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Unveiling face images of a subject given his/her high-level representations extracted from a blackbox Face Recognition engine is extremely challenging. It is because the limitations of accessible information from that engine including its structure and uninterpretable extracted features. This paper presents a novel generative structure with Bijective Metric Learning, namely Bijective Generative Adversarial Networks in a Distillation framework (DiBiGAN), for synthesizing faces of an identity given that person's features. In order to effectively address this problem, this work firstly introduces a bijective metric so that the distance measurement and metric learning process can be directly adopted in image domain for an image reconstruction task. Secondly, a distillation process is introduced to maximize the information exploited from the blackbox face recognition engine. Then a Feature-Conditional Generator Structure with Exponential Weighting Strategy is presented for a more robust generator that can synthesize realistic faces with ID preservation. Results on several benchmarking datasets including CelebA, LFW, AgeDB, CFP-FP against matching engines have demonstrated the effectiveness of DiBiGAN on both image realism and ID preservation properties.