Soft Mixture Denoising: Beyond the Expressive Bottleneck of Diffusion Models
This tackles a fundamental limitation in diffusion models for image synthesis, offering a novel solution to enhance efficiency and accuracy, though it is incremental as it builds on existing diffusion frameworks.
The paper identifies an expressive bottleneck in diffusion models' backward denoising, proving they have unbounded errors, and introduces Soft Mixture Denoising (SMD) to address this, which significantly improves diffusion models like DDPM, especially with few iterations, as shown in experiments on multiple image datasets.
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.