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尺度图方面非常有效。然而，当需要生成包含数千个节点且具有特定图统计特性的大规模图时，其可扩展性仍需提升。本文提出EDGE——一种基于扩散的新型生成图模型，用于解决大规模图的生成任务。为提高计算效率，我们采用离散扩散过程随机移除每一步中的边，最终得到空图，从而促进图的稀疏性。在每一步去噪过程中，EDGE仅关注图中部分节点，因此其边预测数量远少于此前基于扩散的模型。此外，EDGE显式建模图的节点度分布，进一步提升了模型性能。实验表明，EDGE在效率上显著优于现有方法，能够生成包含数千个节点的大规模图，且在生成质量上超越基线模型：本方法生成的图与训练集的图统计特性更为接近。