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# Copyright 2024 Katherine Crowson 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. | |
import math | |
import warnings | |
from dataclasses import dataclass | |
from typing import List, Optional, Tuple, Union | |
import numpy as np | |
import torch | |
from scipy import integrate | |
from ..configuration_utils import ConfigMixin, register_to_config | |
from ..utils import BaseOutput | |
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin | |
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->LMSDiscrete | |
class LMSDiscreteSchedulerOutput(BaseOutput): | |
""" | |
Output class for the scheduler's `step` function output. | |
Args: | |
prev_sample (`torch.FloatTensor` of shape `(batch_size, num_channels, height, width)` for images): | |
Computed sample `(x_{t-1})` of previous timestep. `prev_sample` should be used as next model input in the | |
denoising loop. | |
pred_original_sample (`torch.FloatTensor` of shape `(batch_size, num_channels, height, width)` for images): | |
The predicted denoised sample `(x_{0})` based on the model output from the current timestep. | |
`pred_original_sample` can be used to preview progress or for guidance. | |
""" | |
prev_sample: torch.FloatTensor | |
pred_original_sample: Optional[torch.FloatTensor] = None | |
# 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 LMSDiscreteScheduler(SchedulerMixin, ConfigMixin): | |
""" | |
A linear multistep scheduler for discrete beta schedules. | |
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` or `scaled_linear`. | |
trained_betas (`np.ndarray`, *optional*): | |
Pass an array of betas directly to the constructor to bypass `beta_start` and `beta_end`. | |
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}. | |
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). | |
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 | |
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, | |
use_karras_sigmas: Optional[bool] = False, | |
prediction_type: str = "epsilon", | |
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) | |
sigmas = np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5) | |
sigmas = np.concatenate([sigmas[::-1], [0.0]]).astype(np.float32) | |
self.sigmas = torch.from_numpy(sigmas) | |
# setable values | |
self.num_inference_steps = None | |
self.use_karras_sigmas = use_karras_sigmas | |
self.set_timesteps(num_train_timesteps, None) | |
self.derivatives = [] | |
self.is_scale_input_called = False | |
self._step_index = None | |
self._begin_index = None | |
self.sigmas = self.sigmas.to("cpu") # to avoid too much CPU/GPU communication | |
def init_noise_sigma(self): | |
# standard deviation of the initial noise distribution | |
if self.config.timestep_spacing in ["linspace", "trailing"]: | |
return self.sigmas.max() | |
return (self.sigmas.max() ** 2 + 1) ** 0.5 | |
def step_index(self): | |
""" | |
The index counter for current timestep. It will increae 1 after each scheduler step. | |
""" | |
return self._step_index | |
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 scale_model_input( | |
self, sample: torch.FloatTensor, timestep: Union[float, torch.FloatTensor] | |
) -> 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. | |
timestep (`float` or `torch.FloatTensor`): | |
The current timestep in the diffusion chain. | |
Returns: | |
`torch.FloatTensor`: | |
A scaled input sample. | |
""" | |
if self.step_index is None: | |
self._init_step_index(timestep) | |
sigma = self.sigmas[self.step_index] | |
sample = sample / ((sigma**2 + 1) ** 0.5) | |
self.is_scale_input_called = True | |
return sample | |
def get_lms_coefficient(self, order, t, current_order): | |
""" | |
Compute the linear multistep coefficient. | |
Args: | |
order (): | |
t (): | |
current_order (): | |
""" | |
def lms_derivative(tau): | |
prod = 1.0 | |
for k in range(order): | |
if current_order == k: | |
continue | |
prod *= (tau - self.sigmas[t - k]) / (self.sigmas[t - current_order] - self.sigmas[t - k]) | |
return prod | |
integrated_coeff = integrate.quad(lms_derivative, self.sigmas[t], self.sigmas[t + 1], epsrel=1e-4)[0] | |
return integrated_coeff | |
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. | |
""" | |
self.num_inference_steps = num_inference_steps | |
# "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, dtype=np.float32)[ | |
::-1 | |
].copy() | |
elif self.config.timestep_spacing == "leading": | |
step_ratio = self.config.num_train_timesteps // self.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(0, num_inference_steps) * step_ratio).round()[::-1].copy().astype(np.float32) | |
timesteps += self.config.steps_offset | |
elif self.config.timestep_spacing == "trailing": | |
step_ratio = self.config.num_train_timesteps / self.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.float32) | |
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) | |
sigmas = np.interp(timesteps, np.arange(0, len(sigmas)), sigmas) | |
if self.use_karras_sigmas: | |
sigmas = self._convert_to_karras(in_sigmas=sigmas) | |
timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in sigmas]) | |
sigmas = np.concatenate([sigmas, [0.0]]).astype(np.float32) | |
self.sigmas = torch.from_numpy(sigmas).to(device=device) | |
self.timesteps = torch.from_numpy(timesteps).to(device=device) | |
self._step_index = None | |
self._begin_index = None | |
self.sigmas = self.sigmas.to("cpu") # to avoid too much CPU/GPU communication | |
self.derivatives = [] | |
# Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler.index_for_timestep | |
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() | |
# Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._init_step_index | |
def _init_step_index(self, timestep): | |
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 | |
# copied from diffusers.schedulers.scheduling_euler_discrete._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_euler_discrete._convert_to_karras | |
def _convert_to_karras(self, in_sigmas: torch.FloatTensor) -> 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, self.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 step( | |
self, | |
model_output: torch.FloatTensor, | |
timestep: Union[float, torch.FloatTensor], | |
sample: torch.FloatTensor, | |
order: int = 4, | |
return_dict: bool = True, | |
) -> Union[LMSDiscreteSchedulerOutput, Tuple]: | |
""" | |
Predict the sample from the previous timestep by reversing the SDE. This function propagates the diffusion | |
process from the learned model outputs (most often the predicted noise). | |
Args: | |
model_output (`torch.FloatTensor`): | |
The direct output from learned diffusion model. | |
timestep (`float` or `torch.FloatTensor`): | |
The current discrete timestep in the diffusion chain. | |
sample (`torch.FloatTensor`): | |
A current instance of a sample created by the diffusion process. | |
order (`int`, defaults to 4): | |
The order of the linear multistep method. | |
return_dict (`bool`, *optional*, defaults to `True`): | |
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 not self.is_scale_input_called: | |
warnings.warn( | |
"The `scale_model_input` function should be called before `step` to ensure correct denoising. " | |
"See `StableDiffusionPipeline` for a usage example." | |
) | |
if self.step_index is None: | |
self._init_step_index(timestep) | |
sigma = self.sigmas[self.step_index] | |
# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise | |
if self.config.prediction_type == "epsilon": | |
pred_original_sample = sample - sigma * model_output | |
elif self.config.prediction_type == "v_prediction": | |
# * c_out + input * c_skip | |
pred_original_sample = model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1)) | |
elif self.config.prediction_type == "sample": | |
pred_original_sample = model_output | |
else: | |
raise ValueError( | |
f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`" | |
) | |
# 2. Convert to an ODE derivative | |
derivative = (sample - pred_original_sample) / sigma | |
self.derivatives.append(derivative) | |
if len(self.derivatives) > order: | |
self.derivatives.pop(0) | |
# 3. Compute linear multistep coefficients | |
order = min(self.step_index + 1, order) | |
lms_coeffs = [self.get_lms_coefficient(order, self.step_index, curr_order) for curr_order in range(order)] | |
# 4. Compute previous sample based on the derivatives path | |
prev_sample = sample + sum( | |
coeff * derivative for coeff, derivative in zip(lms_coeffs, reversed(self.derivatives)) | |
) | |
# upon completion increase step index by one | |
self._step_index += 1 | |
if not return_dict: | |
return (prev_sample,) | |
return LMSDiscreteSchedulerOutput(prev_sample=prev_sample, pred_original_sample=pred_original_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) | |
# self.begin_index is None when 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] | |
else: | |
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) | |
noisy_samples = original_samples + noise * sigma | |
return noisy_samples | |
def __len__(self): | |
return self.config.num_train_timesteps | |