Reconsidering Noise for Denoising Diffusion Probabilistic Models

Stephen D. Liang

Keywords: Diffusion Models, Noise, Probabilistic Models

TL;DR: Reconsidering Noise for Diffusion Models

Abstract: Denoising Diffusion Probabilistic Models (DDPMs) typically utilize white Gaussian noise in their processes. In this paper, we explore several theoretical aspects of noise in DDPMs. We derive a necessary condition for the input of the forward diffusion process to match the denoised output, as well as a sufficient condition for when they differ. Our findings show that minimizing the Mean Square Error (MSE) between the actual and predicted noise in a DDPM is more effective with colored Gaussian noise than with white Gaussian noise, and that non-Gaussian noise offers further improvements in MSE minimization. Additionally, we demonstrate that the probability of error between the input and denoised output in a DDPM is reduced when using colored Gaussian noise compared to white Gaussian noise. Furthermore, we show that a DDPM trained with white Gaussian noise can effectively denoise processes involving any zero-mean symmetric distribution noise. Theoretical results are validated through experiments using the Hugging Face Hub 1000 butterfly pictures dataset and the LSUN Church-256 dataset, with experimental outcomes confirming our theoretical findings.

Submission Number: 64