In this paper, we present GRASP, a novel graph generative model based on 1) the spectral decomposition of the graph Laplacian matrix and 2) a diffusion process. Specifically, we propose to use a denoising model to sample eigenvectors and eigenvalues from which we can reconstruct the graph Laplacian and adjacency matrix. Our permutation invariant model can also handle node features by concatenating them to the eigenvectors of each node. Using the Laplacian spectrum allows us to naturally capture the structural characteristics of the graph and work directly in the node space while avoiding the quadratic complexity bottleneck that limits the applicability of other methods. This is achieved by truncating the spectrum, which as we show in our experiments results in a faster yet accurate generative process. An extensive set of experiments on both synthetic and real world graphs demonstrates the strengths of our model against state-of-the-art alternatives.

翻译：本文提出GRASP，一种基于图拉普拉斯矩阵频谱分解和扩散过程的新型图生成模型。具体而言，我们采用去噪模型对特征向量与特征值进行采样，进而重构图拉普拉斯矩阵和邻接矩阵。这种置换不变模型通过将节点特征拼接至各节点特征向量，还可处理节点特征。利用拉普拉斯频谱使我们能够自然地捕捉图的结构特性，直接在节点空间中进行操作，同时避免了限制其他方法适用性的二次复杂度瓶颈。我们通过截断频谱实现这一目标——实验表明截断能在保持生成过程准确性的同时提升效率。在合成图与真实图上的大量实验证明了该模型相较于当前最优方法的优势。