Random Walk Diffusion For Graph Generation

Abstract

Graph generation addresses the problem of generating new graphs that have a data distribution similar to real-world graphs. Recently, the task of graph generation has gained increasing attention with applications ranging from data augmentation to constructing molecular graphs with specific properties. Previous diffusion-based approaches have shown promising results in terms of the quality of the generated graphs. However, most methods are designed for generating small graphs and do not scale well to large graphs. In this work, we introduce ARROW-Diff, a novel random walk-based diffusion approach for graph generation. It utilizes an order agnostic autoregressive diffusion model enabling us to generate graphs at a very large scale. ARROW-Diff encompasses an iterative procedure that builds the final graph from sampled random walks based on an edge classification task and directed by node degrees. Our method outperforms all baseline methods in terms of training and generation time and can be trained both on single- and multi-graph datasets. Moreover, it outperforms most baselines on multiple graph statistics reflecting the high quality of the generated graphs.