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.

Graph anomaly detection has attracted significant attention due to its critical applications, such as identifying money laundering in financial systems and detecting fake reviews on social networks. However, two major challenges persist: (1) anomaly detection at the node, edge, and graph levels is often addressed in isolation, hindering the integration of complementary information to identify anomalies arising from collective behaviors; and (2) the inherent label sparsity in graph data, coupled with the difficulty of obtaining high-quality annotations, exacerbates bias in detection. To address these challenges, we propose UniFORM, a unified self-supervised anomaly detection framework comprising two modules: UIO and UMC. UIO unifies node-, edge-, and graph-level tasks from a subgraph perspective, leveraging an energy-based GNN for iterative multi-granular anomaly detection. UMC enhances meta-learning through contrastive learning and employs Langevin dynamics to generate phantom samples as substitutes for anomalous data, reducing reliance on labeled data. Extensive experiments on real-world datasets demonstrate that UniFORM significantly outperforms state-of-the-art methods across multiple granularities.