Graph-signal generators use the structure of a graph to model distributions over signals, but the graph itself is often noisy or imperfectly estimated. Structural errors can then propagate through a generative model and distort the output distribution. The authors focus on continuous-time models that pair a graph filter with a learned graph neural network, a setting where robustness remained largely unexplored.
To address that gap, the paper derives a Wasserstein stability bound that relates graph perturbations to changes in the generated signal distribution. Using that bound, the authors propose a framework for designing graph filters that balance structural stability against signal smoothing. They characterize an optimal filter family and give polynomial filters with explicit, provable stability guarantees.
Experiments on synthetic graphs and real-world fMRI signals suggest the proposed filters improve structural stability while preserving generative performance. These are the authors' reported results from a preprint submitted to IEEE Transactions on Signal Processing.