We propose a novel deep learning architecture for regressing disparity from a rectified pair of stereo images. We leverage knowledge of the problem's geometry to form a cost volume using deep feature representations. We learn to incorporate contextual information using 3-D convolutions over this volume. Disparity values are regressed from the cost volume using a proposed differentiable soft argmin operation, which allows us to train our method end-to-end to sub-pixel accuracy without any additional post-processing or regularization. We evaluate our method on the Scene Flow and KITTI datasets and on KITTI we set a new state-of-the-art benchmark, while being significantly faster than competing approaches.