Karras Sigma Schedule

Problem Statement

The EDM / Karras samplers parameterize diffusion by noise level sigma instead of a discrete beta schedule, and place the sampling sigmas on a warped grid controlled by rho. Build that schedule.

Background

Karras et al. (2022) define N sampling steps whose sigmas interpolate between sigma_max and sigma_min in a rho-warped space (higher rho concentrates steps near sigma_min):

$\sigma_i = \left(\sigma_{\max}^{1/\rho} + \frac{i}{N-1}\big(\sigma_{\min}^{1/\rho} - \sigma_{\max}^{1/\rho}\big)\right)^{\rho}, \quad i = 0, \dots, N-1$

so sigma_0 = sigma_max and sigma_{N-1} = sigma_min. A final sigma = 0 is appended for the last denoising jump to a clean sample.

Your Task

Implement:

def karras_sigmas(N, sigma_min, sigma_max, rho=7.0):

Return a list of N + 1 sigmas (the N warped values followed by 0.0), rounded to 4 decimals.

Input Format

• N (int): number of sampling steps, N >= 2.
• sigma_min, sigma_max (float): 0 < sigma_min < sigma_max.
• rho (float): warp exponent.

Output Format

• A list of N + 1 floats rounded to 4 decimals.

Sample

print(karras_sigmas(3, 0.1, 10.0, 7.0))

Output:

[10.0, 1.4507, 0.1, 0.0]