# Copyright 2023 UC Berkeley Team and The HuggingFace Team. All rights reserved.
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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
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# http://www.apache.org/licenses/LICENSE-2.0
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# 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
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# DISCLAIMER: This file is strongly influenced by https://github.com/ermongroup/ddim
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 BaseOutput, randn_tensor
from .scheduling_utils import KarrasDiffusionSchedulers, 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,
alpha_transform_type="cosine",
):
"""
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.
alpha_transform_type (`str`, *optional*, default to `cosine`): the type of noise schedule for alpha_bar.
Choose from `cosine` or `exp`
Returns:
betas (`np.ndarray`): the betas used by the scheduler to step the model outputs
"""
if alpha_transform_type == "cosine":
def alpha_bar_fn(t):
return math.cos((t + 0.008) / 1.008 * math.pi / 2) ** 2
elif alpha_transform_type == "exp":
def alpha_bar_fn(t):
return math.exp(t * -12.0)
else:
raise ValueError(f"Unsupported alpha_tranform_type: {alpha_transform_type}")
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_fn(t2) / alpha_bar_fn(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`, `squaredcos_cap_v2` or `sigmoid`.
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 for numerical stability.
clip_sample_range (`float`, default `1.0`):
the maximum magnitude for sample clipping. Valid only when `clip_sample=True`.
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`.
timestep_spacing (`str`, default `"leading"`):
The way the timesteps should be scaled. Refer to Table 2. of [Common Diffusion Noise Schedules and Sample
Steps are Flawed](https://arxiv.org/abs/2305.08891) for more information.
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.
"""
_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,
variance_type: str = "fixed_small",
clip_sample: bool = True,
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,
timestep_spacing: str = "leading",
steps_offset: int = 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)
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.custom_timesteps = False
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: Optional[int] = None,
device: Union[str, torch.device] = None,
timesteps: Optional[List[int]] = None,
):
"""
Sets the discrete timesteps used for the diffusion chain. Supporting function to be run before inference.
Args:
num_inference_steps (`Optional[int]`):
the number of diffusion steps used when generating samples with a pre-trained model. If passed, then
`timesteps` must be `None`.
device (`str` or `torch.device`, optional):
the device to which the timesteps are moved to.
custom_timesteps (`List[int]`, optional):
custom timesteps used to support arbitrary spacing between timesteps. If `None`, then the default
timestep spacing strategy of equal spacing between timesteps is used. If passed, `num_inference_steps`
must be `None`.
"""
if num_inference_steps is not None and timesteps is not None:
raise ValueError("Can only pass one of `num_inference_steps` or `custom_timesteps`.")
if timesteps is not None:
for i in range(1, len(timesteps)):
if timesteps[i] >= timesteps[i - 1]:
raise ValueError("`custom_timesteps` must be in descending order.")
if timesteps[0] >= self.config.num_train_timesteps:
raise ValueError(
f"`timesteps` must start before `self.config.train_timesteps`:"
f" {self.config.num_train_timesteps}."
)
timesteps = np.array(timesteps, dtype=np.int64)
self.custom_timesteps = True
else:
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
self.custom_timesteps = False
# "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
if self.config.timestep_spacing == "linspace":
timesteps = (
np.linspace(0, self.config.num_train_timesteps - 1, num_inference_steps)
.round()[::-1]
.copy()
.astype(np.int64)
)
elif self.config.timestep_spacing == "leading":
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)
timesteps += self.config.steps_offset
elif self.config.timestep_spacing == "trailing":
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.round(np.arange(self.config.num_train_timesteps, 0, -step_ratio)).astype(np.int64)
timesteps -= 1
else:
raise ValueError(
f"{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'linspace', 'leading' or 'trailing'."
)
self.timesteps = torch.from_numpy(timesteps).to(device)
def _get_variance(self, t, predicted_variance=None, variance_type=None):
prev_t = self.previous_timestep(t)
alpha_prod_t = self.alphas_cumprod[t]
alpha_prod_t_prev = self.alphas_cumprod[prev_t] if prev_t >= 0 else self.one
current_beta_t = 1 - alpha_prod_t / alpha_prod_t_prev
# For t > 0, compute predicted variance βt (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) * current_beta_t
# we always take the log of variance, so clamp it to ensure it's not 0
variance = torch.clamp(variance, min=1e-20)
if variance_type is None:
variance_type = self.config.variance_type
# hacks - were probably added for training stability
if variance_type == "fixed_small":
variance = variance
# for rl-diffuser https://arxiv.org/abs/2205.09991
elif variance_type == "fixed_small_log":
variance = torch.log(variance)
variance = torch.exp(0.5 * variance)
elif variance_type == "fixed_large":
variance = current_beta_t
elif variance_type == "fixed_large_log":
# Glide max_log
variance = torch.log(current_beta_t)
elif variance_type == "learned":
return predicted_variance
elif variance_type == "learned_range":
min_log = torch.log(variance)
max_log = torch.log(current_beta_t)
frac = (predicted_variance + 1) / 2
variance = frac * max_log + (1 - frac) * min_log
return variance
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 step(
self,
model_output: torch.FloatTensor,
timestep: int,
sample: torch.FloatTensor,
generator=None,
return_dict: bool = True,
) -> 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.
"""
t = timestep
prev_t = self.previous_timestep(t)
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[prev_t] if prev_t >= 0 else self.one
beta_prod_t = 1 - alpha_prod_t
beta_prod_t_prev = 1 - alpha_prod_t_prev
current_alpha_t = alpha_prod_t / alpha_prod_t_prev
current_beta_t = 1 - current_alpha_t
# 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.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
else:
raise ValueError(
f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample` or"
" `v_prediction` for the DDPMScheduler."
)
# 3. 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
)
# 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) * current_beta_t) / beta_prod_t
current_sample_coeff = current_alpha_t ** (0.5) * beta_prod_t_prev / beta_prod_t
# 5. Compute predicted previous sample µ_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
variance_noise = randn_tensor(
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
elif self.variance_type == "learned_range":
variance = self._get_variance(t, predicted_variance=predicted_variance)
variance = torch.exp(0.5 * 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
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
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
def previous_timestep(self, timestep):
if self.custom_timesteps:
index = (self.timesteps == timestep).nonzero(as_tuple=True)[0][0]
if index == self.timesteps.shape[0] - 1:
prev_t = torch.tensor(-1)
else:
prev_t = self.timesteps[index + 1]
else:
num_inference_steps = (
self.num_inference_steps if self.num_inference_steps else self.config.num_train_timesteps
)
prev_t = timestep - self.config.num_train_timesteps // num_inference_steps
return prev_t