Title: DiffGED: Computing Graph Edit Distance via Diffusion-based Graph Matching
Primary area: learning on graphs and other geometries & topologies
Keywords: Graph Edit Distance, Graph matching, Generative model

Abstract: Graph Edit Distance (GED), which aims to find an edit path with minimum number of edit operations to transform one graph into another, is a fundamental NP-hard problem and a widely used graph similarity measure. Recent matching-based hybrid approaches have demonstrated better scalability than A* search-based hybrids by reformulating GED as a graph matching problem. In these methods, a neural network predicts a single deterministic node matching matrix, from which top-$k$ node mappings are extracted iteratively to derive candidate edit paths. However, these methods often suffer from highly correlated candidates that easily lead to suboptimal solutions, while the iterative extraction becomes inefficient for large $k$. In this paper, we propose DiffGED, the first generative approach for GED computation. Specifically, we formulate the graph matching problem as a generative task, and employ a diffusion-based model to generate multiple diverse node matching matrices simultaneously, from which diverse node mappings can be efficiently extracted. The generative diversity introduced by the diffusion process enables DiffGED to avoid suboptimal solutions and achieve superior solution quality close to the exact solution. Experiments on real-world datasets show that DiffGED generates multiple diverse edit paths with accuracy comparable to exact solutions, while running faster than existing hybrid approaches.