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Compared with depth-based 3D hand pose estimation, it is more challenging to infer 3D hand pose from monocular RGB images, due to substantial depth ambiguity and the difficulty of obtaining fully-annotated training data. Different from existing learning-based monocular RGB-input approaches that require accurate 3D annotations for training, we propose to leverage the depth images that can be easily obtained from commodity RGB-D cameras during training, while during testing we take only RGB inputs for 3D joint predictions. In this way, we alleviate the burden of the costly 3D annotations in real-world dataset. Particularly, we propose a weakly-supervised method, adaptating from fully-annotated synthetic dataset to weakly-labeled real-world dataset with the aid of a depth regularizer, which generates depth maps from predicted 3D pose and serves as weak supervision for 3D pose regression. Extensive experiments on benchmark datasets validate the effectiveness of the proposed depth regularizer in both weakly-supervised and fully-supervised settings.