Diffusion Forward Step

Problem

Sample a noised latent with the diffusion forward process: x_t = sqrt(alpha_bar) * x_0 + sqrt(1 - alpha_bar) * eps.

The signature is diffusion_forward(x0, eps, alpha_bar). x0 and eps are vectors of the same length.

Hint

The mixing weights sqrt(alpha_bar) and sqrt(1 - alpha_bar) keep the variance at 1.

case 1

in: [[1,2],[0,0],1]

expected: [1,2]

case 2

in: [[0,0],[1,1],0]

expected: [1,1]

case 3

in: [[1],[1],0.5]

expected: [1.4142135624]

case 4

in: [[2,-2],[1,-1],0.25]

expected: [1.8660254038,-1.8660254038]

Starter codePython

import math
def diffusion_forward(x0, eps, alpha_bar):
    # Your code here
    pass

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