Graph Discrete Diffusion: a Spectral Study

Diffusion models have become central to generative modeling, yet the discrete structure of graphs has prompted the development of specialized approaches and hindered the theoretical understanding of their dynamics.In this work, we investigate how the noising and denoising processes in the graph discrete diffusion model DiGress manifest in the spectral domain. We first assess whether the learned reverse process accurately mirrors the forward noise process and analyze the temporal evolution of graph spectra. Our results reveal a gradual shift toward a random graph configuration, with the final density depending on the noise model. Unlike in image diffusion, we do not observe a clear separation between low- and high-frequency perturbations in the graph spectra. This suggests that alternative perturbation strategies in the spectral domain may warrant further exploration.