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In this work, we investigate the problem of face reconstruction given a facial feature representation extracted from a blackbox face recognition engine. Indeed, it is a very challenging problem in practice due to the limitations of abstracted information from the engine. We, therefore, introduce a new method named Attention-based Bijective Generative Adversarial Networks in a Distillation framework (DAB-GAN) to synthesize the faces of a subject given his/her extracted face recognition features. Given any unconstrained unseen facial features of a subject, the DAB-GAN can reconstruct his/her facial images in high definition. The DAB-GAN method includes a novel attention-based generative structure with the newly defined Bijective Metrics Learning approach. The framework starts by introducing a bijective metric so that the distance measurement and metric learning process can be directly adopted in the image domain for an image reconstruction task. The information from the blackbox face recognition engine will be optimally exploited using the global distillation process. Then an attention-based generator is presented for a highly robust generator to synthesize realistic faces with ID preservation. We have evaluated our method on the challenging face recognition databases, i.e., CelebA, LFW, CFP-FP, CP-LFW, AgeDB, CA-LFW, and consistently achieved state-of-the-art results. The advancement of DAB-GAN is also proven in both image realism and ID preservation properties.