# Copyright 2022 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.
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# http://www.apache.org/licenses/LICENSE-2.0
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import warnings
from dataclasses import dataclass
from typing import List, Optional, Tuple, Union
import numpy as np
import torch
from scipy import integrate
from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import _COMPATIBLE_STABLE_DIFFUSION_SCHEDULERS, BaseOutput
from .scheduling_utils import SchedulerMixin
@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->LMSDiscrete
class LMSDiscreteSchedulerOutput(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
class LMSDiscreteScheduler(SchedulerMixin, ConfigMixin):
"""
Linear Multistep Scheduler 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#L181
[`~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.
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)
"""
_compatibles = _COMPATIBLE_STABLE_DIFFUSION_SCHEDULERS.copy()
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",
):
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
)
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)
# standard deviation of the initial noise distribution
self.init_noise_sigma = self.sigmas.max()
# 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.derivatives = []
self.is_scale_input_called = False
def scale_model_input(
self, sample: torch.FloatTensor, timestep: Union[float, torch.FloatTensor]
) -> torch.FloatTensor:
"""
Scales the denoising model input by `(sigma**2 + 1) ** 0.5` to match the K-LMS algorithm.
Args:
sample (`torch.FloatTensor`): input sample
timestep (`float` or `torch.FloatTensor`): the current timestep in the diffusion chain
Returns:
`torch.FloatTensor`: scaled input sample
"""
if isinstance(timestep, torch.Tensor):
timestep = timestep.to(self.timesteps.device)
step_index = (self.timesteps == timestep).nonzero().item()
sigma = self.sigmas[step_index]
sample = sample / ((sigma**2 + 1) ** 0.5)
self.is_scale_input_called = True
return sample
def get_lms_coefficient(self, order, t, current_order):
"""
Compute a linear multistep coefficient.
Args:
order (TODO):
t (TODO):
current_order (TODO):
"""
def lms_derivative(tau):
prod = 1.0
for k in range(order):
if current_order == k:
continue
prod *= (tau - self.sigmas[t - k]) / (self.sigmas[t - current_order] - self.sigmas[t - k])
return prod
integrated_coeff = integrate.quad(lms_derivative, self.sigmas[t], self.sigmas[t + 1], epsrel=1e-4)[0]
return integrated_coeff
def set_timesteps(self, num_inference_steps: int, device: Union[str, torch.device] = 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
timesteps = np.linspace(0, self.config.num_train_timesteps - 1, num_inference_steps, dtype=float)[::-1].copy()
sigmas = np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5)
sigmas = np.interp(timesteps, np.arange(0, len(sigmas)), sigmas)
sigmas = np.concatenate([sigmas, [0.0]]).astype(np.float32)
self.sigmas = torch.from_numpy(sigmas).to(device=device)
if str(device).startswith("mps"):
# mps does not support float64
self.timesteps = torch.from_numpy(timesteps).to(device, dtype=torch.float32)
else:
self.timesteps = torch.from_numpy(timesteps).to(device=device)
self.derivatives = []
def step(
self,
model_output: torch.FloatTensor,
timestep: Union[float, torch.FloatTensor],
sample: torch.FloatTensor,
order: int = 4,
return_dict: bool = True,
) -> Union[LMSDiscreteSchedulerOutput, 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 (`float`): current timestep in the diffusion chain.
sample (`torch.FloatTensor`):
current instance of sample being created by diffusion process.
order: coefficient for multi-step inference.
return_dict (`bool`): option for returning tuple rather than LMSDiscreteSchedulerOutput class
Returns:
[`~schedulers.scheduling_utils.LMSDiscreteSchedulerOutput`] or `tuple`:
[`~schedulers.scheduling_utils.LMSDiscreteSchedulerOutput`] if `return_dict` is True, otherwise a `tuple`.
When returning a tuple, the first element is the sample tensor.
"""
if not self.is_scale_input_called:
warnings.warn(
"The `scale_model_input` function should be called before `step` to ensure correct denoising. "
"See `StableDiffusionPipeline` for a usage example."
)
if isinstance(timestep, torch.Tensor):
timestep = timestep.to(self.timesteps.device)
step_index = (self.timesteps == timestep).nonzero().item()
sigma = self.sigmas[step_index]
# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
if self.config.prediction_type == "epsilon":
pred_original_sample = sample - sigma * 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
self.derivatives.append(derivative)
if len(self.derivatives) > order:
self.derivatives.pop(0)
# 3. Compute linear multistep coefficients
order = min(step_index + 1, order)
lms_coeffs = [self.get_lms_coefficient(order, step_index, curr_order) for curr_order in range(order)]
# 4. Compute previous sample based on the derivatives path
prev_sample = sample + sum(
coeff * derivative for coeff, derivative in zip(lms_coeffs, reversed(self.derivatives))
)
if not return_dict:
return (prev_sample,)
return LMSDiscreteSchedulerOutput(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