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# Copyright (c) 2022 PaddlePaddle Authors. All Rights Reserved. | |
# Copyright 2022 Google Brain 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/yang-song/score_sde_pytorch | |
import math | |
from dataclasses import dataclass | |
from typing import List, Optional, Tuple, Union | |
import paddle | |
from ..configuration_utils import ConfigMixin, register_to_config | |
from ..utils import BaseOutput | |
from .scheduling_utils import SchedulerMixin, SchedulerOutput | |
class SdeVeOutput(BaseOutput): | |
""" | |
Output class for the ScoreSdeVeScheduler's step function output. | |
Args: | |
prev_sample (`paddle.Tensor` 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 (`paddle.Tensor` of shape `(batch_size, num_channels, height, width)` for images): | |
Mean averaged `prev_sample`. Same as `prev_sample`, only mean-averaged over previous timesteps. | |
""" | |
prev_sample: paddle.Tensor | |
prev_sample_mean: paddle.Tensor | |
class ScoreSdeVeScheduler(SchedulerMixin, ConfigMixin): | |
""" | |
The variance exploding stochastic differential equation (SDE) scheduler. | |
For more information, see the original paper: https://arxiv.org/abs/2011.13456 | |
[`~ConfigMixin`] takes care of storing all config attributes that are passed in the scheduler's `__init__` | |
function, such as `num_train_timesteps`. They can be accessed via `scheduler.config.num_train_timesteps`. | |
[`SchedulerMixin`] provides general loading and saving functionality via the [`SchedulerMixin.save_pretrained`] and | |
[`~SchedulerMixin.from_pretrained`] functions. | |
Args: | |
num_train_timesteps (`int`): number of diffusion steps used to train the model. | |
snr (`float`): | |
coefficient weighting the step from the model_output sample (from the network) to the random noise. | |
sigma_min (`float`): | |
initial noise scale for sigma sequence in sampling procedure. The minimum sigma should mirror the | |
distribution of the data. | |
sigma_max (`float`): maximum value used for the range of continuous timesteps passed into the model. | |
sampling_eps (`float`): the end value of sampling, where timesteps decrease progressively from 1 to | |
epsilon. | |
correct_steps (`int`): number of correction steps performed on a produced sample. | |
""" | |
order = 1 | |
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: paddle.Tensor, timestep: Optional[int] = None) -> paddle.Tensor: | |
""" | |
Ensures interchangeability with schedulers that need to scale the denoising model input depending on the | |
current timestep. | |
Args: | |
sample (`paddle.Tensor`): input sample | |
timestep (`int`, optional): current timestep | |
Returns: | |
`paddle.Tensor`: scaled input sample | |
""" | |
return sample | |
def set_timesteps(self, num_inference_steps: int, sampling_eps: float = None): | |
""" | |
Sets the continuous timesteps used for the diffusion chain. Supporting function 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): final timestep value (overrides value given at Scheduler instantiation). | |
""" | |
sampling_eps = sampling_eps if sampling_eps is not None else self.config.sampling_eps | |
self.timesteps = paddle.linspace(1, sampling_eps, num_inference_steps) | |
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. Supporting function to be run before inference. | |
The sigmas control the weight of the `drift` and `diffusion` components of 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): | |
initial noise scale value (overrides value given at Scheduler instantiation). | |
sigma_max (`float`, optional): final noise scale value (overrides value given at Scheduler instantiation). | |
sampling_eps (`float`, optional): final timestep value (overrides value given at 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 = paddle.exp( | |
paddle.linspace(math.log(sigma_min), math.log(sigma_max), num_inference_steps) | |
) | |
self.sigmas = paddle.to_tensor([sigma_min * (sigma_max / sigma_min) ** t for t in self.timesteps]) | |
def get_adjacent_sigma(self, timesteps, t): | |
return paddle.where( | |
timesteps == 0, | |
paddle.zeros_like(t), | |
self.discrete_sigmas[timesteps - 1], | |
) | |
def step_pred( | |
self, | |
model_output: paddle.Tensor, | |
timestep: int, | |
sample: paddle.Tensor, | |
generator: Optional[Union[paddle.Generator, List[paddle.Generator]]] = None, | |
return_dict: bool = True, | |
) -> Union[SdeVeOutput, Tuple]: | |
""" | |
Predict the sample at the previous timestep by reversing the SDE. Core function to propagate the diffusion | |
process from the learned model outputs (most often the predicted noise). | |
Args: | |
model_output (`paddle.Tensor`): direct output from learned diffusion model. | |
timestep (`int`): current discrete timestep in the diffusion chain. | |
sample (`paddle.Tensor`): | |
current instance of sample being created by diffusion process. | |
generator: random number generator. | |
return_dict (`bool`): option for returning tuple rather than SchedulerOutput class | |
Returns: | |
[`~schedulers.scheduling_sde_ve.SdeVeOutput`] or `tuple`: [`~schedulers.scheduling_sde_ve.SdeVeOutput`] if | |
`return_dict` is True, otherwise a `tuple`. When returning a tuple, 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 * paddle.ones((sample.shape[0],)) # paddle.repeat_interleave(timestep, sample.shape[0]) | |
timesteps = (timestep * (len(self.timesteps) - 1)).cast("int64") | |
sigma = self.discrete_sigmas[timesteps] | |
adjacent_sigma = self.get_adjacent_sigma(timesteps, timestep) | |
drift = paddle.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 = paddle.randn(sample.shape, generator=generator) | |
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: paddle.Tensor, | |
sample: paddle.Tensor, | |
generator: Optional[Union[paddle.Generator, List[paddle.Generator]]] = None, | |
return_dict: bool = True, | |
) -> Union[SchedulerOutput, Tuple]: | |
""" | |
Correct the predicted sample based on the output model_output of the network. This is often run repeatedly | |
after making the prediction for the previous timestep. | |
Args: | |
model_output (`paddle.Tensor`): direct output from learned diffusion model. | |
sample (`paddle.Tensor`): | |
current instance of sample being created by diffusion process. | |
generator: random number generator. | |
return_dict (`bool`): option for returning tuple rather than SchedulerOutput class | |
Returns: | |
[`~schedulers.scheduling_sde_ve.SdeVeOutput`] or `tuple`: [`~schedulers.scheduling_sde_ve.SdeVeOutput`] if | |
`return_dict` is True, otherwise a `tuple`. When returning a tuple, 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 = paddle.randn(sample.shape, generator=generator) | |
# compute step size from the model_output, the noise, and the snr | |
grad_norm = paddle.norm(model_output.reshape([model_output.shape[0], -1]), axis=-1).mean() | |
noise_norm = paddle.norm(noise.reshape([noise.shape[0], -1]), axis=-1).mean() | |
step_size = (self.config.snr * noise_norm / grad_norm) ** 2 * 2 | |
step_size = step_size * paddle.ones((sample.shape[0],)) | |
# 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 __len__(self): | |
return self.config.num_train_timesteps | |