# Copyright 2023 Katherine Crowson 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
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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,
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# See the License for the specific language governing permissions and
# limitations under the License.
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, logging
from ..utils.torch_utils import randn_tensor
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin
logger = logging.get_logger(__name__) # pylint: disable=invalid-name
@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerDiscrete
class EulerDiscreteSchedulerOutput(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,
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 EulerDiscreteScheduler(SchedulerMixin, ConfigMixin):
"""
Euler scheduler.
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).
interpolation_type(`str`, defaults to `"linear"`, *optional*):
The interpolation type to compute intermediate sigmas for the scheduler denoising steps. Should be on of
`"linear"` or `"log_linear"`.
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 = 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,
prediction_type: str = "epsilon",
interpolation_type: str = "linear",
use_karras_sigmas: Optional[bool] = False,
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)
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)
sigmas = np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5)
sigmas = np.concatenate([sigmas[::-1], [0.0]]).astype(np.float32)
self.sigmas = torch.from_numpy(sigmas)
# setable values
self.num_inference_steps = None
timesteps = np.linspace(0, num_train_timesteps - 1, num_train_timesteps, dtype=float)[::-1].copy()
self.timesteps = torch.from_numpy(timesteps)
self.is_scale_input_called = False
self.use_karras_sigmas = use_karras_sigmas
self._step_index = None
@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
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. Scales the denoising model input by `(sigma**2 + 1) ** 0.5` to match the Euler algorithm.
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)
self.is_scale_input_called = True
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 (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
# "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, dtype=np.float32)[
::-1
].copy()
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.float32)
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.arange(self.config.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)
if self.config.interpolation_type == "linear":
sigmas = np.interp(timesteps, np.arange(0, len(sigmas)), sigmas)
elif self.config.interpolation_type == "log_linear":
sigmas = torch.linspace(np.log(sigmas[-1]), np.log(sigmas[0]), num_inference_steps + 1).exp()
else:
raise ValueError(
f"{self.config.interpolation_type} is not implemented. Please specify interpolation_type to either"
" 'linear' or 'log_linear'"
)
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)
self.sigmas = torch.from_numpy(sigmas).to(device=device)
self.timesteps = torch.from_numpy(timesteps).to(device=device)
self._step_index = None
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 https://github.com/crowsonkb/k-diffusion/blob/686dbad0f39640ea25c8a8c6a6e56bb40eacefa2/k_diffusion/sampling.py#L17
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
def _init_step_index(self, timestep):
if isinstance(timestep, torch.Tensor):
timestep = timestep.to(self.timesteps.device)
index_candidates = (self.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)
if len(index_candidates) > 1:
step_index = index_candidates[1]
else:
step_index = index_candidates[0]
self._step_index = step_index.item()
def step(
self,
model_output: torch.FloatTensor,
timestep: Union[float, torch.FloatTensor],
sample: torch.FloatTensor,
s_churn: float = 0.0,
s_tmin: float = 0.0,
s_tmax: float = float("inf"),
s_noise: float = 1.0,
generator: Optional[torch.Generator] = None,
return_dict: bool = True,
) -> Union[EulerDiscreteSchedulerOutput, 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.
s_churn (`float`):
s_tmin (`float`):
s_tmax (`float`):
s_noise (`float`, defaults to 1.0):
Scaling factor for noise added to the sample.
generator (`torch.Generator`, *optional*):
A random number generator.
return_dict (`bool`):
Whether or not to return a [`~schedulers.scheduling_euler_discrete.EulerDiscreteSchedulerOutput`] or
tuple.
Returns:
[`~schedulers.scheduling_euler_discrete.EulerDiscreteSchedulerOutput`] or `tuple`:
If return_dict is `True`, [`~schedulers.scheduling_euler_discrete.EulerDiscreteSchedulerOutput`] is
returned, otherwise a tuple is returned where the first element is the sample tensor.
"""
if (
isinstance(timestep, int)
or isinstance(timestep, torch.IntTensor)
or isinstance(timestep, torch.LongTensor)
):
raise ValueError(
(
"Passing integer indices (e.g. from `enumerate(timesteps)`) as timesteps to"
" `EulerDiscreteScheduler.step()` is not supported. Make sure to pass"
" one of the `scheduler.timesteps` as a timestep."
),
)
if not self.is_scale_input_called:
logger.warning(
"The `scale_model_input` function should be called before `step` to ensure correct denoising. "
"See `StableDiffusionPipeline` for a usage example."
)
if self.step_index is None:
self._init_step_index(timestep)
sigma = self.sigmas[self.step_index]
gamma = min(s_churn / (len(self.sigmas) - 1), 2**0.5 - 1) if s_tmin <= sigma <= s_tmax else 0.0
noise = randn_tensor(
model_output.shape, dtype=model_output.dtype, device=model_output.device, generator=generator
)
eps = noise * s_noise
sigma_hat = sigma * (gamma + 1)
if gamma > 0:
sample = sample + eps * (sigma_hat**2 - sigma**2) ** 0.5
# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
# NOTE: "original_sample" should not be an expected prediction_type but is left in for
# backwards compatibility
if self.config.prediction_type == "original_sample" or self.config.prediction_type == "sample":
pred_original_sample = model_output
elif self.config.prediction_type == "epsilon":
pred_original_sample = sample - sigma_hat * model_output
elif self.config.prediction_type == "v_prediction":
# * c_out + input * c_skip
pred_original_sample = model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
else:
raise ValueError(
f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`"
)
# 2. Convert to an ODE derivative
derivative = (sample - pred_original_sample) / sigma_hat
dt = self.sigmas[self.step_index + 1] - sigma_hat
prev_sample = sample + derivative * dt
# upon completion increase step index by one
self._step_index += 1
if not return_dict:
return (prev_sample,)
return EulerDiscreteSchedulerOutput(prev_sample=prev_sample, pred_original_sample=pred_original_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 = [(schedule_timesteps == t).nonzero().item() 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