Tippett-minimum Fusion of Representation-space Diffusion Models for Multi-Encoder Out-of-Distribution Detection

Abstract

We address out-of-distribution (OOD) detection across the full spectrum of distribution shifts -- global domain changes, semantic divergence, texture differences, and covariate corruptions -- through a multi-encoder fusion of per-encoder representation-space diffusion models (RDMs). We statistically identify each encoder's sensitivity to specific shift types from ID data alone and introduce EncMin2L -- an encoder-agnostic two-level $\min (\cdot )$-gate that combines and calibrates per-encoder diffusion-based likelihood detectors without OOD labels, outperforming monolithic multi-encoder baselines at $2.3\times$ lower parameter cost. Two ID-data diagnostics: $\hat{I}{\cdot }^2$ (class-conditional F-test) and $\hat{I}”\hat{I}¼$ (log-likelihood shift under synthetic corruptions) -- quantify encoder specialization, while a Tippett minimum $p$-value combination aggregates per-encoder scores into a single, calibration-stable OOD signal. EncMin2L achieves $\ge 0.94$ AUROC across all four shift types simultaneously, outperforming the state-of-the-art representation-space diffusion OOD detectors across overlapping benchmarks.

14 pages