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Cross-modality face image synthesis such as sketch-to-photo, NIR-to-RGB, and RGB-to-depth has wide applications in face recognition, face animation, and digital entertainment. Conventional cross-modality synthesis methods usually require paired training data, i.e., each subject has images of both modalities. However, paired data can be difficult to acquire, while unpaired data commonly exist. In this paper, we propose a novel semi-supervised cross-modality synthesis method (namely CMOS-GAN), which can leverage both paired and unpaired face images to learn a robust cross-modality synthesis model. Specifically, CMOS-GAN uses a generator of encoder-decoder architecture for new modality synthesis. We leverage pixel-wise loss, adversarial loss, classification loss, and face feature loss to exploit the information from both paired multi-modality face images and unpaired face images for model learning. In addition, since we expect the synthetic new modality can also be helpful for improving face recognition accuracy, we further use a modified triplet loss to retain the discriminative features of the subject in the synthetic modality. Experiments on three cross-modality face synthesis tasks (NIR-to-VIS, RGB-to-depth, and sketch-to-photo) show the effectiveness of the proposed approach compared with the state-of-the-art. In addition, we also collect a large-scale RGB-D dataset (VIPL-MumoFace-3K) for the RGB-to-depth synthesis task. We plan to open-source our code and VIPL-MumoFace-3K dataset to the community (https://github.com/skgyu/CMOS-GAN). [ABSTRACT FROM AUTHOR]