Unifying Bayesian Flow Networks and Diffusion Models through Stochastic Differential Equations
arxiv(2024)
摘要
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.
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