Euler Ancestral Step

Problem

One Euler ancestral sampling step. Estimate x0 = (x_t - sigma_t * eps) / alpha_t, compute sigma_up = sqrt((1 - ab_prev)/(1 - ab_t)) * sqrt(1 - ab_t/ab_prev) and sigma_down2 = max(0, 1 - ab_prev - sigma_up^2), then return sqrt(ab_prev) * x0 + sqrt(sigma_down2) * eps + sigma_up * noise, with one seeded random.gauss(0, 1) noise draw.

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

Hint

Ancestral samplers inject fresh noise at every step, trading determinism for stochastic diversity.

Test cases

case 1

in: [1,0,0.5,0.8,0]

expected: 1.629635872

case 2

in: [0,1,0.25,0.5,1]

expected: -0.0727627669

case 3

in: [2,0.5,0.5,0.8,42]

expected: 2.1386059868

case 4

in: [1,0,0.9,0.95,7]

expected: 0.9858930698

Starter codePython

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

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