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，然而现有方法大多难以处理大规模图，原因在于既要表示所有节点对之间的完整联合分布，又要同时捕捉图的全局与局部结构，这带来了极大复杂性。为克服这些难题，我们提出一种新方法：通过将单个节点逐步扩展为目标图来生成图。在每一步中，通过去噪扩散以局部方式添加节点和边，首先构建全局结构，再细化局部细节。这种局部生成方式无需对全节点对联合分布进行建模，在保持高表达能力的同时实现显著计算效率提升（相对于节点数量的子二次方运行时间），并通过多尺度生成维持高表达能力。实验表明，我们的模型在多个标准基准数据集上达到当前最优性能，且成功扩展至至少含5000个节点的图。该方法还能首次成功外推至训练分布之外的图，展现出远超现有方法的泛化能力。