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scheduling_heun_discrete.py
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scheduling_heun_discrete.py
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# Copyright 2023 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
#
# 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) -> 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 HeunDiscreteScheduler(SchedulerMixin, ConfigMixin):
"""
Implements Algorithm 2 (Heun steps) from Karras et al. (2022). for discrete beta schedules. Based on the original
k-diffusion implementation by Katherine Crowson:
https://github.com/crowsonkb/k-diffusion/blob/481677d114f6ea445aa009cf5bd7a9cdee909e47/k_diffusion/sampling.py#L90
[`~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.
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` or `scaled_linear`.
trained_betas (`np.ndarray`, optional):
option to pass an array of betas directly to the constructor to bypass `beta_start`, `beta_end` etc.
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`.
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).
use_karras_sigmas (`bool`, *optional*, defaults to `False`):
This parameter controls whether to use Karras sigmas (Karras et al. (2022) scheme) for step sizes in the
noise schedule during the sampling process. If True, the sigmas will be determined according to a sequence
of noise levels {蟽i} as defined in Equation (5) of the paper https://arxiv.org/pdf/2206.00364.pdf.
"""
_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,
):
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)
# set all values
self.set_timesteps(num_train_timesteps, None, num_train_timesteps)
self.use_karras_sigmas = use_karras_sigmas
def index_for_timestep(self, timestep, schedule_timesteps=None):
if schedule_timesteps is None:
schedule_timesteps = self.timesteps
indices = (schedule_timesteps == timestep).nonzero()
if self.state_in_first_order:
pos = -1
else:
pos = 0
return indices[pos].item()
def scale_model_input(
self,
sample: torch.FloatTensor,
timestep: Union[float, torch.FloatTensor],
) -> torch.FloatTensor:
"""
Args:
Ensures interchangeability with schedulers that need to scale the denoising model input depending on the
current timestep.
sample (`torch.FloatTensor`): input sample timestep (`int`, optional): current timestep
Returns:
`torch.FloatTensor`: scaled input sample
"""
step_index = self.index_for_timestep(timestep)
sigma = self.sigmas[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 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.
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
timesteps = np.linspace(0, num_train_timesteps - 1, num_inference_steps, dtype=float)[::-1].copy()
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.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:]])
# standard deviation of the initial noise distribution
self.init_noise_sigma = self.sigmas.max()
timesteps = torch.from_numpy(timesteps)
timesteps = torch.cat([timesteps[:1], timesteps[1:].repeat_interleave(2)])
if str(device).startswith("mps"):
# mps does not support float64
self.timesteps = timesteps.to(device, dtype=torch.float32)
else:
self.timesteps = timesteps.to(device=device)
# empty dt and derivative
self.prev_derivative = None
self.dt = None
# 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(sigma)
# 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)."""
sigma_min: float = in_sigmas[-1].item()
sigma_max: float = 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
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]:
"""
Args:
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).
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.
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.
"""
step_index = self.index_for_timestep(timestep)
if self.state_in_first_order:
sigma = self.sigmas[step_index]
sigma_next = self.sigmas[step_index + 1]
else:
# 2nd order / Heun's method
sigma = self.sigmas[step_index - 1]
sigma_next = self.sigmas[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":
raise NotImplementedError("prediction_type not implemented yet: sample")
else:
raise ValueError(
f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`"
)
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
if not return_dict:
return (prev_sample,)
return SchedulerOutput(prev_sample=prev_sample)
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)
step_indices = [self.index_for_timestep(t, schedule_timesteps) for t in timesteps]
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