EDICT / my_diffusers /schedulers /scheduling_ddim.py
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# 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 typing import Optional, Tuple, Union
import numpy as np
import torch
from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils import SchedulerMixin, SchedulerOutput
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 np.array(betas, dtype=np.float64)
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`.
[`~ConfigMixin`] also provides general loading and saving functionality via the [`~ConfigMixin.save_config`] and
[`~ConfigMixin.from_config`] functios.
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): TODO
timestep_values (`np.ndarray`, optional): TODO
clip_sample (`bool`, default `True`):
option to clip predicted sample between -1 and 1 for numerical stability.
set_alpha_to_one (`bool`, default `True`):
if alpha for final step is 1 or the final alpha of the "non-previous" one.
tensor_format (`str`): whether the scheduler expects pytorch or numpy arrays.
"""
@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,
timestep_values: Optional[np.ndarray] = None,
clip_sample: bool = True,
set_alpha_to_one: bool = True,
tensor_format: str = "pt",
):
if trained_betas is not None:
self.betas = np.asarray(trained_betas)
if beta_schedule == "linear":
self.betas = np.linspace(beta_start, beta_end, num_train_timesteps, dtype=np.float64)
elif beta_schedule == "scaled_linear":
# this schedule is very specific to the latent diffusion model.
self.betas = np.linspace(beta_start**0.5, beta_end**0.5, num_train_timesteps, dtype=np.float64) ** 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 = np.cumprod(self.alphas, axis=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 paratemer simply to one or
# whether we use the final alpha of the "non-previous" one.
self.final_alpha_cumprod = np.array(1.0) if set_alpha_to_one else self.alphas_cumprod[0]
# setable values
self.num_inference_steps = None
self.timesteps = np.arange(0, num_train_timesteps)[::-1].copy()
self.tensor_format = tensor_format
self.set_format(tensor_format=tensor_format)
# print(self.alphas.shape)
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, offset: int = 0):
"""
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.
offset (`int`): TODO
"""
self.num_inference_steps = num_inference_steps
if num_inference_steps <= 1000:
self.timesteps = np.arange(
0, self.config.num_train_timesteps, self.config.num_train_timesteps // self.num_inference_steps
)[::-1].copy()
else:
print("Hitting new logic, allowing fractional timesteps")
self.timesteps = np.linspace(
0, self.config.num_train_timesteps-1, self.num_inference_steps, endpoint=True
)[::-1].copy()
self.timesteps += offset
self.set_format(tensor_format=self.tensor_format)
def step(
self,
model_output: Union[torch.FloatTensor, np.ndarray],
timestep: int,
sample: Union[torch.FloatTensor, np.ndarray],
eta: float = 0.0,
use_clipped_model_output: bool = False,
generator=None,
return_dict: bool = True,
) -> Union[SchedulerOutput, 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` or `np.ndarray`): direct output from learned diffusion model.
timestep (`int`): current discrete timestep in the diffusion chain.
sample (`torch.FloatTensor` or `np.ndarray`):
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`): TODO
generator: random number generator.
return_dict (`bool`): option for returning tuple rather than SchedulerOutput class
Returns:
[`~schedulers.scheduling_utils.SchedulerOutput`] or `tuple`:
[`~schedulers.scheduling_utils.SchedulerOutput`] 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 pointingc 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
pred_original_sample = (sample - beta_prod_t ** (0.5) * model_output) / alpha_prod_t ** (0.5)
# 4. Clip "predicted x_0"
if self.config.clip_sample:
pred_original_sample = self.clip(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:
device = model_output.device if torch.is_tensor(model_output) else "cpu"
noise = torch.randn(model_output.shape, generator=generator).to(device)
variance = self._get_variance(timestep, prev_timestep) ** (0.5) * eta * noise
if not torch.is_tensor(model_output):
variance = variance.numpy()
prev_sample = prev_sample + variance
if not return_dict:
return (prev_sample,)
return SchedulerOutput(prev_sample=prev_sample)
def add_noise(
self,
original_samples: Union[torch.FloatTensor, np.ndarray],
noise: Union[torch.FloatTensor, np.ndarray],
timesteps: Union[torch.IntTensor, np.ndarray],
) -> Union[torch.FloatTensor, np.ndarray]:
sqrt_alpha_prod = self.alphas_cumprod[timesteps] ** 0.5
sqrt_alpha_prod = self.match_shape(sqrt_alpha_prod, original_samples)
sqrt_one_minus_alpha_prod = (1 - self.alphas_cumprod[timesteps]) ** 0.5
sqrt_one_minus_alpha_prod = self.match_shape(sqrt_one_minus_alpha_prod, original_samples)
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