Variational Bayesian Flow Network for Graph Generation

TL;DR

This paper introduces VBFN, a novel graph generation model that uses variational Bayesian methods to better encode node-edge coupling, improving fidelity and diversity over existing models.

Contribution

VBFN employs a variational lifting approach with structured precisions for coupled node-edge updates, addressing limitations of classical Bayesian Flow Networks.

Findings

VBFN outperforms baseline methods on synthetic and molecular graph datasets.

VBFN enhances graph generation fidelity and diversity.

Structured precisions enable effective node-edge coupling without label leakage.

Abstract

Graph generation aims to sample discrete node and edge attributes while satisfying coupled structural constraints. Diffusion models for graphs often adopt largely factorized forward-noising, and many flow-matching methods start from factorized reference noise and coordinate-wise interpolation, so node-edge coupling is not encoded by the generative geometry and must be recovered implicitly by the core network, which can be brittle after discrete decoding. Bayesian Flow Networks (BFNs) evolve distribution parameters and naturally support discrete generation. But classical BFNs typically rely on factorized beliefs and independent channels, which limit geometric evidence fusion. We propose Variational Bayesian Flow Network (VBFN), which performs a variational lifting to a tractable joint Gaussian variational belief family governed by structured precisions. Each Bayesian update reduces to solving a symmetric positive definite linear system, enabling coupled node and edge updates within a single fusion step. We construct sample-agnostic sparse precisions from a representation-induced dependency graph, thereby avoiding label leakage while enforcing node-edge consistency. On synthetic and molecular graph datasets, VBFN improves fidelity and diversity, and surpasses baseline methods.