381 lines
18 KiB
Python
381 lines
18 KiB
Python
# Copyright 2022 Stanford University 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 code is strongly influenced by https://github.com/pesser/pytorch_diffusion
|
||
# and https://github.com/hojonathanho/diffusion
|
||
|
||
import math
|
||
from dataclasses import dataclass
|
||
from typing import List, Optional, Tuple, Union
|
||
|
||
import numpy as np
|
||
import torch
|
||
|
||
from ..configuration_utils import ConfigMixin, register_to_config
|
||
from ..utils import _COMPATIBLE_STABLE_DIFFUSION_SCHEDULERS, BaseOutput, deprecate
|
||
from .scheduling_utils import SchedulerMixin
|
||
|
||
|
||
@dataclass
|
||
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->DDIM
|
||
class DDIMSchedulerOutput(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) -> torch.Tensor:
|
||
"""
|
||
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)
|
||
|
||
|
||
class DDIMScheduler(SchedulerMixin, ConfigMixin):
|
||
"""
|
||
Denoising diffusion implicit models is a scheduler that extends the denoising procedure introduced in denoising
|
||
diffusion probabilistic models (DDPMs) with non-Markovian guidance.
|
||
|
||
[`~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/2010.02502
|
||
|
||
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.
|
||
clip_sample (`bool`, default `True`):
|
||
option to clip predicted sample between -1 and 1 for numerical stability.
|
||
set_alpha_to_one (`bool`, default `True`):
|
||
each diffusion step uses the value of alphas product at that step and at the previous one. For the final
|
||
step there is no previous alpha. When this option is `True` the previous alpha product is fixed to `1`,
|
||
otherwise it uses the value of alpha at step 0.
|
||
steps_offset (`int`, default `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, as done in
|
||
stable diffusion.
|
||
prediction_type (`str`, default `epsilon`, optional):
|
||
prediction type of the scheduler function, one of `epsilon` (predicting the noise of the diffusion
|
||
process), `sample` (directly predicting the noisy sample`) or `v_prediction` (see section 2.4
|
||
https://imagen.research.google/video/paper.pdf)
|
||
"""
|
||
|
||
_compatibles = _COMPATIBLE_STABLE_DIFFUSION_SCHEDULERS.copy()
|
||
_deprecated_kwargs = ["predict_epsilon"]
|
||
order = 1
|
||
|
||
@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[Union[np.ndarray, List[float]]] = None,
|
||
clip_sample: bool = True,
|
||
set_alpha_to_one: bool = True,
|
||
steps_offset: int = 0,
|
||
prediction_type: str = "epsilon",
|
||
**kwargs,
|
||
):
|
||
message = (
|
||
"Please make sure to instantiate your scheduler with `prediction_type` instead. E.g. `scheduler ="
|
||
" DDIMScheduler.from_pretrained(<model_id>, prediction_type='epsilon')`."
|
||
)
|
||
predict_epsilon = deprecate("predict_epsilon", "0.12.0", message, take_from=kwargs)
|
||
if predict_epsilon is not None:
|
||
self.register_to_config(prediction_type="epsilon" if predict_epsilon else "sample")
|
||
|
||
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)
|
||
|
||
# At every step in ddim, we are looking into the previous alphas_cumprod
|
||
# For the final step, there is no previous alphas_cumprod because we are already at 0
|
||
# `set_alpha_to_one` decides whether we set this parameter simply to one or
|
||
# whether we use the final alpha of the "non-previous" one.
|
||
self.final_alpha_cumprod = torch.tensor(1.0) if set_alpha_to_one else self.alphas_cumprod[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().astype(np.int64))
|
||
|
||
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 _get_variance(self, timestep, prev_timestep):
|
||
alpha_prod_t = self.alphas_cumprod[timestep]
|
||
alpha_prod_t_prev = self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod
|
||
beta_prod_t = 1 - alpha_prod_t
|
||
beta_prod_t_prev = 1 - alpha_prod_t_prev
|
||
|
||
variance = (beta_prod_t_prev / beta_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev)
|
||
|
||
return variance
|
||
|
||
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.
|
||
"""
|
||
self.num_inference_steps = num_inference_steps
|
||
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.int64)
|
||
self.timesteps = torch.from_numpy(timesteps).to(device)
|
||
self.timesteps += self.config.steps_offset
|
||
|
||
def step(
|
||
self,
|
||
model_output: torch.FloatTensor,
|
||
timestep: int,
|
||
sample: torch.FloatTensor,
|
||
eta: float = 0.0,
|
||
use_clipped_model_output: bool = False,
|
||
generator=None,
|
||
variance_noise: Optional[torch.FloatTensor] = None,
|
||
return_dict: bool = True,
|
||
) -> Union[DDIMSchedulerOutput, 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.
|
||
eta (`float`): weight of noise for added noise in diffusion step.
|
||
use_clipped_model_output (`bool`): if `True`, compute "corrected" `model_output` from the clipped
|
||
predicted original sample. Necessary because predicted original sample is clipped to [-1, 1] when
|
||
`self.config.clip_sample` is `True`. If no clipping has happened, "corrected" `model_output` would
|
||
coincide with the one provided as input and `use_clipped_model_output` will have not effect.
|
||
generator: random number generator.
|
||
variance_noise (`torch.FloatTensor`): instead of generating noise for the variance using `generator`, we
|
||
can directly provide the noise for the variance itself. This is useful for methods such as
|
||
CycleDiffusion. (https://arxiv.org/abs/2210.05559)
|
||
return_dict (`bool`): option for returning tuple rather than DDIMSchedulerOutput class
|
||
|
||
Returns:
|
||
[`~schedulers.scheduling_utils.DDIMSchedulerOutput`] or `tuple`:
|
||
[`~schedulers.scheduling_utils.DDIMSchedulerOutput`] if `return_dict` is True, otherwise a `tuple`. When
|
||
returning a tuple, the first element is the sample tensor.
|
||
|
||
"""
|
||
if self.num_inference_steps is None:
|
||
raise ValueError(
|
||
"Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler"
|
||
)
|
||
|
||
# See formulas (12) and (16) of DDIM paper https://arxiv.org/pdf/2010.02502.pdf
|
||
# Ideally, read DDIM paper in-detail understanding
|
||
|
||
# Notation (<variable name> -> <name in paper>
|
||
# - pred_noise_t -> e_theta(x_t, t)
|
||
# - pred_original_sample -> f_theta(x_t, t) or x_0
|
||
# - std_dev_t -> sigma_t
|
||
# - eta -> η
|
||
# - pred_sample_direction -> "direction pointing to x_t"
|
||
# - pred_prev_sample -> "x_t-1"
|
||
|
||
# 1. get previous step value (=t-1)
|
||
prev_timestep = timestep - self.config.num_train_timesteps // self.num_inference_steps
|
||
|
||
# 2. compute alphas, betas
|
||
alpha_prod_t = self.alphas_cumprod[timestep]
|
||
alpha_prod_t_prev = self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod
|
||
|
||
beta_prod_t = 1 - alpha_prod_t
|
||
|
||
# 3. compute predicted original sample from predicted noise also called
|
||
# "predicted x_0" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
|
||
if self.config.prediction_type == "epsilon":
|
||
pred_original_sample = (sample - beta_prod_t ** (0.5) * model_output) / alpha_prod_t ** (0.5)
|
||
elif self.config.prediction_type == "sample":
|
||
pred_original_sample = model_output
|
||
elif self.config.prediction_type == "v_prediction":
|
||
pred_original_sample = (alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output
|
||
# predict V
|
||
model_output = (alpha_prod_t**0.5) * model_output + (beta_prod_t**0.5) * sample
|
||
else:
|
||
raise ValueError(
|
||
f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or"
|
||
" `v_prediction`"
|
||
)
|
||
|
||
# 4. Clip "predicted x_0"
|
||
if self.config.clip_sample:
|
||
pred_original_sample = torch.clamp(pred_original_sample, -1, 1)
|
||
|
||
# 5. compute variance: "sigma_t(η)" -> see formula (16)
|
||
# σ_t = sqrt((1 − α_t−1)/(1 − α_t)) * sqrt(1 − α_t/α_t−1)
|
||
variance = self._get_variance(timestep, prev_timestep)
|
||
std_dev_t = eta * variance ** (0.5)
|
||
|
||
if use_clipped_model_output:
|
||
# the model_output is always re-derived from the clipped x_0 in Glide
|
||
model_output = (sample - alpha_prod_t ** (0.5) * pred_original_sample) / beta_prod_t ** (0.5)
|
||
|
||
# 6. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
|
||
pred_sample_direction = (1 - alpha_prod_t_prev - std_dev_t**2) ** (0.5) * model_output
|
||
|
||
# 7. compute x_t without "random noise" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
|
||
prev_sample = alpha_prod_t_prev ** (0.5) * pred_original_sample + pred_sample_direction
|
||
|
||
if eta > 0:
|
||
# randn_like does not support generator https://github.com/pytorch/pytorch/issues/27072
|
||
device = model_output.device
|
||
if variance_noise is not None and generator is not None:
|
||
raise ValueError(
|
||
"Cannot pass both generator and variance_noise. Please make sure that either `generator` or"
|
||
" `variance_noise` stays `None`."
|
||
)
|
||
|
||
if variance_noise is None:
|
||
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
|
||
)
|
||
variance = self._get_variance(timestep, prev_timestep) ** (0.5) * eta * variance_noise
|
||
|
||
prev_sample = prev_sample + variance
|
||
|
||
if not return_dict:
|
||
return (prev_sample,)
|
||
|
||
return DDIMSchedulerOutput(prev_sample=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 get_velocity(
|
||
self, sample: torch.FloatTensor, noise: torch.FloatTensor, timesteps: torch.IntTensor
|
||
) -> torch.FloatTensor:
|
||
# Make sure alphas_cumprod and timestep have same device and dtype as sample
|
||
self.alphas_cumprod = self.alphas_cumprod.to(device=sample.device, dtype=sample.dtype)
|
||
timesteps = timesteps.to(sample.device)
|
||
|
||
sqrt_alpha_prod = self.alphas_cumprod[timesteps] ** 0.5
|
||
sqrt_alpha_prod = sqrt_alpha_prod.flatten()
|
||
while len(sqrt_alpha_prod.shape) < len(sample.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(sample.shape):
|
||
sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.unsqueeze(-1)
|
||
|
||
velocity = sqrt_alpha_prod * noise - sqrt_one_minus_alpha_prod * sample
|
||
return velocity
|
||
|
||
def __len__(self):
|
||
return self.config.num_train_timesteps
|