Diffusion-based generative graph models have been proven effective in generating high-quality small graphs. However, they need to be more scalable for generating large graphs containing thousands of nodes desiring graph statistics. In this work, we propose EDGE, a new diffusion-based generative graph model that addresses generative tasks with large graphs. To improve computation efficiency, we encourage graph sparsity by using a discrete diffusion process that randomly removes edges at each time step and finally obtains an empty graph. EDGE only focuses on a portion of nodes in the graph at each denoising step. It makes much fewer edge predictions than previous diffusion-based models. Moreover, EDGE admits explicitly modeling the node degrees of the graphs, further improving the model performance. The empirical study shows that EDGE is much more efficient than competing methods and can generate large graphs with thousands of nodes. It also outperforms baseline models in generation quality: graphs generated by our approach have more similar graph statistics to those of the training graphs.

翻译：基于扩散的生成图模型已被证明在生成高质量小图方面有效。然而，在生成包含数千个节点的大规模图并期望保留图统计特性时，这些模型的可扩展性仍有待提升。本文提出EDGE——一种新的基于扩散的生成图模型，专门解决大规模图的生成任务。为提高计算效率，我们通过离散扩散过程鼓励图稀疏性：该过程在每步时间步长中随机移除边，最终获得空图。EDGE在每一步去噪过程中仅关注图中部分节点，相比现有扩散模型大幅减少了边预测数量。此外，EDGE允许显式建模图的节点度，进一步提升了模型性能。实证研究表明，EDGE在效率上远超现有方法，能够生成包含数千个节点的大规模图。在生成质量方面，我们的方法同样优于基线模型：通过EDGE生成的图在统计特性上与训练图更加相似。