Unifying Bayesian Flow Networks and Diffusion Models through Stochastic Differential Equations
This work addresses the need for faster and higher-quality generative models in machine learning, offering incremental improvements by adapting existing diffusion model techniques to BFNs.
The paper tackles the problem of improving Bayesian flow networks (BFNs) by connecting them to diffusion models through stochastic differential equations, resulting in specialized solvers that achieve a 5-20 times speed increase and better sample quality with limited function evaluations (e.g., 10).
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.