Graph generation has emerged as a critical task in fields ranging from drug discovery to circuit design. Contemporary approaches, notably diffusion and flow-based models, have achieved solid graph generative performance through constructing a probability path that interpolates between reference and data distributions. However, these methods typically model the evolution of individual nodes and edges independently and use linear interpolations in the disjoint space of nodes/edges to build the path. This disentangled interpolation breaks the interconnected patterns of graphs, making the constructed probability path irregular and non-smooth, which causes poor training dynamics and faulty sampling convergence. To address the limitation, this paper first presents a theoretically grounded framework for probability path construction in graph generative models. Specifically, we model the joint evolution of the nodes and edges by representing graphs as connected systems parameterized by Markov random fields (MRF). We then leverage the optimal transport displacement between MRF objects to design a smooth probability path that ensures the co-evolution of graph components. Based on this, we introduce BWFlow, a flow-matching framework for graph generation that utilizes the derived optimal probability path to benefit the training and sampling algorithm design. Experimental evaluations in plain graph generation and molecule generation validate the effectiveness of BWFlow with competitive performance, better training convergence, and efficient sampling.

翻译：图生成已成为从药物发现到电路设计等多个领域的关键任务。当代方法，特别是基于扩散和流的模型，通过构建在参考分布与数据分布之间插值的概率路径，已实现了稳健的图生成性能。然而，这些方法通常独立地对节点和边的演化进行建模，并在节点/边的不相交空间中使用线性插值来构建路径。这种解耦的插值破坏了图的互连模式，使得构建的概率路径不规则且不光滑，从而导致训练动态不佳和采样收敛错误。为解决这一局限，本文首先提出了一个具有理论基础的图生成模型概率路径构建框架。具体而言，我们通过将图表示为由马尔可夫随机场参数化的连通系统，来建模节点和边的联合演化。然后，我们利用MRF对象之间的最优传输位移来设计一条光滑的概率路径，以确保图组件的协同演化。在此基础上，我们引入了BWFlow，一个用于图生成的流匹配框架，它利用推导出的最优概率路径来优化训练和采样算法设计。在普通图生成和分子生成任务中的实验评估验证了BWFlow的有效性，其表现出具有竞争力的性能、更好的训练收敛性和高效的采样。