Discrete Bayesian Sample Inference for Graph Generation

TL;DR

GraphBSI is a novel one-shot graph generative model based on Bayesian Sample Inference that effectively handles discrete graph structures and achieves state-of-the-art results in molecular and synthetic graph generation.

Contribution

Introduces GraphBSI, a new one-shot graph generation method using Bayesian Sample Inference with a theoretical connection to diffusion models and Bayesian Flow Networks.

Findings

Achieves state-of-the-art performance on Moses and GuacaMol benchmarks.

Effectively models discrete graph data through iterative belief refinement.

Outperforms existing one-shot graph generative models.

Abstract

Generating graph-structured data is crucial in applications such as molecular generation, knowledge graphs, and network analysis. However, their discrete, unordered nature makes them difficult for traditional generative models, leading to the rise of discrete diffusion and flow matching models. In this work, we introduce GraphBSI, a novel one-shot graph generative model based on Bayesian Sample Inference (BSI). Instead of evolving samples directly, GraphBSI iteratively refines a belief over graphs in the continuous space of distribution parameters, naturally handling discrete structures. Further, we state BSI as a stochastic differential equation (SDE) and derive a noise-controlled family of SDEs that preserves the marginal distributions via an approximation of the score function. Our theoretical analysis further reveals the connection to Bayesian Flow Networks and Diffusion models. Finally, in our empirical evaluation, we demonstrate state-of-the-art performance on molecular and synthetic graph generation, outperforming existing one-shot graph generative models on the standard benchmarks Moses and GuacaMol.