  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.

Machine Learning;Artificial Intelligence