# Copyright 2024 Katherine Crowson, The HuggingFace Team and hlky. 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
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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
# limitations under the License.
import math
from typing import List, Optional, Tuple, Union
import numpy as np
import torch
from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput
# Copied from diffusers.schedulers.scheduling_ddpm.betas_for_alpha_bar
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 HeunDiscreteScheduler(SchedulerMixin, ConfigMixin):
"""
Scheduler with Heun steps for discrete beta schedules.
This model inherits from [`SchedulerMixin`] and [`ConfigMixin`]. Check the superclass documentation for the generic
methods the library implements for all schedulers such as loading and saving.
Args:
num_train_timesteps (`int`, defaults to 1000):
The number of diffusion steps to train the model.
beta_start (`float`, defaults to 0.0001):
The starting `beta` value of inference.
beta_end (`float`, defaults to 0.02):
The final `beta` value.
beta_schedule (`str`, defaults to `"linear"`):
The beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Choose from
`linear` or `scaled_linear`.
trained_betas (`np.ndarray`, *optional*):
Pass an array of betas directly to the constructor to bypass `beta_start` and `beta_end`.
prediction_type (`str`, defaults to `epsilon`, *optional*):
Prediction type of the scheduler function; can be `epsilon` (predicts the noise of the diffusion process),
`sample` (directly predicts the noisy sample`) or `v_prediction` (see section 2.4 of [Imagen
Video](https://imagen.research.google/video/paper.pdf) paper).
clip_sample (`bool`, defaults to `True`):
Clip the predicted sample for numerical stability.
clip_sample_range (`float`, defaults to 1.0):
The maximum magnitude for sample clipping. Valid only when `clip_sample=True`.
use_karras_sigmas (`bool`, *optional*, defaults to `False`):
Whether to use Karras sigmas for step sizes in the noise schedule during the sampling process. If `True`,
the sigmas are determined according to a sequence of noise levels {σi}.
timestep_spacing (`str`, defaults to `"linspace"`):
The way the timesteps should be scaled. Refer to Table 2 of the [Common Diffusion Noise Schedules and
Sample Steps are Flawed](https://huggingface.co/papers/2305.08891) for more information.
steps_offset (`int`, defaults to 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 like in Stable
Diffusion.
"""
_compatibles = [e.name for e in KarrasDiffusionSchedulers]
order = 2
@register_to_config
def __init__(
self,
num_train_timesteps: int = 1000,
beta_start: float = 0.00085, # sensible defaults
beta_end: float = 0.012,
beta_schedule: str = "linear",
trained_betas: Optional[Union[np.ndarray, List[float]]] = None,
prediction_type: str = "epsilon",
use_karras_sigmas: Optional[bool] = False,
clip_sample: Optional[bool] = False,
clip_sample_range: float = 1.0,
timestep_spacing: str = "linspace",
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, alpha_transform_type="cosine")
elif beta_schedule == "exp":
self.betas = betas_for_alpha_bar(num_train_timesteps, alpha_transform_type="exp")
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)
# set all values
self.set_timesteps(num_train_timesteps, None, num_train_timesteps)
self.use_karras_sigmas = use_karras_sigmas
self._step_index = None
self._begin_index = None
self.sigmas = self.sigmas.to("cpu") # to avoid too much CPU/GPU communication
# Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler.index_for_timestep
def index_for_timestep(self, timestep, schedule_timesteps=None):
if schedule_timesteps is None:
schedule_timesteps = self.timesteps
indices = (schedule_timesteps == timestep).nonzero()
# The sigma index that is taken for the **very** first `step`
# is always the second index (or the last index if there is only 1)
# This way we can ensure we don't accidentally skip a sigma in
# case we start in the middle of the denoising schedule (e.g. for image-to-image)
pos = 1 if len(indices) > 1 else 0
return indices[pos].item()
@property
def init_noise_sigma(self):
# standard deviation of the initial noise distribution
if self.config.timestep_spacing in ["linspace", "trailing"]:
return self.sigmas.max()
return (self.sigmas.max() ** 2 + 1) ** 0.5
@property
def step_index(self):
"""
The index counter for current timestep. It will increae 1 after each scheduler step.
"""
return self._step_index
@property
def begin_index(self):
"""
The index for the first timestep. It should be set from pipeline with `set_begin_index` method.
"""
return self._begin_index
# Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.set_begin_index
def set_begin_index(self, begin_index: int = 0):
"""
Sets the begin index for the scheduler. This function should be run from pipeline before the inference.
Args:
begin_index (`int`):
The begin index for the scheduler.
"""
self._begin_index = begin_index
def scale_model_input(
self,
sample: torch.FloatTensor,
timestep: Union[float, torch.FloatTensor],
) -> torch.FloatTensor:
"""
Ensures interchangeability with schedulers that need to scale the denoising model input depending on the
current timestep.
Args:
sample (`torch.FloatTensor`):
The input sample.
timestep (`int`, *optional*):
The current timestep in the diffusion chain.
Returns:
`torch.FloatTensor`:
A scaled input sample.
"""
if self.step_index is None:
self._init_step_index(timestep)
sigma = self.sigmas[self.step_index]
sample = sample / ((sigma**2 + 1) ** 0.5)
return sample
def set_timesteps(
self,
num_inference_steps: int,
device: Union[str, torch.device] = None,
num_train_timesteps: Optional[int] = None,
):
"""
Sets the discrete timesteps used for the diffusion chain (to be run before inference).
Args:
num_inference_steps (`int`):
The number of diffusion steps used when generating samples with a pre-trained model.
device (`str` or `torch.device`, *optional*):
The device to which the timesteps should be moved to. If `None`, the timesteps are not moved.
"""
self.num_inference_steps = num_inference_steps
num_train_timesteps = num_train_timesteps or self.config.num_train_timesteps
# "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, num_train_timesteps - 1, num_inference_steps, dtype=np.float32)[::-1].copy()
elif self.config.timestep_spacing == "leading":
step_ratio = 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.float32)
timesteps += self.config.steps_offset
elif self.config.timestep_spacing == "trailing":
step_ratio = 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(num_train_timesteps, 0, -step_ratio)).round().copy().astype(np.float32)
timesteps -= 1
else:
raise ValueError(
f"{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'linspace', 'leading' or 'trailing'."
)
sigmas = np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5)
log_sigmas = np.log(sigmas)
sigmas = np.interp(timesteps, np.arange(0, len(sigmas)), sigmas)
if self.config.use_karras_sigmas:
sigmas = self._convert_to_karras(in_sigmas=sigmas, num_inference_steps=self.num_inference_steps)
timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in sigmas])
sigmas = np.concatenate([sigmas, [0.0]]).astype(np.float32)
sigmas = torch.from_numpy(sigmas).to(device=device)
self.sigmas = torch.cat([sigmas[:1], sigmas[1:-1].repeat_interleave(2), sigmas[-1:]])
timesteps = torch.from_numpy(timesteps)
timesteps = torch.cat([timesteps[:1], timesteps[1:].repeat_interleave(2)])
self.timesteps = timesteps.to(device=device)
# empty dt and derivative
self.prev_derivative = None
self.dt = None
self._step_index = None
self._begin_index = None
self.sigmas = self.sigmas.to("cpu") # to avoid too much CPU/GPU communication
# Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._sigma_to_t
def _sigma_to_t(self, sigma, log_sigmas):
# get log sigma
log_sigma = np.log(np.maximum(sigma, 1e-10))
# get distribution
dists = log_sigma - log_sigmas[:, np.newaxis]
# get sigmas range
low_idx = np.cumsum((dists >= 0), axis=0).argmax(axis=0).clip(max=log_sigmas.shape[0] - 2)
high_idx = low_idx + 1
low = log_sigmas[low_idx]
high = log_sigmas[high_idx]
# interpolate sigmas
w = (low - log_sigma) / (low - high)
w = np.clip(w, 0, 1)
# transform interpolation to time range
t = (1 - w) * low_idx + w * high_idx
t = t.reshape(sigma.shape)
return t
# Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_karras
def _convert_to_karras(self, in_sigmas: torch.FloatTensor, num_inference_steps) -> torch.FloatTensor:
"""Constructs the noise schedule of Karras et al. (2022)."""
# Hack to make sure that other schedulers which copy this function don't break
# TODO: Add this logic to the other schedulers
if hasattr(self.config, "sigma_min"):
sigma_min = self.config.sigma_min
else:
sigma_min = None
if hasattr(self.config, "sigma_max"):
sigma_max = self.config.sigma_max
else:
sigma_max = None
sigma_min = sigma_min if sigma_min is not None else in_sigmas[-1].item()
sigma_max = sigma_max if sigma_max is not None else in_sigmas[0].item()
rho = 7.0 # 7.0 is the value used in the paper
ramp = np.linspace(0, 1, num_inference_steps)
min_inv_rho = sigma_min ** (1 / rho)
max_inv_rho = sigma_max ** (1 / rho)
sigmas = (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
return sigmas
@property
def state_in_first_order(self):
return self.dt is None
# Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._init_step_index
def _init_step_index(self, timestep):
if self.begin_index is None:
if isinstance(timestep, torch.Tensor):
timestep = timestep.to(self.timesteps.device)
self._step_index = self.index_for_timestep(timestep)
else:
self._step_index = self._begin_index
def step(
self,
model_output: Union[torch.FloatTensor, np.ndarray],
timestep: Union[float, torch.FloatTensor],
sample: Union[torch.FloatTensor, np.ndarray],
return_dict: bool = True,
) -> Union[SchedulerOutput, Tuple]:
"""
Predict the sample from the previous timestep by reversing the SDE. This function propagates the diffusion
process from the learned model outputs (most often the predicted noise).
Args:
model_output (`torch.FloatTensor`):
The direct output from learned diffusion model.
timestep (`float`):
The current discrete timestep in the diffusion chain.
sample (`torch.FloatTensor`):
A current instance of a sample created by the diffusion process.
return_dict (`bool`):
Whether or not to return a [`~schedulers.scheduling_utils.SchedulerOutput`] or tuple.
Returns:
[`~schedulers.scheduling_utils.SchedulerOutput`] or `tuple`:
If return_dict is `True`, [`~schedulers.scheduling_utils.SchedulerOutput`] is returned, otherwise a
tuple is returned where the first element is the sample tensor.
"""
if self.step_index is None:
self._init_step_index(timestep)
if self.state_in_first_order:
sigma = self.sigmas[self.step_index]
sigma_next = self.sigmas[self.step_index + 1]
else:
# 2nd order / Heun's method
sigma = self.sigmas[self.step_index - 1]
sigma_next = self.sigmas[self.step_index]
# currently only gamma=0 is supported. This usually works best anyways.
# We can support gamma in the future but then need to scale the timestep before
# passing it to the model which requires a change in API
gamma = 0
sigma_hat = sigma * (gamma + 1) # Note: sigma_hat == sigma for now
# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
if self.config.prediction_type == "epsilon":
sigma_input = sigma_hat if self.state_in_first_order else sigma_next
pred_original_sample = sample - sigma_input * model_output
elif self.config.prediction_type == "v_prediction":
sigma_input = sigma_hat if self.state_in_first_order else sigma_next
pred_original_sample = model_output * (-sigma_input / (sigma_input**2 + 1) ** 0.5) + (
sample / (sigma_input**2 + 1)
)
elif self.config.prediction_type == "sample":
pred_original_sample = model_output
else:
raise ValueError(
f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`"
)
if self.config.clip_sample:
pred_original_sample = pred_original_sample.clamp(
-self.config.clip_sample_range, self.config.clip_sample_range
)
if self.state_in_first_order:
# 2. Convert to an ODE derivative for 1st order
derivative = (sample - pred_original_sample) / sigma_hat
# 3. delta timestep
dt = sigma_next - sigma_hat
# store for 2nd order step
self.prev_derivative = derivative
self.dt = dt
self.sample = sample
else:
# 2. 2nd order / Heun's method
derivative = (sample - pred_original_sample) / sigma_next
derivative = (self.prev_derivative + derivative) / 2
# 3. take prev timestep & sample
dt = self.dt
sample = self.sample
# free dt and derivative
# Note, this puts the scheduler in "first order mode"
self.prev_derivative = None
self.dt = None
self.sample = None
prev_sample = sample + derivative * dt
# upon completion increase step index by one
self._step_index += 1
if not return_dict:
return (prev_sample,)
return SchedulerOutput(prev_sample=prev_sample)
# Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler.add_noise
def add_noise(
self,
original_samples: torch.FloatTensor,
noise: torch.FloatTensor,
timesteps: torch.FloatTensor,
) -> torch.FloatTensor:
# Make sure sigmas and timesteps have the same device and dtype as original_samples
sigmas = self.sigmas.to(device=original_samples.device, dtype=original_samples.dtype)
if original_samples.device.type == "mps" and torch.is_floating_point(timesteps):
# mps does not support float64
schedule_timesteps = self.timesteps.to(original_samples.device, dtype=torch.float32)
timesteps = timesteps.to(original_samples.device, dtype=torch.float32)
else:
schedule_timesteps = self.timesteps.to(original_samples.device)
timesteps = timesteps.to(original_samples.device)
# self.begin_index is None when scheduler is used for training, or pipeline does not implement set_begin_index
if self.begin_index is None:
step_indices = [self.index_for_timestep(t, schedule_timesteps) for t in timesteps]
else:
step_indices = [self.begin_index] * timesteps.shape[0]
sigma = sigmas[step_indices].flatten()
while len(sigma.shape) < len(original_samples.shape):
sigma = sigma.unsqueeze(-1)
noisy_samples = original_samples + noise * sigma
return noisy_samples
def __len__(self):
return self.config.num_train_timesteps