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samplers.py
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samplers.py
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from abc import ABC, abstractmethod
from collections import deque
from dataclasses import dataclass
from functools import cached_property
import torch
@dataclass
class InstantaneousPrediction:
sigma: float
x_t: torch.Tensor
pred_x_0: torch.Tensor
@cached_property
def pred_eps(self):
return (self.x_t - self.pred_x_0) / self.sigma
class Sampler(ABC):
@abstractmethod
def reset(self):
pass
@abstractmethod
def step(self, sigma_t: float, sigma_t_plus_1: float, pred_at_x_t: InstantaneousPrediction):
"""
Take a step from sigma_t to sigma_t_plus_1.
"""
pass
class EulerSampler(Sampler):
def reset(self):
pass
def step(self, sigma_t: float, sigma_t_plus_1: float, pred_at_x_t: InstantaneousPrediction):
return pred_at_x_t.x_t + pred_at_x_t.pred_eps * (sigma_t_plus_1 - sigma_t)
class MultistepDPMSampler(Sampler):
def reset(self):
self.history: deque[InstantaneousPrediction] = deque(maxlen=2) # Order k=3
def step(self, sigma_t: float, sigma_t_plus_1: float, pred_at_x_t: InstantaneousPrediction):
if len(self.history) == 0:
x_t_plus_1 = self.step_first_order(sigma_t, sigma_t_plus_1, pred_at_x_t)
elif len(self.history) == 1:
x_t_plus_1 = self.step_second_order(sigma_t, sigma_t_plus_1, pred_at_x_t)
else:
x_t_plus_1 = self.step_third_order(sigma_t, sigma_t_plus_1, pred_at_x_t)
self.history.append(pred_at_x_t)
return x_t_plus_1
def step_first_order(self, sigma_t: float, sigma_t_plus_1: float, pred_at_x_t: InstantaneousPrediction):
d_sigma = sigma_t_plus_1 - sigma_t
return pred_at_x_t.x_t + pred_at_x_t.pred_eps * d_sigma
def step_second_order(self, sigma_t: float, sigma_t_plus_1: float, pred_at_x_t: InstantaneousPrediction):
pred_at_x_t_minus_1 = self.history[-1]
d_sigma = sigma_t_plus_1 - sigma_t
pred_first_derivative = (
(pred_at_x_t.pred_eps - pred_at_x_t_minus_1.pred_eps) /
(pred_at_x_t.sigma - pred_at_x_t_minus_1.sigma)
)
return (
pred_at_x_t.x_t +
pred_at_x_t.pred_eps * d_sigma +
(1/2) * pred_first_derivative * d_sigma ** 2
)
def step_third_order(self, sigma_t: float, sigma_t_plus_1: float, pred_at_x_t: InstantaneousPrediction):
pred_at_x_t_minus_1 = self.history[-1]
pred_at_x_t_minus_2 = self.history[-2]
d_sigma = sigma_t_plus_1 - sigma_t
pred_first_derivative = (
(pred_at_x_t.pred_eps - pred_at_x_t_minus_1.pred_eps) /
(pred_at_x_t.sigma - pred_at_x_t_minus_1.sigma)
)
pred_first_derivative_past = (
(pred_at_x_t_minus_1.pred_eps - pred_at_x_t_minus_2.pred_eps) /
(pred_at_x_t_minus_1.sigma - pred_at_x_t_minus_2.sigma)
)
pred_second_derivative = (
(pred_first_derivative - pred_first_derivative_past) /
(0.5 * (pred_at_x_t.sigma + pred_at_x_t_minus_1.sigma) -
0.5 * (pred_at_x_t_minus_1.sigma + pred_at_x_t_minus_2.sigma))
)
return (
pred_at_x_t.x_t +
pred_at_x_t.pred_eps * d_sigma +
(1/2) * pred_first_derivative * d_sigma ** 2 +
(1/6) * pred_second_derivative * d_sigma ** 3
)