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This work explores the use of self-supervised contrastive learning to the simultaneous detection of two types of OOD samples: unseen classes and adversarial perturbations. First, we pair self-supervised contrastive learning with the maximum mean discrepancy (MMD) two-sample test. This approach enables us to robustly test whether two independent sets of samples originate from the same distribution, and we demonstrate its effectiveness by discriminating between CIFAR-10 and CIFAR-10.1 with higher confidence than previous work. Motivated by this success, we introduce CADet (Contrastive Anomaly Detection), a novel method for OOD detection of single samples. CADet draws inspiration from MMD, but leverages the similarity between contrastive transformations of a same sample. CADet outperforms existing adversarial detection methods in identifying adversarially perturbed samples on ImageNet and achieves comparable performance to unseen label detection methods on two challenging benchmarks: ImageNet-O and iNaturalist. 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