# Copyright 2024 Katherine Crowson 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,
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import math
from dataclasses import dataclass
from typing import Optional, Tuple, Union
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 SchedulerMixin
logger = logging.get_logger(__name__) # pylint: disable=invalid-name
@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerDiscrete
class EDMEulerSchedulerOutput(BaseOutput):
"""
Output class for the scheduler's `step` function output.
Args:
prev_sample (`torch.Tensor` 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.Tensor` 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.Tensor
pred_original_sample: Optional[torch.Tensor] = None
class EDMEulerScheduler(SchedulerMixin, ConfigMixin):
"""
Implements the Euler scheduler in EDM formulation as presented in Karras et al. 2022 [1].
[1] Karras, Tero, et al. "Elucidating the Design Space of Diffusion-Based Generative Models."
https://arxiv.org/abs/2206.00364
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:
sigma_min (`float`, *optional*, defaults to 0.002):
Minimum noise magnitude in the sigma schedule. This was set to 0.002 in the EDM paper [1]; a reasonable
range is [0, 10].
sigma_max (`float`, *optional*, defaults to 80.0):
Maximum noise magnitude in the sigma schedule. This was set to 80.0 in the EDM paper [1]; a reasonable
range is [0.2, 80.0].
sigma_data (`float`, *optional*, defaults to 0.5):
The standard deviation of the data distribution. This is set to 0.5 in the EDM paper [1].
sigma_schedule (`str`, *optional*, defaults to `karras`):
Sigma schedule to compute the `sigmas`. By default, we the schedule introduced in the EDM paper
(https://arxiv.org/abs/2206.00364). Other acceptable value is "exponential". The exponential schedule was
incorporated in this model: https://huggingface.co/stabilityai/cosxl.
num_train_timesteps (`int`, defaults to 1000):
The number of diffusion steps to train the model.
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).
rho (`float`, *optional*, defaults to 7.0):
The rho parameter used for calculating the Karras sigma schedule, which is set to 7.0 in the EDM paper [1].
"""
_compatibles = []
order = 1
@register_to_config
def __init__(
self,
sigma_min: float = 0.002,
sigma_max: float = 80.0,
sigma_data: float = 0.5,
sigma_schedule: str = "karras",
num_train_timesteps: int = 1000,
prediction_type: str = "epsilon",
rho: float = 7.0,
):
if sigma_schedule not in ["karras", "exponential"]:
raise ValueError(f"Wrong value for provided for `{sigma_schedule=}`.`")
# setable values
self.num_inference_steps = None
ramp = torch.linspace(0, 1, num_train_timesteps)
if sigma_schedule == "karras":
sigmas = self._compute_karras_sigmas(ramp)
elif sigma_schedule == "exponential":
sigmas = self._compute_exponential_sigmas(ramp)
self.timesteps = self.precondition_noise(sigmas)
self.sigmas = torch.cat([sigmas, torch.zeros(1, device=sigmas.device)])
self.is_scale_input_called = False
self._step_index = None
self._begin_index = None
self.sigmas = self.sigmas.to("cpu") # to avoid too much CPU/GPU communication
@property
def init_noise_sigma(self):
# standard deviation of the initial noise distribution
return (self.config.sigma_max**2 + 1) ** 0.5
@property
def step_index(self):
"""
The index counter for current timestep. It will increase 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 precondition_inputs(self, sample, sigma):
c_in = 1 / ((sigma**2 + self.config.sigma_data**2) ** 0.5)
scaled_sample = sample * c_in
return scaled_sample
def precondition_noise(self, sigma):
if not isinstance(sigma, torch.Tensor):
sigma = torch.tensor([sigma])
c_noise = 0.25 * torch.log(sigma)
return c_noise
def precondition_outputs(self, sample, model_output, sigma):
sigma_data = self.config.sigma_data
c_skip = sigma_data**2 / (sigma**2 + sigma_data**2)
if self.config.prediction_type == "epsilon":
c_out = sigma * sigma_data / (sigma**2 + sigma_data**2) ** 0.5
elif self.config.prediction_type == "v_prediction":
c_out = -sigma * sigma_data / (sigma**2 + sigma_data**2) ** 0.5
else:
raise ValueError(f"Prediction type {self.config.prediction_type} is not supported.")
denoised = c_skip * sample + c_out * model_output
return denoised
def scale_model_input(self, sample: torch.Tensor, timestep: Union[float, torch.Tensor]) -> torch.Tensor:
"""
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.Tensor`):
The input sample.
timestep (`int`, *optional*):
The current timestep in the diffusion chain.
Returns:
`torch.Tensor`:
A scaled input sample.
"""
if self.step_index is None:
self._init_step_index(timestep)
sigma = self.sigmas[self.step_index]
sample = self.precondition_inputs(sample, sigma)
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
ramp = torch.linspace(0, 1, self.num_inference_steps)
if self.config.sigma_schedule == "karras":
sigmas = self._compute_karras_sigmas(ramp)
elif self.config.sigma_schedule == "exponential":
sigmas = self._compute_exponential_sigmas(ramp)
sigmas = sigmas.to(dtype=torch.float32, device=device)
self.timesteps = self.precondition_noise(sigmas)
self.sigmas = torch.cat([sigmas, torch.zeros(1, device=sigmas.device)])
self._step_index = None
self._begin_index = None
self.sigmas = self.sigmas.to("cpu") # to avoid too much CPU/GPU communication
# Taken from https://github.com/crowsonkb/k-diffusion/blob/686dbad0f39640ea25c8a8c6a6e56bb40eacefa2/k_diffusion/sampling.py#L17
def _compute_karras_sigmas(self, ramp, sigma_min=None, sigma_max=None) -> torch.Tensor:
"""Constructs the noise schedule of Karras et al. (2022)."""
sigma_min = sigma_min or self.config.sigma_min
sigma_max = sigma_max or self.config.sigma_max
rho = self.config.rho
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 _compute_exponential_sigmas(self, ramp, sigma_min=None, sigma_max=None) -> torch.Tensor:
"""Implementation closely follows k-diffusion.
https://github.com/crowsonkb/k-diffusion/blob/6ab5146d4a5ef63901326489f31f1d8e7dd36b48/k_diffusion/sampling.py#L26
"""
sigma_min = sigma_min or self.config.sigma_min
sigma_max = sigma_max or self.config.sigma_max
sigmas = torch.linspace(math.log(sigma_min), math.log(sigma_max), len(ramp)).exp().flip(0)
return sigmas
# 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()
# 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: torch.Tensor,
timestep: Union[float, torch.Tensor],
sample: torch.Tensor,
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[EDMEulerSchedulerOutput, 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.Tensor`):
The direct output from learned diffusion model.
timestep (`float`):
The current discrete timestep in the diffusion chain.
sample (`torch.Tensor`):
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.EDMEulerSchedulerOutput`] or tuple.
Returns:
[`~schedulers.scheduling_euler_discrete.EDMEulerSchedulerOutput`] or `tuple`:
If return_dict is `True`, [`~schedulers.scheduling_euler_discrete.EDMEulerSchedulerOutput`] is
returned, otherwise a tuple is returned where the first element is the sample tensor.
"""
if isinstance(timestep, (int, torch.IntTensor, torch.LongTensor)):
raise ValueError(
(
"Passing integer indices (e.g. from `enumerate(timesteps)`) as timesteps to"
" `EDMEulerScheduler.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)
# Upcast to avoid precision issues when computing prev_sample
sample = sample.to(torch.float32)
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
pred_original_sample = self.precondition_outputs(sample, model_output, sigma_hat)
# 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
# Cast sample back to model compatible dtype
prev_sample = prev_sample.to(model_output.dtype)
# upon completion increase step index by one
self._step_index += 1
if not return_dict:
return (prev_sample,)
return EDMEulerSchedulerOutput(prev_sample=prev_sample, pred_original_sample=pred_original_sample)
# Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler.add_noise
def add_noise(
self,
original_samples: torch.Tensor,
noise: torch.Tensor,
timesteps: torch.Tensor,
) -> torch.Tensor:
# 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]
elif self.step_index is not None:
# add_noise is called after first denoising step (for inpainting)
step_indices = [self.step_index] * timesteps.shape[0]
else:
# add noise is called before first denoising step to create initial latent(img2img)
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