Variational Bayesian Flow Network for Graph Generation

• URL: http://arxiv.org/abs/2601.22524v1
• Date: Fri, 30 Jan 2026 03:59:38 GMT
• Title: Variational Bayesian Flow Network for Graph Generation
• Authors: Yida Xiong, Jiameng Chen, Xiuwen Gong, Jia Wu, Shirui Pan, Wenbin Hu,
• Abstract summary: We propose Variational Bayesian Flow Network (VBFN) for graph generation.<n>VBFN performs variational lifting to a tractable joint Gaussian variational belief family governed by structured precisions.<n>On synthetic and molecular graph datasets, VBFN improves fidelity and diversity, and surpasses baseline methods.
• Score: 54.94088904387278
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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