Fast Graph Generation via Spectral Diffusion

TL;DR

This paper introduces a spectral diffusion model for graph generation that improves quality and efficiency by operating in the graph spectrum space, outperforming existing models.

Contribution

The paper proposes a novel low-rank spectral diffusion approach that enhances graph generation quality and computational efficiency over traditional diffusion models.

Findings

Achieves state-of-the-art graph generation performance.

Reduces computational cost significantly.

Provides stronger theoretical guarantees for spectral diffusion.

Abstract

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.