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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
@dataclass
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
@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: 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
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