Easy

Predict x0 from Noise

~10 mincode completion

Implement predict_x0(xt, eps, alpha_bar) returning of the same shape as xt.

Examples

Inverts t1 of the noising problem

Input
predict_x0(0.7071067811865476, 0, 0.5)
Output
1

Inverts the pair at abar=0.25

Input
predict_x0([0.5, 0.8660254037844386], [0, 1], 0.25)
Output
[1, 0]

abar=1, any eps: x0 = xt

Input
predict_x0([2, -3], [8, 8], 1)
Output
[2, -3]

Hints

Hint 1

Take the square root at the end, not inside the sum.

Hint 2

Do not forget to divide by sqrt alpha bar. That step is easy to skip.

Requirements

  • alpha_bar: scalar in (0, 1]

  • Return x0, same shape as xt

Constraints

  • Allowed library: NumPy only

  • Time limit: 200 ms, Memory: 64 MB

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Where this shows up

~10 min

8 employers weight this skill

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Python
import numpy as np


def predict_x0(xt, eps, alpha_bar):
    """
    Invert the DDPM closed-form noising step.

    Args:
        xt, eps: arrays of the same shape
        alpha_bar: scalar in (0, 1]

    Returns:
        x0, same shape as xt
    """
    # YOUR CODE HERE
    pass
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