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Current approaches to novelty or anomaly detection are based on deep neural networks. Despite their effectiveness, neural networks are also vulnerable to imperceptible deformations of the input data. This is a serious issue in critical applications, or when data alterations are generated by an adversarial attack. While this is a known problem that has been studied in recent years for the case of supervised learn- ing, the case of novelty detection has received very limited attention. Indeed, in this latter setting the learning is typically unsupervised because outlier data is not available during training, and new approaches for this case need to be investigated. We propose a new prior that aims at learning a robust likelihood for the novelty test, as a defense against attacks. We also integrate the same prior with a state-of-the- art novelty detection approach. Because of the geometric properties of that approach, the resulting robust training is computationally very efficient. An initial evaluation of the method indicates that it is effective at improving performance with respect to the standard models in the absence and presence of attacks.