v-Prediction Conversion

Problem

Convert a v-prediction back to the clean sample: x0 = sqrt(alpha_bar_t) * x_t - sqrt(1 - alpha_bar_t) * v.

The signature is v_prediction_to_x0(x_t, v, alpha_bar_t). All values are scalars.

Hint

v-prediction stays well-conditioned at both very low and very high noise levels.

case 1

in: [1,0,0.5]

expected: 0.7071067812

case 2

in: [1,1,1]

expected: 1

case 3

in: [0,1,0]

expected: -1

case 4

in: [2,0.5,0.25]

expected: 0.5669872981

Starter codePython

import math
def v_prediction_to_x0(x_t, v, alpha_bar_t):
    # Your code here
    pass

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