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scheduling_ddpm.py
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scheduling_ddpm.py
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# Copyright 2022 UC Berkeley Team 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/ermongroup/ddim
import math
from dataclasses import dataclass
from typing import Optional, Tuple, Union
import numpy as np
import torch
from ..configuration_utils import ConfigMixin, FrozenDict, register_to_config
from ..utils import _COMPATIBLE_STABLE_DIFFUSION_SCHEDULERS, BaseOutput, deprecate
from .scheduling_utils import SchedulerMixin
@dataclass
class DDPMSchedulerOutput(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
def betas_for_alpha_bar(num_diffusion_timesteps, max_beta=0.999):
"""
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.
Returns:
betas (`np.ndarray`): the betas used by the scheduler to step the model outputs
"""
def alpha_bar(time_step):
return math.cos((time_step + 0.008) / 1.008 * math.pi / 2) ** 2
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(t2) / alpha_bar(t1), max_beta))
return torch.tensor(betas, dtype=torch.float32)
class DDPMScheduler(SchedulerMixin, ConfigMixin):
"""
Denoising diffusion probabilistic models (DDPMs) explores the connections between denoising score matching and
Langevin dynamics sampling.
[`~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.
For more details, see the original paper: https://arxiv.org/abs/2006.11239
Args:
num_train_timesteps (`int`): number of diffusion steps used to train the model.
beta_start (`float`): the starting `beta` value of inference.
beta_end (`float`): the final `beta` value.
beta_schedule (`str`):
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):
option to pass an array of betas directly to the constructor to bypass `beta_start`, `beta_end` etc.
variance_type (`str`):
options to clip the variance used when adding noise to the denoised sample. Choose from `fixed_small`,
`fixed_small_log`, `fixed_large`, `fixed_large_log`, `learned` or `learned_range`.
clip_sample (`bool`, default `True`):
option to clip predicted sample between -1 and 1 for numerical stability.
predict_epsilon (`bool`):
optional flag to use when the model predicts the noise (epsilon), or the samples instead of the noise.
"""
_compatibles = _COMPATIBLE_STABLE_DIFFUSION_SCHEDULERS.copy()
@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,
variance_type: str = "fixed_small",
clip_sample: bool = True,
predict_epsilon: bool = True,
):
if trained_betas is not None:
self.betas = torch.from_numpy(trained_betas)
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)
elif beta_schedule == "sigmoid":
# GeoDiff sigmoid schedule
betas = torch.linspace(-6, 6, num_train_timesteps)
self.betas = torch.sigmoid(betas) * (beta_end - beta_start) + beta_start
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)
self.one = torch.tensor(1.0)
# standard deviation of the initial noise distribution
self.init_noise_sigma = 1.0
# setable values
self.num_inference_steps = None
self.timesteps = torch.from_numpy(np.arange(0, num_train_timesteps)[::-1].copy())
self.variance_type = variance_type
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`): input sample
timestep (`int`, optional): current timestep
Returns:
`torch.FloatTensor`: scaled input sample
"""
return sample
def set_timesteps(self, num_inference_steps: int, device: Union[str, torch.device] = None):
"""
Sets the discrete 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.
"""
num_inference_steps = min(self.config.num_train_timesteps, num_inference_steps)
self.num_inference_steps = num_inference_steps
timesteps = np.arange(
0, self.config.num_train_timesteps, self.config.num_train_timesteps // self.num_inference_steps
)[::-1].copy()
self.timesteps = torch.from_numpy(timesteps).to(device)
def _get_variance(self, t, predicted_variance=None, variance_type=None):
alpha_prod_t = self.alphas_cumprod[t]
alpha_prod_t_prev = self.alphas_cumprod[t - 1] if t > 0 else self.one
# For t > 0, compute predicted variance 尾t (see formula (6) and (7) from https://arxiv.org/pdf/2006.11239.pdf)
# and sample from it to get previous sample
# x_{t-1} ~ N(pred_prev_sample, variance) == add variance to pred_sample
variance = (1 - alpha_prod_t_prev) / (1 - alpha_prod_t) * self.betas[t]
if variance_type is None:
variance_type = self.config.variance_type
# hacks - were probably added for training stability
if variance_type == "fixed_small":
variance = torch.clamp(variance, min=1e-20)
# for rl-diffuser https://arxiv.org/abs/2205.09991
elif variance_type == "fixed_small_log":
variance = torch.log(torch.clamp(variance, min=1e-20))
variance = torch.exp(0.5 * variance)
elif variance_type == "fixed_large":
variance = self.betas[t]
elif variance_type == "fixed_large_log":
# Glide max_log
variance = torch.log(self.betas[t])
elif variance_type == "learned":
return predicted_variance
elif variance_type == "learned_range":
min_log = variance
max_log = self.betas[t]
frac = (predicted_variance + 1) / 2
variance = frac * max_log + (1 - frac) * min_log
return variance
def step(
self,
model_output: torch.FloatTensor,
timestep: int,
sample: torch.FloatTensor,
generator=None,
return_dict: bool = True,
**kwargs,
) -> Union[DDPMSchedulerOutput, 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 (`torch.FloatTensor`): direct output from learned diffusion model.
timestep (`int`): current discrete timestep in the diffusion chain.
sample (`torch.FloatTensor`):
current instance of sample being created by diffusion process.
generator: random number generator.
return_dict (`bool`): option for returning tuple rather than DDPMSchedulerOutput class
Returns:
[`~schedulers.scheduling_utils.DDPMSchedulerOutput`] or `tuple`:
[`~schedulers.scheduling_utils.DDPMSchedulerOutput`] if `return_dict` is True, otherwise a `tuple`. When
returning a tuple, the first element is the sample tensor.
"""
message = (
"Please make sure to instantiate your scheduler with `predict_epsilon` instead. E.g. `scheduler ="
" DDPMScheduler.from_pretrained(<model_id>, predict_epsilon=True)`."
)
predict_epsilon = deprecate("predict_epsilon", "0.10.0", message, take_from=kwargs)
if predict_epsilon is not None and predict_epsilon != self.config.predict_epsilon:
new_config = dict(self.config)
new_config["predict_epsilon"] = predict_epsilon
self._internal_dict = FrozenDict(new_config)
t = timestep
if model_output.shape[1] == sample.shape[1] * 2 and self.variance_type in ["learned", "learned_range"]:
model_output, predicted_variance = torch.split(model_output, sample.shape[1], dim=1)
else:
predicted_variance = None
# 1. compute alphas, betas
alpha_prod_t = self.alphas_cumprod[t]
alpha_prod_t_prev = self.alphas_cumprod[t - 1] if t > 0 else self.one
beta_prod_t = 1 - alpha_prod_t
beta_prod_t_prev = 1 - alpha_prod_t_prev
# 2. compute predicted original sample from predicted noise also called
# "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf
if self.config.predict_epsilon:
pred_original_sample = (sample - beta_prod_t ** (0.5) * model_output) / alpha_prod_t ** (0.5)
else:
pred_original_sample = model_output
# 3. Clip "predicted x_0"
if self.config.clip_sample:
pred_original_sample = torch.clamp(pred_original_sample, -1, 1)
# 4. Compute coefficients for pred_original_sample x_0 and current sample x_t
# See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
pred_original_sample_coeff = (alpha_prod_t_prev ** (0.5) * self.betas[t]) / beta_prod_t
current_sample_coeff = self.alphas[t] ** (0.5) * beta_prod_t_prev / beta_prod_t
# 5. Compute predicted previous sample 碌_t
# See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
pred_prev_sample = pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample
# 6. Add noise
variance = 0
if t > 0:
device = model_output.device
if device.type == "mps":
# randn does not work reproducibly on mps
variance_noise = torch.randn(model_output.shape, dtype=model_output.dtype, generator=generator)
variance_noise = variance_noise.to(device)
else:
variance_noise = torch.randn(
model_output.shape, generator=generator, device=device, dtype=model_output.dtype
)
if self.variance_type == "fixed_small_log":
variance = self._get_variance(t, predicted_variance=predicted_variance) * variance_noise
else:
variance = (self._get_variance(t, predicted_variance=predicted_variance) ** 0.5) * variance_noise
pred_prev_sample = pred_prev_sample + variance
if not return_dict:
return (pred_prev_sample,)
return DDPMSchedulerOutput(prev_sample=pred_prev_sample, pred_original_sample=pred_original_sample)
def add_noise(
self,
original_samples: torch.FloatTensor,
noise: torch.FloatTensor,
timesteps: torch.IntTensor,
) -> torch.FloatTensor:
# Make sure alphas_cumprod and timestep have same device and dtype as original_samples
self.alphas_cumprod = self.alphas_cumprod.to(device=original_samples.device, dtype=original_samples.dtype)
timesteps = timesteps.to(original_samples.device)
sqrt_alpha_prod = self.alphas_cumprod[timesteps] ** 0.5
sqrt_alpha_prod = sqrt_alpha_prod.flatten()
while len(sqrt_alpha_prod.shape) < len(original_samples.shape):
sqrt_alpha_prod = sqrt_alpha_prod.unsqueeze(-1)
sqrt_one_minus_alpha_prod = (1 - self.alphas_cumprod[timesteps]) ** 0.5
sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.flatten()
while len(sqrt_one_minus_alpha_prod.shape) < len(original_samples.shape):
sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.unsqueeze(-1)
noisy_samples = sqrt_alpha_prod * original_samples + sqrt_one_minus_alpha_prod * noise
return noisy_samples
def __len__(self):
return self.config.num_train_timesteps