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This paper addresses the challenge of 3D human pose estimation from a single color image. Despite the general success of the end-to-end learning paradigm, top performing approaches employ a two-step solution consisting of a Convolutional Network (ConvNet) for 2D joint localization and a subsequent optimization step to recover 3D pose. In this paper, we identify the representation of 3D pose as a critical issue with current ConvNet approaches and make two important contributions towards validating the value of end-to-end learning for this task. First, we propose a fine discretization of the 3D space around the subject and train a ConvNet to predict per voxel likelihoods for each joint. This creates a natural representation for 3D pose and greatly improves performance over the direct regression of joint coordinates. Second, to further improve upon initial estimates, we employ a coarse-to-fine prediction scheme. This step addresses the large dimensionality increase and enables iterative refinement and repeated processing of the image features. The proposed approach outperforms all state-of-the-art methods on standard benchmarks achieving a relative error reduction greater than 30% on average. Additionally, we investigate using our volumetric representation in a related architecture which is suboptimal compared to our end-to-end approach, but is of practical interest, since it enables training when no image with corresponding 3D groundtruth is available, and allows us to present compelling results for in-the-wild images.