DPM-Solver Step

Problem

One first-order DPM-Solver step in log-SNR space. With alpha = sqrt(alpha_bar), sigma = sqrt(1 - alpha_bar), lambda = log(alpha / sigma) and h = lambda_prev - lambda_t, the update is x_prev = (sigma_prev / sigma_t) * x_t - alpha_prev * (exp(-h) - 1) * eps_pred.

The signature is dpm_solver_step(x_t, eps_pred, alpha_bar_t, alpha_bar_prev). All values are scalars.

Hint

Solving the probability-flow ODE in log-SNR space makes the step sizes uniform.

Test cases

case 1

in: [1,0,0.5,0.8]

expected: 0.632455532

case 2

in: [0.5,1,0.2,0.5]

expected: 0.7488380981

case 3

in: [-1,0.5,0.3,0.6]

expected: -0.5756502792

case 4

in: [2,-1,0.5,0.9]

expected: 0.261971659

Starter codePython

import math
def dpm_solver_step(x_t, eps_pred, alpha_bar_t, alpha_bar_prev):
    # Your code here
    pass

4 test cases · run your code against them in the editor