Discrete Bayesian Sample Inference for Graph Generation

2025-11-04

AI Summary

Addressing the challenge of generating discrete, unordered graph structures—such as molecules and knowledge graphs—this paper introduces GraphBSI, the first graph generation framework that formulates Bayesian Sample Inference (BSI) as a controllable-noise stochastic differential equation (SDE). Its core contributions are threefold: (i) establishing the first rigorous correspondence between BSI and SDEs; (ii) constructing an SDE family that preserves marginal distributions over graph structures and revealing its theoretical unification with Bayesian flow networks and diffusion models; and (iii) enabling end-to-end, one-shot graph generation via iterative optimization of the belief distribution over graph structures in a continuous parameter space. Evaluated on the Moses and GuacaMol benchmarks, GraphBSI achieves state-of-the-art performance in both molecular and synthetic graph generation, significantly outperforming existing methods.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Graphical Models
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Generating discrete graph-structured data for molecular applications
• Handling unordered discrete structures with continuous distribution parameters
• Improving one-shot graph generation performance over existing models

Innovation

• Bayesian Sample Inference refines graph belief distribution
• Stochastic differential equations approximate score functions
• Continuous space parameterization handles discrete graph structures