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 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 either significantly higher generation quality or much less computational consumption than the baselines.
翻译:生成图形结构化数据是一个具有挑战性的问题,需要学习图形的基本分布。各种模型,如图VAE、图GANs和图扩散模型,已经提出了产生有意义和可靠的图表,其中扩散模型已经达到最先进的性能。在本文中,我们认为,在整个空间运行全面扩散的SDE阻碍学习图形表层生成的传播模型,从而大大恶化生成的图形数据的质量。为了应对这一局限性,我们建议了高效而有效的图形光谱传播模型(GSDM),该模型是由图形频谱空间的低级扩散SDE驱动的。我们的光谱传播模型进一步证明享有比标准扩散模型更强大的理论保证。各种数据集的广泛实验表明,我们提议的GSDM是STO模型,其生成质量或计算消耗量比基线要高得多。