Although much progress has been made recently in 3D face reconstruction, most previous work has been devoted to predicting accurate and fine-grained 3D shapes. In contrast, relatively little work has focused on generating high-fidelity face textures. Compared with the prosperity of photo-realistic 2D face image generation, high-fidelity 3D face texture generation has yet to be studied. In this paper, we proposed a novel UV map generation model that predicts the UV map from a single face image. The model consists of a UV sampler and a UV generator. By selectively sampling the input face image's pixels and adjusting their relative locations, the UV sampler generates an incomplete UV map that could faithfully reconstruct the original face. Missing textures in the incomplete UV map are further full-filled by the UV generator. The training is based on pseudo ground truth blended by the 3DMM texture and the input face texture, thus weakly supervised. To deal with the artifacts in the imperfect pseudo UV map, multiple UV map and face image discriminators are leveraged.