# Copyright 2024 Google Brain and The HuggingFace Team. All rights reserved.
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# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
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# http://www.apache.org/licenses/LICENSE-2.0
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# Unless required by applicable law or agreed to in writing, software
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# DISCLAIMER: This file is strongly influenced by https://github.com/yang-song/score_sde_pytorch
import math
from dataclasses import dataclass
from typing import Optional, Tuple, Union
import torch
from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput
from ..utils.torch_utils import randn_tensor
from .scheduling_utils import SchedulerMixin, SchedulerOutput
@dataclass
class SdeVeOutput(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.
prev_sample_mean (`torch.FloatTensor` of shape `(batch_size, num_channels, height, width)` for images):
Mean averaged `prev_sample` over previous timesteps.
"""
prev_sample: torch.FloatTensor
prev_sample_mean: torch.FloatTensor
class ScoreSdeVeScheduler(SchedulerMixin, ConfigMixin):
"""
`ScoreSdeVeScheduler` is a variance exploding stochastic differential equation (SDE) scheduler.
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.
snr (`float`, defaults to 0.15):
A coefficient weighting the step from the `model_output` sample (from the network) to the random noise.
sigma_min (`float`, defaults to 0.01):
The initial noise scale for the sigma sequence in the sampling procedure. The minimum sigma should mirror
the distribution of the data.
sigma_max (`float`, defaults to 1348.0):
The maximum value used for the range of continuous timesteps passed into the model.
sampling_eps (`float`, defaults to 1e-5):
The end value of sampling where timesteps decrease progressively from 1 to epsilon.
correct_steps (`int`, defaults to 1):
The number of correction steps performed on a produced sample.
"""
order = 1
@register_to_config
def __init__(
self,
num_train_timesteps: int = 2000,
snr: float = 0.15,
sigma_min: float = 0.01,
sigma_max: float = 1348.0,
sampling_eps: float = 1e-5,
correct_steps: int = 1,
):
# standard deviation of the initial noise distribution
self.init_noise_sigma = sigma_max
# setable values
self.timesteps = None
self.set_sigmas(num_train_timesteps, sigma_min, sigma_max, sampling_eps)
def scale_model_input(self, sample: torch.FloatTensor, timestep: Optional[int] = None) -> 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 (`int`, *optional*):
The current timestep in the diffusion chain.
Returns:
`torch.FloatTensor`:
A scaled input sample.
"""
return sample
def set_timesteps(
self, num_inference_steps: int, sampling_eps: float = None, device: Union[str, torch.device] = None
):
"""
Sets the continuous 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.
sampling_eps (`float`, *optional*):
The final timestep value (overrides value given during scheduler instantiation).
device (`str` or `torch.device`, *optional*):
The device to which the timesteps should be moved to. If `None`, the timesteps are not moved.
"""
sampling_eps = sampling_eps if sampling_eps is not None else self.config.sampling_eps
self.timesteps = torch.linspace(1, sampling_eps, num_inference_steps, device=device)
def set_sigmas(
self, num_inference_steps: int, sigma_min: float = None, sigma_max: float = None, sampling_eps: float = None
):
"""
Sets the noise scales used for the diffusion chain (to be run before inference). The sigmas control the weight
of the `drift` and `diffusion` components of the sample update.
Args:
num_inference_steps (`int`):
The number of diffusion steps used when generating samples with a pre-trained model.
sigma_min (`float`, optional):
The initial noise scale value (overrides value given during scheduler instantiation).
sigma_max (`float`, optional):
The final noise scale value (overrides value given during scheduler instantiation).
sampling_eps (`float`, optional):
The final timestep value (overrides value given during scheduler instantiation).
"""
sigma_min = sigma_min if sigma_min is not None else self.config.sigma_min
sigma_max = sigma_max if sigma_max is not None else self.config.sigma_max
sampling_eps = sampling_eps if sampling_eps is not None else self.config.sampling_eps
if self.timesteps is None:
self.set_timesteps(num_inference_steps, sampling_eps)
self.sigmas = sigma_min * (sigma_max / sigma_min) ** (self.timesteps / sampling_eps)
self.discrete_sigmas = torch.exp(torch.linspace(math.log(sigma_min), math.log(sigma_max), num_inference_steps))
self.sigmas = torch.tensor([sigma_min * (sigma_max / sigma_min) ** t for t in self.timesteps])
def get_adjacent_sigma(self, timesteps, t):
return torch.where(
timesteps == 0,
torch.zeros_like(t.to(timesteps.device)),
self.discrete_sigmas[timesteps - 1].to(timesteps.device),
)
def step_pred(
self,
model_output: torch.FloatTensor,
timestep: int,
sample: torch.FloatTensor,
generator: Optional[torch.Generator] = None,
return_dict: bool = True,
) -> Union[SdeVeOutput, 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 (`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`, *optional*, defaults to `True`):
Whether or not to return a [`~schedulers.scheduling_sde_ve.SdeVeOutput`] or `tuple`.
Returns:
[`~schedulers.scheduling_sde_ve.SdeVeOutput`] or `tuple`:
If return_dict is `True`, [`~schedulers.scheduling_sde_ve.SdeVeOutput`] is returned, otherwise a tuple
is returned where the first element is the sample tensor.
"""
if self.timesteps is None:
raise ValueError(
"`self.timesteps` is not set, you need to run 'set_timesteps' after creating the scheduler"
)
timestep = timestep * torch.ones(
sample.shape[0], device=sample.device
) # torch.repeat_interleave(timestep, sample.shape[0])
timesteps = (timestep * (len(self.timesteps) - 1)).long()
# mps requires indices to be in the same device, so we use cpu as is the default with cuda
timesteps = timesteps.to(self.discrete_sigmas.device)
sigma = self.discrete_sigmas[timesteps].to(sample.device)
adjacent_sigma = self.get_adjacent_sigma(timesteps, timestep).to(sample.device)
drift = torch.zeros_like(sample)
diffusion = (sigma**2 - adjacent_sigma**2) ** 0.5
# equation 6 in the paper: the model_output modeled by the network is grad_x log pt(x)
# also equation 47 shows the analog from SDE models to ancestral sampling methods
diffusion = diffusion.flatten()
while len(diffusion.shape) < len(sample.shape):
diffusion = diffusion.unsqueeze(-1)
drift = drift - diffusion**2 * model_output
# equation 6: sample noise for the diffusion term of
noise = randn_tensor(
sample.shape, layout=sample.layout, generator=generator, device=sample.device, dtype=sample.dtype
)
prev_sample_mean = sample - drift # subtract because `dt` is a small negative timestep
# TODO is the variable diffusion the correct scaling term for the noise?
prev_sample = prev_sample_mean + diffusion * noise # add impact of diffusion field g
if not return_dict:
return (prev_sample, prev_sample_mean)
return SdeVeOutput(prev_sample=prev_sample, prev_sample_mean=prev_sample_mean)
def step_correct(
self,
model_output: torch.FloatTensor,
sample: torch.FloatTensor,
generator: Optional[torch.Generator] = None,
return_dict: bool = True,
) -> Union[SchedulerOutput, Tuple]:
"""
Correct the predicted sample based on the `model_output` of the network. This is often run repeatedly after
making the prediction for the previous timestep.
Args:
model_output (`torch.FloatTensor`):
The direct output from learned diffusion model.
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`, *optional*, defaults to `True`):
Whether or not to return a [`~schedulers.scheduling_sde_ve.SdeVeOutput`] or `tuple`.
Returns:
[`~schedulers.scheduling_sde_ve.SdeVeOutput`] or `tuple`:
If return_dict is `True`, [`~schedulers.scheduling_sde_ve.SdeVeOutput`] is returned, otherwise a tuple
is returned where the first element is the sample tensor.
"""
if self.timesteps is None:
raise ValueError(
"`self.timesteps` is not set, you need to run 'set_timesteps' after creating the scheduler"
)
# For small batch sizes, the paper "suggest replacing norm(z) with sqrt(d), where d is the dim. of z"
# sample noise for correction
noise = randn_tensor(sample.shape, layout=sample.layout, generator=generator).to(sample.device)
# compute step size from the model_output, the noise, and the snr
grad_norm = torch.norm(model_output.reshape(model_output.shape[0], -1), dim=-1).mean()
noise_norm = torch.norm(noise.reshape(noise.shape[0], -1), dim=-1).mean()
step_size = (self.config.snr * noise_norm / grad_norm) ** 2 * 2
step_size = step_size * torch.ones(sample.shape[0]).to(sample.device)
# self.repeat_scalar(step_size, sample.shape[0])
# compute corrected sample: model_output term and noise term
step_size = step_size.flatten()
while len(step_size.shape) < len(sample.shape):
step_size = step_size.unsqueeze(-1)
prev_sample_mean = sample + step_size * model_output
prev_sample = prev_sample_mean + ((step_size * 2) ** 0.5) * noise
if not return_dict:
return (prev_sample,)
return SchedulerOutput(prev_sample=prev_sample)
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
timesteps = timesteps.to(original_samples.device)
sigmas = self.discrete_sigmas.to(original_samples.device)[timesteps]
noise = (
noise * sigmas[:, None, None, None]
if noise is not None
else torch.randn_like(original_samples) * sigmas[:, None, None, None]
)
noisy_samples = noise + original_samples
return noisy_samples
def __len__(self):
return self.config.num_train_timesteps