Fast Graph Generation via Spectral Diffusion

Generating graph-structured data is a challenging problem, which requires learning the underlying distribution of graphs. Various models such as graph VAE, graph GANs, and graph diffusion models have been proposed to generate meaningful and reliable graphs, among which the diffusion models have achieved state-of-the-art performance. In this paper, we argue that running full-rank diffusion SDEs on the whole graph adjacency matrix space hinders diffusion models from learning graph topology generation, and hence significantly deteriorates the quality of generated graph data. To address this limitation, we propose an efficient yet effective Graph Spectral Diffusion Model (GSDM), which is driven by low-rank diffusion SDEs on the graph spectrum space. Our spectral diffusion model is further proven to enjoy a substantially stronger theoretical guarantee than standard diffusion models. Extensive experiments across various datasets demonstrate that our proposed GSDM turns out to be the SOTA model, by exhibiting both significantly higher generation quality and much less computational consumption than the baselines.