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# 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.
#
# =========================================================================
# Adapted from https://github.com/huggingface/diffusers
# which has the following license:
# https://github.com/huggingface/diffusers/blob/main/LICENSE
#
# 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.
# =========================================================================
from __future__ import annotations
import numpy as np
import torch
from .ddpm import DDPMPredictionType
from .scheduler import Scheduler
DDIMPredictionType = DDPMPredictionType
class DDIMScheduler(Scheduler):
"""
Denoising diffusion implicit models is a scheduler that extends the denoising procedure introduced in denoising
diffusion probabilistic models (DDPMs) with non-Markovian guidance. Based on: Song et al. "Denoising Diffusion
Implicit Models" https://arxiv.org/abs/2010.02502
Args:
num_train_timesteps: number of diffusion steps used to train the model.
schedule: member of NoiseSchedules, name of noise schedule function in component store
clip_sample: option to clip predicted sample between -1 and 1 for numerical stability.
set_alpha_to_one: 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: an offset added to the inference steps. You can use a combination of `steps_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: member of DDPMPredictionType
clip_sample_min: minimum clipping value when clip_sample equals True
clip_sample_max: maximum clipping value when clip_sample equals True
schedule_args: arguments to pass to the schedule function
"""
def __init__(
self,
num_train_timesteps: int = 1000,
schedule: str = "linear_beta",
clip_sample: bool = True,
set_alpha_to_one: bool = True,
steps_offset: int = 0,
prediction_type: str = DDIMPredictionType.EPSILON,
clip_sample_min: float = -1.0,
clip_sample_max: float = 1.0,
**schedule_args,
) -> None:
super().__init__(num_train_timesteps, schedule, **schedule_args)
if prediction_type not in DDIMPredictionType.__members__.values():
raise ValueError("Argument `prediction_type` must be a member of DDIMPredictionType")
self.prediction_type = prediction_type
# 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
self.timesteps = torch.from_numpy(np.arange(0, self.num_train_timesteps)[::-1].astype(np.int64))
self.clip_sample = clip_sample
self.clip_sample_values = [clip_sample_min, clip_sample_max]
self.steps_offset = steps_offset
# default the number of inference timesteps to the number of train steps
self.num_inference_steps: int
self.set_timesteps(self.num_train_timesteps)
def set_timesteps(self, num_inference_steps: int, device: str | torch.device | None = None) -> None:
"""
Sets the discrete timesteps used for the diffusion chain. Supporting function to be run before inference.
Args:
num_inference_steps: number of diffusion steps used when generating samples with a pre-trained model.
device: target device to put the data.
"""
if num_inference_steps > self.num_train_timesteps:
raise ValueError(
f"`num_inference_steps`: {num_inference_steps} cannot be larger than `self.num_train_timesteps`:"
f" {self.num_train_timesteps} as the unet model trained with this scheduler can only handle"
f" maximal {self.num_train_timesteps} timesteps."
)
self.num_inference_steps = num_inference_steps
step_ratio = self.num_train_timesteps // self.num_inference_steps
if self.steps_offset >= step_ratio:
raise ValueError(
f"`steps_offset`: {self.steps_offset} cannot be greater than or equal to "
f"`num_train_timesteps // num_inference_steps : {step_ratio}` as this will cause timesteps to exceed"
f" the max train timestep."
)
# 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.steps_offset
def _get_variance(self, timestep: int, prev_timestep: int) -> torch.Tensor:
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: torch.Tensor = (beta_prod_t_prev / beta_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev)
return variance
def step(
self,
model_output: torch.Tensor,
timestep: int,
sample: torch.Tensor,
eta: float = 0.0,
generator: torch.Generator | None = None,
) -> tuple[torch.Tensor, torch.Tensor]:
"""
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: direct output from learned diffusion model.
timestep: current discrete timestep in the diffusion chain.
sample: current instance of sample being created by diffusion process.
eta: weight of noise for added noise in diffusion step.
generator: random number generator.
Returns:
pred_prev_sample: Predicted previous sample
pred_original_sample: Predicted original sample
"""
# 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>
# - model_output -> 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.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
# predefinitions satisfy pylint/mypy, these values won't be ultimately used
pred_original_sample = sample
pred_epsilon = model_output
# 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.prediction_type == DDIMPredictionType.EPSILON:
pred_original_sample = (sample - (beta_prod_t**0.5) * model_output) / (alpha_prod_t**0.5)
pred_epsilon = model_output
elif self.prediction_type == DDIMPredictionType.SAMPLE:
pred_original_sample = model_output
pred_epsilon = (sample - (alpha_prod_t**0.5) * pred_original_sample) / (beta_prod_t**0.5)
elif self.prediction_type == DDIMPredictionType.V_PREDICTION:
pred_original_sample = (alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output
pred_epsilon = (alpha_prod_t**0.5) * model_output + (beta_prod_t**0.5) * sample
# 4. Clip "predicted x_0"
if self.clip_sample:
pred_original_sample = torch.clamp(
pred_original_sample, self.clip_sample_values[0], self.clip_sample_values[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
# 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 * pred_epsilon
# 7. compute x_t-1 without "random noise" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
pred_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: torch.device = torch.device(model_output.device if torch.is_tensor(model_output) else "cpu")
noise = torch.randn(model_output.shape, dtype=model_output.dtype, generator=generator, device=device)
variance = self._get_variance(timestep, prev_timestep) ** 0.5 * eta * noise
pred_prev_sample = pred_prev_sample + variance
return pred_prev_sample, pred_original_sample
def reversed_step(
self, model_output: torch.Tensor, timestep: int, sample: torch.Tensor
) -> tuple[torch.Tensor, torch.Tensor]:
"""
Predict the sample at the next 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: direct output from learned diffusion model.
timestep: current discrete timestep in the diffusion chain.
sample: current instance of sample being created by diffusion process.
Returns:
pred_prev_sample: Predicted previous sample
pred_original_sample: Predicted original sample
"""
# See Appendix F at https://arxiv.org/pdf/2105.05233.pdf, or Equation (6) in https://arxiv.org/pdf/2203.04306.pdf
# Notation (<variable name> -> <name in paper>
# - model_output -> 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_post_sample -> "x_t+1"
# 1. get previous step value (=t+1)
prev_timestep = timestep + self.num_train_timesteps // self.num_inference_steps
# 2. compute alphas, betas at timestep t+1
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
# predefinitions satisfy pylint/mypy, these values won't be ultimately used
pred_original_sample = sample
pred_epsilon = model_output
# 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.prediction_type == DDIMPredictionType.EPSILON:
pred_original_sample = (sample - beta_prod_t ** (0.5) * model_output) / alpha_prod_t ** (0.5)
pred_epsilon = model_output
elif self.prediction_type == DDIMPredictionType.SAMPLE:
pred_original_sample = model_output
pred_epsilon = (sample - alpha_prod_t ** (0.5) * pred_original_sample) / beta_prod_t ** (0.5)
elif self.prediction_type == DDIMPredictionType.V_PREDICTION:
pred_original_sample = (alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output
pred_epsilon = (alpha_prod_t**0.5) * model_output + (beta_prod_t**0.5) * sample
# 4. Clip "predicted x_0"
if self.clip_sample:
pred_original_sample = torch.clamp(
pred_original_sample, self.clip_sample_values[0], self.clip_sample_values[1]
)
# 5. 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) ** (0.5) * pred_epsilon
# 6. compute x_t+1 without "random noise" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
pred_post_sample = alpha_prod_t_prev ** (0.5) * pred_original_sample + pred_sample_direction
return pred_post_sample, pred_original_sample
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