ((self.config.num_train_timesteps - clipped_idx).numpy()).item()
# "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
if self.config.timestep_spacing == "linspace":
timesteps = (
np.linspace(0, last_timestep - 1, num_inference_steps + 1).round()[::-1][:-1].copy().astype(np.int64)
)
elif self.config.timestep_spacing == "leading":
step_ratio = last_timestep // (num_inference_steps + 1)
# creates integer timesteps by multiplying by ratio
# casting to int to avoid issues when num_inference_step is power of 3
timesteps = (np.arange(0, num_inference_steps + 1) * step_ratio).round()[::-1][:-1].copy().astype(np.int64)
timesteps += self.config.steps_offset
elif self.config.timestep_spacing == "trailing":
step_ratio = self.config.num_train_timesteps / num_inference_steps
# creates integer timesteps by multiplying by ratio
# casting to int to avoid issues when num_inference_step is power of 3
timesteps = np.arange(last_timestep, 0, -step_ratio).round().copy().astype(np.int64)
timesteps -= 1
else:
raise ValueError(
f"{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'linspace', 'leading' or 'trailing'."
)
sigmas = np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5)
log_sigmas = np.log(sigmas)
if self.config.use_karras_sigmas:
sigmas = np.flip(sigmas).copy()
sigmas = self._convert_to_karras(in_sigmas=sigmas, num_inference_steps=num_inference_steps)
timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in sigmas]).round()
sigmas = np.concatenate([sigmas, sigmas[-1:]]).astype(np.float32)
else:
sigmas = np.interp(timesteps, np.arange(0, len(sigmas)), sigmas)
sigma_last = ((1 - self.alphas_cumprod[0]) / self.alphas_cumprod[0]) ** 0.5
sigmas = np.concatenate([sigmas, [sigma_last]]).astype(np.float32)
self.sigmas = torch.from_numpy(sigmas).to(device=device)
self.timesteps = torch.from_numpy(timesteps).to(device)
self.num_inference_steps = len(timesteps)
self.model_outputs = [
None,
] * self.config.solver_order
self.lower_order_nums = 0
# add an index counter for schedulers that allow duplicated timesteps
self._step_index = None
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMScheduler._threshold_sample
def _threshold_sample(self, sample: torch.FloatTensor) -> torch.FloatTensor:
"""
"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, height, width = 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 * height * width)
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, height, width)
sample = sample.to(dtype)
return sample
# Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._sigma_to_t
def _sigma_to_t(self, sigma, log_sigmas):
# get log sigma
log_sigma = np.log(sigma)
# get distribution
dists = log_sigma - log_sigmas[:, np.newaxis]
# get sigmas range
low_idx = np.cumsum((dists >= 0), axis=0).argmax(axis=0).clip(max=log_sigmas.shape[0] - 2)
high_idx = low_idx + 1
low = log_sigmas[low_idx]
high = log_sigmas[high_idx]
# interpolate sigmas
w = (low - log_sigma) / (low - high)
w = np.clip(w, 0, 1)
# transform interpolation to time range
t = (1 - w) * low_idx + w * high_idx
t = t.reshape(sigma.shape)
return t
def _sigma_to_alpha_sigma_t(self, sigma):
alpha_t = 1 / ((sigma**2 + 1) ** 0.5)
sigma_t = sigma * alpha_t
return alpha_t, sigma_t
# Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_karras
def _convert_to_karras(self, in_sigmas: torch.FloatTensor, num_inference_steps) -> torch.FloatTensor:
"""Constructs the noise schedule of Karras et al. (2022)."""
sigma_min: float = in_sigmas[-1].item()
sigma_max: float = in_sigmas[0].item()
rho = 7.0 # 7.0 is the value used in the paper
ramp = np.linspace(0, 1, num_inference_steps)
min_inv_rho = sigma_min ** (1 / rho)
max_inv_rho = sigma_max ** (1 / rho)
sigmas = (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
return sigmas
def convert_model_output(
self,
model_output: torch.FloatTensor,
*args,
sample: torch.FloatTensor = None,
**kwargs,
) -> torch.FloatTensor:
"""
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.FloatTensor`):
The direct output from the learned diffusion model.
sample (`torch.FloatTensor`):
A current instance of a sample created by the diffusion process.
Returns:
`torch.FloatTensor`:
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 == "epsilon":
# DPM-Solver and DPM-Solver++ only need the "mean" output.
if self.config.variance_type in ["learned", "learned_range"]:
model_output = model_output[:, :3]
sigma = self.sigmas[self.step_index]
alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
x0_pred = (sample - sigma_t * model_output) / alpha_t
elif self.config.prediction_type == "sample":
x0_pred = model_output
elif self.config.prediction_type == "v_prediction":
sigma = self.sigmas[self.step_index]
alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
x0_pred = alpha_t * sample - sigma_t * model_output
else:
raise ValueError(
f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or"
" `v_prediction` for the DPMSolverMultistepScheduler."
)
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 == "epsilon":
# DPM-Solver and DPM-Solver++ only need the "mean" output.
if self.config.variance_type in ["learned", "learned_range"]:
epsilon = model_output[:, :3]
else:
epsilon = model_output
elif self.config.prediction_type == "sample":
sigma = self.sigmas[self.step_index]
alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
epsilon = (sample - alpha_t * model_output) / sigma_t
elif self.config.prediction_type == "v_prediction":
sigma = self.sigmas[self.step_index]
alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
epsilon = alpha_t * model_output + sigma_t * sample
else:
raise ValueError(
f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or"
" `v_prediction` for the DPMSolverMultistepScheduler."
)
if self.config.thresholding:
sigma = self.sigmas[self.step_index]
alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
x0_pred = (sample - sigma_t * epsilon) / alpha_t
x0_pred = self._threshold_sample(x0_pred)
epsilon = (sample - alpha_t * x0_pred) / sigma_t
return epsilon
def dpm_solver_first_order_update(
self,
model_output: torch.FloatTensor,
*args,
sample: torch.FloatTensor = None,
noise: Optional[torch.FloatTensor] = None,
**kwargs,
) -> torch.FloatTensor:
"""
One step for the first-order DPMSolver (equivalent to DDIM).
Args:
model_output (`torch.FloatTensor`):
The direct output from the learned diffusion model.
sample (`torch.FloatTensor`):
A current instance of a sample created by the diffusion process.
Returns:
`torch.FloatTensor`:
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]
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
def multistep_dpm_solver_second_order_update(
self,
model_output_list: List[torch.FloatTensor],
*args,
sample: torch.FloatTensor = None,
noise: Optional[torch.FloatTensor] = None,
**kwargs,
) -> torch.FloatTensor:
"""
One step for the second-order multistep DPMSolver.
Args:
model_output_list (`List[torch.FloatTensor]`):
The direct outputs from learned diffusion model at current and latter timesteps.
sample (`torch.FloatTensor`):
A current instance of a sample created by the diffusion process.
Returns:
`torch.FloatTensor`:
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],
self.sigmas[self.step_index],
self.sigmas[self.step_index - 1],
)
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
def multistep_dpm_solver_third_order_update(
self,
model_output_list: List[torch.FloatTensor],
*args,
sample: torch.FloatTensor = None,
**kwargs,
) -> torch.FloatTensor:
"""
One step for the third-order multistep DPMSolver.
Args:
model_output_list (`List[torch.FloatTensor]`):
The direct outputs from learned diffusion model at current and latter timesteps.
sample (`torch.FloatTensor`):
A current instance of a sample created by diffusion process.
Returns:
`torch.FloatTensor`:
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],
self.sigmas[self.step_index],
self.sigmas[self.step_index - 1],
self.sigmas[self.step_index - 2],
)
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
def _init_step_index(self, timestep):
if isinstance(timestep, torch.Tensor):
timestep = timestep.to(self.timesteps.device)
index_candidates = (self.timesteps == timestep).nonzero()
if len(index_candidates) == 0:
step_index = len(self.timesteps) - 1
# 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)
elif len(index_candidates) > 1:
step_index = index_candidates[1].item()
else:
step_index = index_candidates[0].item()
self._step_index = step_index
def step(
self,
model_output: torch.FloatTensor,
timestep: int,
sample: torch.FloatTensor,
generator=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.FloatTensor`):
The direct output from learned diffusion model.
timestep (`int`):
The current discrete timestep in the diffusion chain.
sample (`torch.FloatTensor`):
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 [`~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)
lower_order_final = (
(self.step_index == len(self.timesteps) - 1) and self.config.lower_order_final and len(self.timesteps) < 15
)
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
if self.config.algorithm_type in ["sde-dpmsolver", "sde-dpmsolver++"]:
noise = randn_tensor(
model_output.shape, generator=generator, device=model_output.device, dtype=model_output.dtype
)
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
# upon completion increase step index by one
self._step_index += 1
if not return_dict:
return (prev_sample,)
return SchedulerOutput(prev_sample=prev_sample)
def scale_model_input(self, sample: torch.FloatTensor, *args, **kwargs) -> torch.FloatTensor:
"""
Ensures interchangeability with schedulers that need to scale the denoising model input depending on the
current timestep.
Args:
sample (`torch.FloatTensor`):
The input sample.
Returns:
`torch.FloatTensor`:
A scaled input sample.
"""
return sample
# Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler.add_noise
def add_noise(
self,
original_samples: torch.FloatTensor,
noise: torch.FloatTensor,
timesteps: torch.FloatTensor,
) -> torch.FloatTensor:
# 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)
step_indices = [(schedule_timesteps == t).nonzero().item() for t in timesteps]
sigma = sigmas[step_indices].flatten()
while len(sigma.shape) < len(original_samples.shape):
sigma = sigma.unsqueeze(-1)
noisy_samples = original_samples + noise * sigma
return noisy_samples
def __len__(self):
return self.config.num_train_timesteps