Optimizing Noise Schedules in Diffusion Models

We study the model error in discrete-time diffusion models: even with a perfect denoiser, forcing the reverse transitions to be Gaussian introduces error. We prove a universal upper bound on the Gaussianization error at every step, under only a finite-second-moment assumption on the data. We derive the noise schedule that minimizes the upper bound in closed form, and show that it makes the noise-to-signal odds ratio grow geometrically in the step index. Across seven image datasets, our schedules consistently improve negative log-likelihood over standard schedules, while also improving FID in many cases.