# Copyright 2024 FLAIR Lab 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: check https://arxiv.org/abs/2204.13902 and https://github.com/qsh-zh/deis for more info
# The codebase is modified based on https://github.com/huggingface/diffusers/blob/main/src/diffusers/schedulers/scheduling_dpmsolver_multistep.py
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, is_scipy_available
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput
if is_scipy_available():
import scipy.stats
# 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_transform_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 DEISMultistepScheduler(SchedulerMixin, ConfigMixin):
"""
`DEISMultistepScheduler` is a fast high order solver for diffusion ordinary differential equations (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 DEIS 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`):
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`.
algorithm_type (`str`, defaults to `deis`):
The algorithm type for the solver.
lower_order_final (`bool`, defaults to `True`):
Whether to use lower-order solvers in the final steps. Only valid for < 15 inference steps.
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}.
use_exponential_sigmas (`bool`, *optional*, defaults to `False`):
Whether to use exponential sigmas for step sizes in the noise schedule during the sampling process.
use_beta_sigmas (`bool`, *optional*, defaults to `False`):
Whether to use beta sigmas for step sizes in the noise schedule during the sampling process. Refer to [Beta
Sampling is All You Need](https://huggingface.co/papers/2407.12173) for more information.
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, as required by some model families.
"""
_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[np.ndarray] = 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 = "deis",
solver_type: str = "logrho",
lower_order_final: bool = True,
use_karras_sigmas: Optional[bool] = False,
use_exponential_sigmas: Optional[bool] = False,
use_beta_sigmas: Optional[bool] = False,
use_flow_sigmas: Optional[bool] = False,
flow_shift: Optional[float] = 1.0,
timestep_spacing: str = "linspace",
steps_offset: int = 0,
):
if self.config.use_beta_sigmas and not is_scipy_available():
raise ImportError("Make sure to install scipy if you want to use beta sigmas.")
if sum([self.config.use_beta_sigmas, self.config.use_exponential_sigmas, self.config.use_karras_sigmas]) > 1:
raise ValueError(
"Only one of `config.use_beta_sigmas`, `config.use_exponential_sigmas`, `config.use_karras_sigmas` can be used."
)
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} 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)
self.sigmas = ((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5
# standard deviation of the initial noise distribution
self.init_noise_sigma = 1.0
# settings for DEIS
if algorithm_type not in ["deis"]:
if algorithm_type in ["dpmsolver", "dpmsolver++"]:
self.register_to_config(algorithm_type="deis")
else:
raise NotImplementedError(f"{algorithm_type} is not implemented for {self.__class__}")
if solver_type not in ["logrho"]:
if solver_type in ["midpoint", "heun", "bh1", "bh2"]:
self.register_to_config(solver_type="logrho")
else:
raise NotImplementedError(f"solver type {solver_type} 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
self._begin_index = None
self.sigmas = self.sigmas.to("cpu") # to avoid too much CPU/GPU communication
@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
def set_timesteps(self, num_inference_steps: int, 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.
"""
# "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, self.config.num_train_timesteps - 1, num_inference_steps + 1)
.round()[::-1][:-1]
.copy()
.astype(np.int64)
)
elif self.config.timestep_spacing == "leading":
step_ratio = self.config.num_train_timesteps // (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(self.config.num_train_timesteps, 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)
elif self.config.use_exponential_sigmas:
sigmas = np.flip(sigmas).copy()
sigmas = self._convert_to_exponential(in_sigmas=sigmas, num_inference_steps=num_inference_steps)
timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in sigmas])
sigmas = np.concatenate([sigmas, sigmas[-1:]]).astype(np.float32)
elif self.config.use_beta_sigmas:
sigmas = np.flip(sigmas).copy()
sigmas = self._convert_to_beta(in_sigmas=sigmas, num_inference_steps=num_inference_steps)
timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in sigmas])
sigmas = np.concatenate([sigmas, sigmas[-1:]]).astype(np.float32)
elif self.config.use_flow_sigmas:
alphas = np.linspace(1, 1 / self.config.num_train_timesteps, num_inference_steps + 1)
sigmas = 1.0 - alphas
sigmas = np.flip(self.config.flow_shift * sigmas / (1 + (self.config.flow_shift - 1) * sigmas))[:-1]
timesteps = (sigmas * self.config.num_train_timesteps).copy()
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)
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
# add an index counter for schedulers that allow duplicated timesteps
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_euler_discrete.EulerDiscreteScheduler._sigma_to_t
def _sigma_to_t(self, sigma, log_sigmas):
# get log sigma
log_sigma = np.log(np.maximum(sigma, 1e-10))
# 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
# Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler._sigma_to_alpha_sigma_t
def _sigma_to_alpha_sigma_t(self, sigma):
if self.config.use_flow_sigmas:
alpha_t = 1 - sigma
sigma_t = sigma
else:
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.Tensor, num_inference_steps) -> torch.Tensor:
"""Constructs the noise schedule of Karras et al. (2022)."""
# Hack to make sure that other schedulers which copy this function don't break
# TODO: Add this logic to the other schedulers
if hasattr(self.config, "sigma_min"):
sigma_min = self.config.sigma_min
else:
sigma_min = None
if hasattr(self.config, "sigma_max"):
sigma_max = self.config.sigma_max
else:
sigma_max = None
sigma_min = sigma_min if sigma_min is not None else in_sigmas[-1].item()
sigma_max = sigma_max if sigma_max is not None else 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
# Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_exponential
def _convert_to_exponential(self, in_sigmas: torch.Tensor, num_inference_steps: int) -> torch.Tensor:
"""Constructs an exponential noise schedule."""
# Hack to make sure that other schedulers which copy this function don't break
# TODO: Add this logic to the other schedulers
if hasattr(self.config, "sigma_min"):
sigma_min = self.config.sigma_min
else:
sigma_min = None
if hasattr(self.config, "sigma_max"):
sigma_max = self.config.sigma_max
else:
sigma_max = None
sigma_min = sigma_min if sigma_min is not None else in_sigmas[-1].item()
sigma_max = sigma_max if sigma_max is not None else in_sigmas[0].item()
sigmas = np.exp(np.linspace(math.log(sigma_max), math.log(sigma_min), num_inference_steps))
return sigmas
# Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_beta
def _convert_to_beta(
self, in_sigmas: torch.Tensor, num_inference_steps: int, alpha: float = 0.6, beta: float = 0.6
) -> torch.Tensor:
"""From "Beta Sampling is All You Need" [arXiv:2407.12173] (Lee et. al, 2024)"""
# Hack to make sure that other schedulers which copy this function don't break
# TODO: Add this logic to the other schedulers
if hasattr(self.config, "sigma_min"):
sigma_min = self.config.sigma_min
else:
sigma_min = None
if hasattr(self.config, "sigma_max"):
sigma_max = self.config.sigma_max
else:
sigma_max = None
sigma_min = sigma_min if sigma_min is not None else in_sigmas[-1].item()
sigma_max = sigma_max if sigma_max is not None else in_sigmas[0].item()
sigmas = np.array(
[
sigma_min + (ppf * (sigma_max - sigma_min))
for ppf in [
scipy.stats.beta.ppf(timestep, alpha, beta)
for timestep in 1 - np.linspace(0, 1, num_inference_steps)
]
]
)
return sigmas
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 DEIS algorithm needs.
Args:
model_output (`torch.Tensor`):
The direct output from the 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.
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`",
)
sigma = self.sigmas[self.step_index]
alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
if self.config.prediction_type == "epsilon":
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":
x0_pred = alpha_t * sample - sigma_t * model_output
elif 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 DEISMultistepScheduler."
)
if self.config.thresholding:
x0_pred = self._threshold_sample(x0_pred)
if self.config.algorithm_type == "deis":
return (sample - alpha_t * x0_pred) / sigma_t
else:
raise NotImplementedError("only support log-rho multistep deis now")
def deis_first_order_update(
self,
model_output: torch.Tensor,
*args,
sample: torch.Tensor = None,
**kwargs,
) -> torch.Tensor:
"""
One step for the first-order DEIS (equivalent to DDIM).
Args:
model_output (`torch.Tensor`):
The direct output from the learned diffusion model.
timestep (`int`):
The current discrete timestep in the diffusion chain.
prev_timestep (`int`):
The previous discrete timestep in the diffusion chain.
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]
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 == "deis":
x_t = (alpha_t / alpha_s) * sample - (sigma_t * (torch.exp(h) - 1.0)) * model_output
else:
raise NotImplementedError("only support log-rho multistep deis now")
return x_t
def multistep_deis_second_order_update(
self,
model_output_list: List[torch.Tensor],
*args,
sample: torch.Tensor = None,
**kwargs,
) -> torch.Tensor:
"""
One step for the second-order multistep DEIS.
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],
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)
m0, m1 = model_output_list[-1], model_output_list[-2]
rho_t, rho_s0, rho_s1 = sigma_t / alpha_t, sigma_s0 / alpha_s0, sigma_s1 / alpha_s1
if self.config.algorithm_type == "deis":
def ind_fn(t, b, c):
# Integrate[(log(t) - log(c)) / (log(b) - log(c)), {t}]
return t * (-np.log(c) + np.log(t) - 1) / (np.log(b) - np.log(c))
coef1 = ind_fn(rho_t, rho_s0, rho_s1) - ind_fn(rho_s0, rho_s0, rho_s1)
coef2 = ind_fn(rho_t, rho_s1, rho_s0) - ind_fn(rho_s0, rho_s1, rho_s0)
x_t = alpha_t * (sample / alpha_s0 + coef1 * m0 + coef2 * m1)
return x_t
else:
raise NotImplementedError("only support log-rho multistep deis now")
def multistep_deis_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 DEIS.
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],
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)
m0, m1, m2 = model_output_list[-1], model_output_list[-2], model_output_list[-3]
rho_t, rho_s0, rho_s1, rho_s2 = (
sigma_t / alpha_t,
sigma_s0 / alpha_s0,
sigma_s1 / alpha_s1,
sigma_s2 / alpha_s2,
)
if self.config.algorithm_type == "deis":
def ind_fn(t, b, c, d):
# Integrate[(log(t) - log(c))(log(t) - log(d)) / (log(b) - log(c))(log(b) - log(d)), {t}]
numerator = t * (
np.log(c) * (np.log(d) - np.log(t) + 1)
- np.log(d) * np.log(t)
+ np.log(d)
+ np.log(t) ** 2
- 2 * np.log(t)
+ 2
)
denominator = (np.log(b) - np.log(c)) * (np.log(b) - np.log(d))
return numerator / denominator
coef1 = ind_fn(rho_t, rho_s0, rho_s1, rho_s2) - ind_fn(rho_s0, rho_s0, rho_s1, rho_s2)
coef2 = ind_fn(rho_t, rho_s1, rho_s2, rho_s0) - ind_fn(rho_s0, rho_s1, rho_s2, rho_s0)
coef3 = ind_fn(rho_t, rho_s2, rho_s0, rho_s1) - ind_fn(rho_s0, rho_s2, rho_s0, rho_s1)
x_t = alpha_t * (sample / alpha_s0 + coef1 * m0 + coef2 * m1 + coef3 * m2)
return x_t
else:
raise NotImplementedError("only support log-rho multistep deis now")
# Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.index_for_timestep
def index_for_timestep(self, timestep, schedule_timesteps=None):
if schedule_timesteps is None:
schedule_timesteps = self.timesteps
index_candidates = (schedule_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()
return step_index
# Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler._init_step_index
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
def step(
self,
model_output: torch.Tensor,
timestep: Union[int, torch.Tensor],
sample: torch.Tensor,
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 DEIS.
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.
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.solver_order == 1 or self.lower_order_nums < 1 or lower_order_final:
prev_sample = self.deis_first_order_update(model_output, sample=sample)
elif self.config.solver_order == 2 or self.lower_order_nums < 2 or lower_order_second:
prev_sample = self.multistep_deis_second_order_update(self.model_outputs, sample=sample)
else:
prev_sample = self.multistep_deis_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.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.add_noise
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