Graph Generation via Spectral Diffusion

While these models may excel in capturing a set of predefined properties, they are often In this paper, we present GRASP, a novel graph unable to represent a wider range of aspects observed in generative model based on 1) the spectral decomposition real-world graphs. In addition, in several domains network of the graph Laplacian matrix and 2) a properties are largely unknown, which further limits the diffusion process. Specifically, we propose to use applicability of these traditional techniques. For instance, a denoising model to sample eigenvectors and the Barabási-Albert model (Albert & Barabási, 2002) allows eigenvalues from which we can reconstruct the to create graphs that exhibit the scale-free nature found graph Laplacian and adjacency matrix. Our permutation in empirical degree distributions, however it is unable to invariant model can also handle node capture other facets of real-world graphs, e.g., community features by concatenating them to the eigenvectors structure. Overcoming these shortcomings has then become of each node. Using the Laplacian spectrum a necessary step towards enhancing the expressivity and allows us to naturally capture the structural characteristics fidelity of generated graphs, which in turn would extend the of the graph and work directly in the range of possible applications of graph generative models.