Soft Mixture Denoising: Beyond the Expressive Bottleneck of Diffusion Models

TL;DR

This paper reveals an expressive bottleneck in current diffusion models' denoising process, introduces Soft Mixture Denoising (SMD) to overcome this limitation, and demonstrates improved performance especially with fewer backward steps.

Contribution

The paper identifies a fundamental expressive bottleneck in diffusion models and proposes SMD, a new method that enhances their approximation capabilities and efficiency.

Findings

Diffusion models have an unbounded error in denoising.

SMD enables diffusion models to approximate Gaussian mixtures effectively.

SMD improves performance with fewer backward iterations.

Abstract

Because diffusion models have shown impressive performances in a number of tasks, such as image synthesis, there is a trend in recent works to prove (with certain assumptions) that these models have strong approximation capabilities. In this paper, we show that current diffusion models actually have an expressive bottleneck in backward denoising and some assumption made by existing theoretical guarantees is too strong. Based on this finding, we prove that diffusion models have unbounded errors in both local and global denoising. In light of our theoretical studies, we introduce soft mixture denoising (SMD), an expressive and efficient model for backward denoising. SMD not only permits diffusion models to well approximate any Gaussian mixture distributions in theory, but also is simple and efficient for implementation. Our experiments on multiple image datasets show that SMD significantly improves different types of diffusion models (e.g., DDPM), espeically in the situation of few backward iterations.