Due to their convenience and high accuracy, face recognition systems are widely employed in governmental and personal security applications to automatically recognise individuals. Despite recent advances, face recognition systems have shown to be particularly vulnerable to identity attacks (i.e., digital manipulations and attack presentations). Identity attacks pose a big security threat as they can be used to gain unauthorised access and spread misinformation. In this context, most algorithms for detecting identity attacks generalise poorly to attack types that are unknown at training time. To tackle this problem, we introduce a differential anomaly detection framework in which deep face embeddings are first extracted from pairs of images (i.e., reference and probe) and then combined for identity attack detection. The experimental evaluation conducted over several databases shows a high generalisation capability of the proposed method for detecting unknown attacks in both the digital and physical domains.