General Proximal Flow Networks
This work provides a broader framework for iterative generative modeling, potentially benefiting researchers in machine learning by enabling more flexible and geometry-adapted models.
The paper tackled the problem of limited belief-update operators in Bayesian Flow Networks by introducing General Proximal Flow Networks (GPFNs), which generalize these operators to arbitrary divergences like the Wasserstein distance, resulting in measurable improvements in generation quality.
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.