# Copyright 2023 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 diffusers.configuration_utils import ConfigMixin, register_to_config
from diffusers.utils import BaseOutput
try:
from diffusers.utils import randn_tensor
except:
from diffusers.utils.torch_utils import randn_tensor
from diffusers.schedulers.scheduling_utils import KarrasDiffusionSchedulers, 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
# Copied from diffusers.schedulers.scheduling_ddpm.betas_for_alpha_bar
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, dtype=torch.float32)
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 for numerical stability.
clip_sample_range (`float`, default `1.0`):
the maximum magnitude for sample clipping. Valid only when `clip_sample=True`.
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)
thresholding (`bool`, default `False`):
whether to use the "dynamic thresholding" method (introduced by Imagen, https://arxiv.org/abs/2205.11487).
Note that the thresholding method is unsuitable for latent-space diffusion models (such as
stable-diffusion).
dynamic_thresholding_ratio (`float`, default `0.995`):
the ratio for the dynamic thresholding method. Default is `0.995`, the same as Imagen
(https://arxiv.org/abs/2205.11487). Valid only when `thresholding=True`.
sample_max_value (`float`, default `1.0`):
the threshold value for dynamic thresholding. Valid only when `thresholding=True`.
"""
_compatibles = [e.name for e in KarrasDiffusionSchedulers]
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",
thresholding: bool = False,
dynamic_thresholding_ratio: float = 0.995,
clip_sample_range: float = 1.0,
sample_max_value: float = 1.0,
):
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
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMScheduler._threshold_sample
def _threshold_sample(self, sample: torch.FloatTensor) -> torch.FloatTensor:
"""
"Dynamic thresholding: At each sampling step we set s to a certain percentile absolute pixel value in xt0 (the
prediction of x_0 at timestep t), and if s > 1, then we threshold xt0 to the range [-s, s] and then divide by
s. Dynamic thresholding pushes saturated pixels (those near -1 and 1) inwards, thereby actively preventing
pixels from saturation at each step. We find that dynamic thresholding results in significantly better
photorealism as well as better image-text alignment, especially when using very large guidance weights."
https://arxiv.org/abs/2205.11487
"""
dtype = sample.dtype
batch_size, channels, height, width = sample.shape
if dtype not in (torch.float32, torch.float64):
sample = sample.float() # upcast for quantile calculation, and clamp not implemented for cpu half
# Flatten sample for doing quantile calculation along each image
sample = sample.reshape(batch_size, channels * height * width)
abs_sample = sample.abs() # "a certain percentile absolute pixel value"
s = torch.quantile(abs_sample, self.config.dynamic_thresholding_ratio, dim=1)
s = torch.clamp(
s, min=1, max=self.config.sample_max_value
) # When clamped to min=1, equivalent to standard clipping to [-1, 1]
s = s.unsqueeze(1) # (batch_size, 1) because clamp will broadcast along dim=0
sample = torch.clamp(sample, -s, s) / s # "we threshold xt0 to the range [-s, s] and then divide by s"
sample = sample.reshape(batch_size, channels, height, width)
sample = sample.to(dtype)
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.
# """
# if num_inference_steps > self.config.num_train_timesteps:
# raise ValueError(
# f"`num_inference_steps`: {num_inference_steps} cannot be larger than `self.config.train_timesteps`:"
# f" {self.config.num_train_timesteps} as the unet model trained with this scheduler can only handle"
# f" maximal {self.config.num_train_timesteps} timesteps."
# )
# 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 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.
"""
if num_inference_steps > self.config.num_train_timesteps:
raise ValueError(
f"`num_inference_steps`: {num_inference_steps} cannot be larger than `self.config.train_timesteps`:"
f" {self.config.num_train_timesteps} as the unet model trained with this scheduler can only handle"
f" maximal {self.config.num_train_timesteps} timesteps."
)
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.linspace(self.config.steps_offset, self.config.num_train_timesteps, num_inference_steps)
timesteps = timesteps.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
# print('===========', self.config.prediction_type)
# self.config.prediction_type = "v_prediction"
if self.config.prediction_type == "epsilon":
pred_original_sample = (sample - beta_prod_t ** (0.5) * model_output) / alpha_prod_t ** (0.5)
pred_epsilon = model_output
elif self.config.prediction_type == "sample":
pred_original_sample = model_output
pred_epsilon = (sample - alpha_prod_t ** (0.5) * pred_original_sample) / beta_prod_t ** (0.5)
elif self.config.prediction_type == "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
else:
raise ValueError(
f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or"
" `v_prediction`"
)
# 4. Clip or threshold "predicted x_0"
if self.config.thresholding:
pred_original_sample = self._threshold_sample(pred_original_sample)
elif self.config.clip_sample:
pred_original_sample = pred_original_sample.clamp(
-self.config.clip_sample_range, self.config.clip_sample_range
)
# 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 pred_epsilon is always re-derived from the clipped x_0 in Glide
pred_epsilon = (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) * pred_epsilon
# 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:
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:
variance_noise = randn_tensor(
model_output.shape, generator=generator, device=model_output.device, dtype=model_output.dtype
)
variance = std_dev_t * 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)
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMScheduler.add_noise
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
alphas_cumprod = self.alphas_cumprod.to(device=original_samples.device, dtype=original_samples.dtype)
timesteps = timesteps.to(original_samples.device)
sqrt_alpha_prod = 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 - 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
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMScheduler.get_velocity
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
alphas_cumprod = self.alphas_cumprod.to(device=sample.device, dtype=sample.dtype)
timesteps = timesteps.to(sample.device)
sqrt_alpha_prod = 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 - 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