import math
from dataclasses import dataclass
from typing import List, Optional, Tuple, Union
import numpy as np
import torch
from diffusers.schedulers.scheduling_ddim import DDIMSchedulerOutput, DDIMScheduler
from diffusers.schedulers.scheduling_utils import SchedulerMixin
from diffusers.configuration_utils import register_to_config, ConfigMixin
import pdb
class HEURI_DDIMScheduler(DDIMScheduler, SchedulerMixin, ConfigMixin):
def set_timesteps(self, num_inference_steps: int, t_start: 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.
"""
if num_inference_steps > self.config.num_train_timesteps:
raise ValueError(
f"`num_inference_steps`: {num_inference_steps} cannot be larger than `self.config.train_timesteps`:"
f" {self.config.num_train_timesteps} as the unet model trained with this scheduler can only handle"
f" maximal {self.config.num_train_timesteps} timesteps."
)
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)
.round()[::-1]
.copy()
.astype(np.int64)
)
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.int64)
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.round(np.arange(self.config.num_train_timesteps, 0, -step_ratio)).astype(np.int64)
timesteps -= 1
else:
raise ValueError(
f"{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'leading' or 'trailing'."
)
timesteps = torch.from_numpy(timesteps).to(device)
naive_sampling_step = num_inference_steps //2
# TODO for debug
# naive_sampling_step = 0
self.naive_sampling_step = naive_sampling_step
timesteps[:naive_sampling_step] = timesteps[naive_sampling_step] # refine on step 5 for 5 steps, then backward from step 6
timesteps = [timestep + 1 for timestep in timesteps]
self.timesteps = timesteps
self.gap = self.config.num_train_timesteps // self.num_inference_steps
self.prev_timesteps = [timestep for timestep in self.timesteps[1:]]
self.prev_timesteps.append(torch.zeros_like(self.prev_timesteps[-1]))
def step(
self,
model_output: torch.Tensor,
timestep: int,
prev_timestep: int,
sample: torch.Tensor,
eta: float = 0.0,
use_clipped_model_output: bool = False,
generator=None,
cur_step=None,
variance_noise: Optional[torch.Tensor] = None,
gaus_noise: Optional[torch.Tensor] = None,
return_dict: bool = True,
) -> Union[DDIMSchedulerOutput, 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.
pre_timestep (`float`):
next_timestep
sample (`torch.Tensor`):
A current instance of a sample created by the diffusion process.
eta (`float`):
The weight of noise for added noise in diffusion step.
use_clipped_model_output (`bool`, defaults to `False`):
If `True`, computes "corrected" `model_output` from the clipped predicted original sample. Necessary
because predicted original sample is clipped to [-1, 1] when `self.config.clip_sample` is `True`. If no
clipping has happened, "corrected" `model_output` would coincide with the one provided as input and
`use_clipped_model_output` has no effect.
generator (`torch.Generator`, *optional*):
A random number generator.
variance_noise (`torch.Tensor`):
Alternative to generating noise with `generator` by directly providing the noise for the variance
itself. Useful for methods such as [`CycleDiffusion`].
return_dict (`bool`, *optional*, defaults to `True`):
Whether or not to return a [`~schedulers.scheduling_ddim.DDIMSchedulerOutput`] or `tuple`.
Returns:
[`~schedulers.scheduling_utils.DDIMSchedulerOutput`] or `tuple`:
If return_dict is `True`, [`~schedulers.scheduling_ddim.DDIMSchedulerOutput`] is returned, otherwise a
tuple is returned where the first element is the sample tensor.
"""
if self.num_inference_steps is None:
raise ValueError(
"Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler"
)
# See formulas (12) and (16) of DDIM paper https://arxiv.org/pdf/2010.02502.pdf
# Ideally, read DDIM paper in-detail understanding
# Notation (<variable name> -> <name in paper>
# - pred_noise_t -> e_theta(x_t, t)
# - pred_original_sample -> f_theta(x_t, t) or x_0
# - std_dev_t -> sigma_t
# - eta -> η
# - pred_sample_direction -> "direction pointing to x_t"
# - pred_prev_sample -> "x_t-1"
# 1. get previous step value (=t-1)
# trick from heuri_sampling
if cur_step == self.naive_sampling_step and timestep == prev_timestep:
timestep += self.gap
prev_timestep = prev_timestep # NOTE naive sampling
# 2. compute alphas, betas
alpha_prod_t = self.alphas_cumprod[timestep]
alpha_prod_t_prev = self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod
beta_prod_t = 1 - alpha_prod_t
# 3. compute predicted original sample from predicted noise also called
# "predicted x_0" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
if self.config.prediction_type == "epsilon":
pred_original_sample = (sample - beta_prod_t ** (0.5) * model_output) / alpha_prod_t ** (0.5)
pred_epsilon = model_output
elif self.config.prediction_type == "sample":
pred_original_sample = model_output
pred_epsilon = (sample - alpha_prod_t ** (0.5) * pred_original_sample) / beta_prod_t ** (0.5)
elif self.config.prediction_type == "v_prediction":
pred_original_sample = (alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output
pred_epsilon = (alpha_prod_t**0.5) * model_output + (beta_prod_t**0.5) * sample
else:
raise ValueError(
f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or"
" `v_prediction`"
)
# 4. Clip or threshold "predicted x_0"
if self.config.thresholding:
pred_original_sample = self._threshold_sample(pred_original_sample)
# 5. compute variance: "sigma_t(η)" -> see formula (16)
# σ_t = sqrt((1 − α_t−1)/(1 − α_t)) * sqrt(1 − α_t/α_t−1)
variance = self._get_variance(timestep, prev_timestep)
std_dev_t = eta * variance ** (0.5)
if use_clipped_model_output:
# the pred_epsilon is always re-derived from the clipped x_0 in Glide
pred_epsilon = (sample - alpha_prod_t ** (0.5) * pred_original_sample) / beta_prod_t ** (0.5)
# 6. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
pred_sample_direction = (1 - alpha_prod_t_prev - std_dev_t**2) ** (0.5) * pred_epsilon
# 7. compute x_t without "random noise" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
prev_sample = alpha_prod_t_prev ** (0.5) * pred_original_sample + pred_sample_direction
if eta > 0:
if variance_noise is not None and generator is not None:
raise ValueError(
"Cannot pass both generator and variance_noise. Please make sure that either `generator` or"
" `variance_noise` stays `None`."
)
if variance_noise is None:
variance_noise = randn_tensor(
model_output.shape, generator=generator, device=model_output.device, dtype=model_output.dtype
)
variance = std_dev_t * variance_noise
prev_sample = prev_sample + variance
if cur_step < self.naive_sampling_step:
prev_sample = self.add_noise(pred_original_sample, torch.randn_like(pred_original_sample), timestep)
if not return_dict:
return (prev_sample,)
return DDIMSchedulerOutput(prev_sample=prev_sample, pred_original_sample=pred_original_sample)
def add_noise(
self,
original_samples: torch.Tensor,
noise: torch.Tensor,
timesteps: torch.IntTensor,
) -> torch.Tensor:
# Make sure alphas_cumprod and timestep have same device and dtype as original_samples
# Move the self.alphas_cumprod to device to avoid redundant CPU to GPU data movement
# for the subsequent add_noise calls
self.alphas_cumprod = self.alphas_cumprod.to(device=original_samples.device)
alphas_cumprod = self.alphas_cumprod.to(dtype=original_samples.dtype)
timesteps = timesteps.to(original_samples.device)
sqrt_alpha_prod = alphas_cumprod[timesteps] ** 0.5
sqrt_alpha_prod = sqrt_alpha_prod.flatten()
while len(sqrt_alpha_prod.shape) < len(original_samples.shape):
sqrt_alpha_prod = sqrt_alpha_prod.unsqueeze(-1)
sqrt_one_minus_alpha_prod = (1 - alphas_cumprod[timesteps]) ** 0.5
sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.flatten()
while len(sqrt_one_minus_alpha_prod.shape) < len(original_samples.shape):
sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.unsqueeze(-1)
noisy_samples = sqrt_alpha_prod * original_samples + sqrt_one_minus_alpha_prod * noise
return noisy_samples