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 this https URL.
Abstract (translated)
Bayesian流网络（BFNs）通过贝叶斯推理在扩散模型的（DMs）分布上逐步优化参数，而不是通过贝叶斯推理来优化扩散模型的样本。 由于其不同的可导性，BFN在建模连续和离散数据的同时保持快速抽样的能力。本文旨在通过随机微分方程（SDEs）将BFN与DMs连接起来，以理解并提高BFN。我们识别出BFN中噪声添加过程对应的线性SDE，证明BFN的回归损失与去噪得分匹配，并验证BFN的抽样器作为相应反向时间SDE的初值解。基于这些发现和现有的快速抽样在DM的食谱，我们提出了专用的BFN抽样器，在有限的函数评估（例如10）下，显著优于原始BFN抽样器，在图像和文本数据集上提高样本质量。值得注意的是，我们最好的抽样器在免费的情况下可以实现5~20倍的增长速度。我们的代码可在此处访问：https://url.com/
URL
https://arxiv.org/abs/2404.15766
