The recent progress in generative models has revolutionized the synthesis of highly realistic images, including face images. This technological development has undoubtedly helped face recognition, such as training data augmentation for higher recognition accuracy and data privacy. However, it has also introduced novel challenges concerning the responsible use and proper attribution of computer generated images. We investigate the impact of digital watermarking, a technique for embedding ownership signatures into images, on the effectiveness of face recognition models. We propose a comprehensive pipeline that integrates face image generation, watermarking, and face recognition to systematically examine this question. The proposed watermarking scheme, based on an encoder-decoder architecture, successfully embeds and recovers signatures from both real and synthetic face images while preserving their visual fidelity. Through extensive experiments, we unveil that while watermarking enables robust image attribution, it results in a slight decline in face recognition accuracy, particularly evident for face images with challenging poses and expressions. Additionally, we find that directly training face recognition models on watermarked images offers only a limited alleviation of this performance decline. Our findings underscore the intricate trade off between watermarking and face recognition accuracy. This work represents a pivotal step towards the responsible utilization of generative models in face recognition and serves to initiate discussions regarding the broader implications of watermarking in biometrics.

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