Graph-Aware Diffusion for Signal Generation
This work addresses the challenge of generating graph signals for applications such as recommender systems and sensor networks, offering a more general method compared to existing domain-specific approaches.
The paper tackles the problem of generating graph signals from unknown distributions by proposing a graph-aware generative diffusion model (GAD) that incorporates graph structure through a modified heat equation, achieving improved performance on synthetic and real-world datasets like traffic speed and temperature sensor networks.
We study the problem of generating graph signals from unknown distributions defined over given graphs, relevant to domains such as recommender systems or sensor networks. Our approach builds on generative diffusion models, which are well established in vision and graph generation but remain underexplored for graph signals. Existing methods lack generality, either ignoring the graph structure in the forward process or designing graph-aware mechanisms tailored to specific domains. We adopt a forward process that incorporates the graph through the heat equation. Rather than relying on the standard formulation, we consider a time-warped coefficient to mitigate the exponential decay of the drift term, yielding a graph-aware generative diffusion model (GAD). We analyze its forward dynamics, proving convergence to a Gaussian Markov random field with covariance parametrized by the graph Laplacian, and interpret the backward dynamics as a sequence of graph-signal denoising problems. Finally, we demonstrate the advantages of GAD on synthetic data, real traffic speed measurements, and a temperature sensor network.