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Deep Gaussian processes (DGPs) offer a principled Bayesian framework with hierarchical uncertainty propagation, but their reliable propagation of uncertainty and out-of-distribution (OOD) detection performance remains underexplored and often unreliable in safety-critical settings. In this work, we propose a novel kernel operating in both Euclidean and Wasserstein-2 space to better account for the geometry of representation learning spaces, thus circumventing a common pathology called feature collapse, whereby inliers and outliers get mapped to similar spaces. Empirically, our approach consistently improves OOD detection in convolutional image tasks and shows improved performance on tabular datasets.