Graph neural networks have achieved impressive results in various network modeling tasks, but accurately estimating uncertainty in graphs, especially under distribution shifts, remains challenging. In this paper, we draw on the similarities between the evolution of stochastic partial differential equations (SPDEs) driven by Mater Gaussian Processes and message passing using GNN layers. Drawing inspiration from the Gaussian Process approach, we propose a novel message passing approach that incorporates spatiotemporal noise. This approach simultaneously captures uncertainty across space and time and allows explicit control over the smoothness of the covariance kernel, improving uncertainty estimation in both low- and high-label graphs. Extensive experiments on Out-of-Distribution (OOD) detection on graph datasets with varying label information demonstrate the robustness of our model and its superiority over existing approaches.
