General Proximal Flow Networks

TL;DR

General Proximal Flow Networks extend Bayesian Flow Networks by allowing arbitrary divergence functions, such as Wasserstein distance, to improve generative modeling quality through a unified proximal-operator framework.

Contribution

The paper introduces GPFNs, a flexible framework that generalizes Bayesian Flow Networks by incorporating various divergence functions for belief updates.

Findings

Adapting divergence functions improves generation quality.

The framework unifies proximal optimization with iterative generative modeling.

Standard Bayesian Flow Network updates are a special case.

Abstract

This paper introduces General Proximal Flow Networks (GPFNs), a generalization of Bayesian Flow Networks that broadens the class of admissible belief-update operators. In Bayesian Flow Networks, each update step is a Bayesian posterior update, which is equivalent to a proximal step with respect to the Kullback-Leibler divergence. GPFNs replace this fixed choice with an arbitrary divergence or distance function, such as the Wasserstein distance, yielding a unified proximal-operator framework for iterative generative modeling. The corresponding training and sampling procedures are derived, establishing a formal link to proximal optimization and recovering the standard BFN update as a special case. Empirical evaluations confirm that adapting the divergence to the underlying data geometry yields measurable improvements in generation quality, highlighting the practical benefits of this broader framework.