Title: But is it Valid? Enforcing Structural Constraints on Graph Generative Models
Primary area: learning on graphs and other geometries & topologies
Keywords: graph, generative+model, discrete+diffusion, topology, persistent+homology, topology

Abstract: The problem of graph generation using deep learning has received substantial attention in the recent years. When using graph generative models, one often faces the issue that the generated graphs do not respect hard constraints of the empirical distribution. A common challenge is to guarantee even basic structural properties of the generated graphs, such as connectedness or planarity. In this work, we propose ValiGraph, a graph generative method based on denoising diffusion, which guarantees the generation of graphs respecting a large family of structural properties. In addition we quantify the ability of the models in capturing topological information, we propose the use of extended persistent homology in the evaluation procedure. We show that ValiGraph is superior in capturing the distribution of graph structural features on several datasets.

TL;DR: A noise model for discrete diffusion on graph data, which enables the generation of structurally valid graphs during inference.