Entropy-Minimal Noise Schedules for Denoising Diffusion Probabilistic Models: A Non-Equilibrium Thermodynamics Approach
Tawhid Bin Omar
Affiliation: St. Joseph Higher Secondary School
IJSCAR Vol. 3, Issue 2 (2026) · pp. 10–15
DOI: 10.67149/yhjs2024.5/k2v9p4cz
Abstract
Noise schedules in denoising diffusion probabilistic models (DDPMs) control how quickly information is destroyed during the forward Markov chain. Existing schedules – linear cosine quadratic – were designed by heuristic trial-and-error. We ask: what schedule is optimal for a fixed number of diffusion steps T? We answer this by framing the problem as minimizing the total discretization error of the forward process which is a sum of KL divergences between consecutive noise marginals. Using a Cauchy-Schwarz argument we prove that the unique minimizer is a geometric interpolation of the noise variance equivalently requiring log(1 - alpha_t) to be linear in t. We call this the Entropy-Minimal (EM) schedule as it is the discrete analog of the minimum entropy production principle from non-equilibrium thermodynamics. Experiments on a 2D Gaussian mixture show that the EM schedule achieves a coefficient of variation in per-step KL divergence of 0.03 more than 500x lower than any standard schedule and produces the best generative quality by both Maximum Mean Discrepancy (MMD = 0.0106) and Sliced Wasserstein Distance (SWD = 0.2118).
Keywords: diffusion models, noise schedule, entropy production, stochastic thermodynamics, generative models