In the realm of generative models for graphs, extensive research has been conducted. However, most existing methods struggle with large graphs due to the complexity of representing the entire joint distribution across all node pairs and capturing both global and local graph structures simultaneously. To overcome these issues, we introduce a method that generates a graph by progressively expanding a single node to a target graph. In each step, nodes and edges are added in a localized manner through denoising diffusion, building first the global structure, and then refining the local details. The local generation avoids modeling the entire joint distribution over all node pairs, achieving substantial computational savings with subquadratic runtime relative to node count while maintaining high expressivity through multiscale generation. Our experiments show that our model achieves state-of-the-art performance on well-established benchmark datasets while successfully scaling to graphs with at least 5000 nodes. Our method is also the first to successfully extrapolate to graphs outside of the training distribution, showcasing a much better generalization capability over existing methods.

翻译：在图生成模型领域已有大量研究，但现有方法大多难以处理大规模图，原因在于需要同时建模所有节点对的联合分布并捕获图的全局与局部结构。为解决这些问题，我们提出一种通过逐步将单节点扩展为目标图的方法。每一步通过去噪扩散以局部化方式添加节点和边——先构建全局结构，再细化局部细节。这种局部生成方式避免了对所有节点对联合分布的建模，在保持多尺度生成高表达能力的同时，实现了相对于节点数量的次二次运行时间计算量的大幅降低。实验表明，我们的方法在公认基准数据集上达到最优性能，并成功扩展至至少含5000个节点的图。该方法还是首个能成功外推至训练分布外图结构的方法，展现出远超现有方法的泛化能力。