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.

翻译：生成图结构数据在分子生成、知识图谱及网络分析等应用中至关重要。然而，图结构数据固有的离散性与无序性使其难以被传统生成模型处理，这推动了离散扩散模型与流匹配模型的发展。本文提出GraphBSI——一种基于贝叶斯样本推断（BSI）的新型单次图生成模型。不同于直接对样本进行演化，GraphBSI在分布参数的连续空间中对图的信度（belief）进行迭代精化，从而自然处理离散结构。进一步，我们将BSI表述为随机微分方程（SDE），并推导出噪声可控的SDE族，该族通过评分函数（score function）的近似保持边际分布。理论分析进一步揭示了BSI与贝叶斯流网络及扩散模型之间的联系。最后，实验评估表明，本方法在分子与合成图生成任务中达到了最先进的性能，在标准基准Moses和GuacaMol上优于现有单次图生成模型。