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Modern deepfake detectors have achieved encouraging results, when training and test images are drawn from the same data collection. However, when these detectors are applied to images produced with unknown deepfake-generation techniques, considerable performance degradations are commonly observed. In this paper, we propose a novel deepfake detector, called SeeABLE, that formalizes the detection problem as a (one-class) out-of-distribution detection task and generalizes better to unseen deepfakes. Specifically, SeeABLE first generates local image perturbations (referred to as soft-discrepancies) and then pushes the perturbed faces towards predefined prototypes using a novel regression-based bounded contrastive loss. To strengthen the generalization performance of SeeABLE to unknown deepfake types, we generate a rich set of soft discrepancies and train the detector: (i) to localize, which part of the face was modified, and (ii) to identify the alteration type. To demonstrate the capabilities of SeeABLE, we perform rigorous experiments on several widely-used deepfake datasets and show that our model convincingly outperforms competing state-of-the-art detectors, while exhibiting highly encouraging generalization capabilities.