Unifying Bayesian Flow Networks and Diffusion Models through Stochastic Differential Equations

TL;DR

This paper unifies Bayesian flow networks and diffusion models using stochastic differential equations, leading to improved samplers that are faster and produce higher quality samples for image and text data.

Contribution

It establishes a theoretical connection between BFNs and DMs via SDEs, and develops specialized solvers that significantly enhance sampling speed and quality.

Findings

BFNs correspond to linear SDEs in noise addition

BFN regression losses align with denoise score matching

Proposed solvers outperform original BFN sampler in sample quality and speed

Abstract

Bayesian flow networks (BFNs) iteratively refine the parameters, instead of the samples in diffusion models (DMs), of distributions at various noise levels through Bayesian inference. Owing to its differentiable nature, BFNs are promising in modeling both continuous and discrete data, while simultaneously maintaining fast sampling capabilities. This paper aims to understand and enhance BFNs by connecting them with DMs through stochastic differential equations (SDEs). We identify the linear SDEs corresponding to the noise-addition processes in BFNs, demonstrate that BFN's regression losses are aligned with denoise score matching, and validate the sampler in BFN as a first-order solver for the respective reverse-time SDE. Based on these findings and existing recipes of fast sampling in DMs, we propose specialized solvers for BFNs that markedly surpass the original BFN sampler in terms of sample quality with a limited number of function evaluations (e.g., 10) on both image and text datasets. Notably, our best sampler achieves an increase in speed of 5~20 times for free. Our code is available at https://github.com/ML-GSAI/BFN-Solver.