Breaking One-Size-Fits-All: Revisiting Out-of-Distribution Detection on Graphs Under Diverse Distribution Shifts

Graph OOD detection is crucial in open-world scenarios, where OOD samples may manifest in diverse forms such as open-set deviations, feature-similar shifts, and structural anomalies, each exhibiting distinct geometric characteristics. However, most existing methods adopt a one-size-fits-all geometric assumption (typically Euclidean space), which inadequately captures the diverse nature of real-world distribution shifts. Therefore, adaptively selecting geometric spaces according to the properties of OOD samples is critical for their effective representation and reliable identification. Motivated by this, we revisit the graph OOD detection task under diverse distribution shifts and propose UniGOD, a unified framework serving as a graph foundation model for this task. UniGOD comprises two core modules: GeoUP and DynEVO. GeoUP module adaptively perceives the geometric space (such as Euclidean, hyperbolic, and hyperspherical space) by learning the curvature k of Riemannian manifolds. DynEVO module leverages the dynamic nature of neural SDEs to reveal pronounced uncertainty differences between ID/OOD samples, which are reflected in the divergent evolutionary trajectories of node embeddings induced by k-GNN iterations. With the geometry-dynamics coupling mechanism of the above two modules, UniGOD effectively captures the diverse distribution shifts. Extensive experiments demonstrate its superior performance over existing SOTA methods.