Structured Diffusion Models with Mixture of Gaussians as Prior Distribution

TL;DR

This paper introduces structured diffusion models utilizing a mixture of Gaussians as the prior, enabling the incorporation of data-specific structure and demonstrating advantages in robustness and training efficiency.

Contribution

The paper presents a novel diffusion model framework with a mixture of Gaussians prior, along with a simple training procedure and theoretical analysis of its benefits.

Findings

Outperforms classical diffusion models in experiments

Robust to prior mis-specification

Effective with limited training resources

Abstract

We propose a class of structured diffusion models, in which the prior distribution is chosen as a mixture of Gaussians, rather than a standard Gaussian distribution. The specific mixed Gaussian distribution, as prior, can be chosen to incorporate certain structured information of the data. We develop a simple-to-implement training procedure that smoothly accommodates the use of mixed Gaussian as prior. Theory is provided to quantify the benefits of our proposed models, compared to the classical diffusion models. Numerical experiments with synthetic, image and operational data are conducted to show comparative advantages of our model. Our method is shown to be robust to mis-specifications and in particular suits situations where training resources are limited or faster training in real time is desired.