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# Copyright 2022 NVIDIA 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
#
# 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.
from dataclasses import dataclass
from typing import Optional, Tuple, Union
import numpy as np
import torch
from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput
from .scheduling_utils import SchedulerMixin
@dataclass
class KarrasVeOutput(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.
derivative (`torch.FloatTensor` of shape `(batch_size, num_channels, height, width)` for images):
Derivative of predicted original image sample (x_0).
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
derivative: torch.FloatTensor
pred_original_sample: Optional[torch.FloatTensor] = None
class KarrasVeScheduler(SchedulerMixin, ConfigMixin):
"""
Stochastic sampling from Karras et al. [1] tailored to the Variance-Expanding (VE) models [2]. Use Algorithm 2 and
the VE column of Table 1 from [1] for reference.
[1] Karras, Tero, et al. "Elucidating the Design Space of Diffusion-Based Generative Models."
https://arxiv.org/abs/2206.00364 [2] Song, Yang, et al. "Score-based generative modeling through stochastic
differential equations." https://arxiv.org/abs/2011.13456
[`~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.
For more details on the parameters, see the original paper's Appendix E.: "Elucidating the Design Space of
Diffusion-Based Generative Models." https://arxiv.org/abs/2206.00364. The grid search values used to find the
optimal {s_noise, s_churn, s_min, s_max} for a specific model are described in Table 5 of the paper.
Args:
sigma_min (`float`): minimum noise magnitude
sigma_max (`float`): maximum noise magnitude
s_noise (`float`): the amount of additional noise to counteract loss of detail during sampling.
A reasonable range is [1.000, 1.011].
s_churn (`float`): the parameter controlling the overall amount of stochasticity.
A reasonable range is [0, 100].
s_min (`float`): the start value of the sigma range where we add noise (enable stochasticity).
A reasonable range is [0, 10].
s_max (`float`): the end value of the sigma range where we add noise.
A reasonable range is [0.2, 80].
"""
order = 2
@register_to_config
def __init__(
self,
sigma_min: float = 0.02,
sigma_max: float = 100,
s_noise: float = 1.007,
s_churn: float = 80,
s_min: float = 0.05,
s_max: float = 50,
):
# standard deviation of the initial noise distribution
self.init_noise_sigma = sigma_max
# setable values
self.num_inference_steps: int = None
self.timesteps: np.IntTensor = None
self.schedule: torch.FloatTensor = None # sigma(t_i)
def scale_model_input(self, sample: torch.FloatTensor, timestep: Optional[int] = None) -> torch.FloatTensor:
"""
Ensures interchangeability with schedulers that need to scale the denoising model input depending on the
current timestep.
Args:
sample (`torch.FloatTensor`): input sample
timestep (`int`, optional): current timestep
Returns:
`torch.FloatTensor`: scaled input sample
"""
return sample
def set_timesteps(self, num_inference_steps: int, device: Union[str, torch.device] = None):
"""
Sets the continuous 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.
"""
self.num_inference_steps = num_inference_steps
timesteps = np.arange(0, self.num_inference_steps)[::-1].copy()
self.timesteps = torch.from_numpy(timesteps).to(device)
schedule = [
(
self.config.sigma_max**2
* (self.config.sigma_min**2 / self.config.sigma_max**2) ** (i / (num_inference_steps - 1))
)
for i in self.timesteps
]
self.schedule = torch.tensor(schedule, dtype=torch.float32, device=device)
def add_noise_to_input(
self, sample: torch.FloatTensor, sigma: float, generator: Optional[torch.Generator] = None
) -> Tuple[torch.FloatTensor, float]:
"""
Explicit Langevin-like "churn" step of adding noise to the sample according to a factor gamma_i ≥ 0 to reach a
higher noise level sigma_hat = sigma_i + gamma_i*sigma_i.
TODO Args:
"""
if self.config.s_min <= sigma <= self.config.s_max:
gamma = min(self.config.s_churn / self.num_inference_steps, 2**0.5 - 1)
else:
gamma = 0
# sample eps ~ N(0, S_noise^2 * I)
eps = self.config.s_noise * torch.randn(sample.shape, generator=generator).to(sample.device)
sigma_hat = sigma + gamma * sigma
sample_hat = sample + ((sigma_hat**2 - sigma**2) ** 0.5 * eps)
return sample_hat, sigma_hat
def step(
self,
model_output: torch.FloatTensor,
sigma_hat: float,
sigma_prev: float,
sample_hat: torch.FloatTensor,
return_dict: bool = True,
) -> Union[KarrasVeOutput, 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.
sigma_hat (`float`): TODO
sigma_prev (`float`): TODO
sample_hat (`torch.FloatTensor`): TODO
return_dict (`bool`): option for returning tuple rather than KarrasVeOutput class
KarrasVeOutput: updated sample in the diffusion chain and derivative (TODO double check).
Returns:
[`~schedulers.scheduling_karras_ve.KarrasVeOutput`] or `tuple`:
[`~schedulers.scheduling_karras_ve.KarrasVeOutput`] if `return_dict` is True, otherwise a `tuple`. When
returning a tuple, the first element is the sample tensor.
"""
pred_original_sample = sample_hat + sigma_hat * model_output
derivative = (sample_hat - pred_original_sample) / sigma_hat
sample_prev = sample_hat + (sigma_prev - sigma_hat) * derivative
if not return_dict:
return (sample_prev, derivative)
return KarrasVeOutput(
prev_sample=sample_prev, derivative=derivative, pred_original_sample=pred_original_sample
)
def step_correct(
self,
model_output: torch.FloatTensor,
sigma_hat: float,
sigma_prev: float,
sample_hat: torch.FloatTensor,
sample_prev: torch.FloatTensor,
derivative: torch.FloatTensor,
return_dict: bool = True,
) -> Union[KarrasVeOutput, Tuple]:
"""
Correct the predicted sample based on the output model_output of the network. TODO complete description
Args:
model_output (`torch.FloatTensor`): direct output from learned diffusion model.
sigma_hat (`float`): TODO
sigma_prev (`float`): TODO
sample_hat (`torch.FloatTensor`): TODO
sample_prev (`torch.FloatTensor`): TODO
derivative (`torch.FloatTensor`): TODO
return_dict (`bool`): option for returning tuple rather than KarrasVeOutput class
Returns:
prev_sample (TODO): updated sample in the diffusion chain. derivative (TODO): TODO
"""
pred_original_sample = sample_prev + sigma_prev * model_output
derivative_corr = (sample_prev - pred_original_sample) / sigma_prev
sample_prev = sample_hat + (sigma_prev - sigma_hat) * (0.5 * derivative + 0.5 * derivative_corr)
if not return_dict:
return (sample_prev, derivative)
return KarrasVeOutput(
prev_sample=sample_prev, derivative=derivative, pred_original_sample=pred_original_sample
)
def add_noise(self, original_samples, noise, timesteps):
raise NotImplementedError()
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