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Multi-view stereo (MVS) is the golden mean between the accuracy of active depth sensing and the practicality of monocular depth estimation. Cost volume based approaches employing 3D convolutional neural networks (CNNs) have considerably improved the accuracy of MVS systems. However, this accuracy comes at a high computational cost which impedes practical adoption. Distinct from cost volume approaches, we propose an efficient depth estimation approach by first (a) detecting and evaluating descriptors for interest points, then (b) learning to match and triangulate a small set of interest points, and finally (c) densifying this sparse set of 3D points using CNNs. An end-to-end network efficiently performs all three steps within a deep learning framework and trained with intermediate 2D image and 3D geometric supervision, along with depth supervision. Crucially, our first step complements pose estimation using interest point detection and descriptor learning. We demonstrate state-of-the-art results on depth estimation with lower compute for different scene lengths. Furthermore, our method generalizes to newer environments and the descriptors output by our network compare favorably to strong baselines. Code is available at https://github.com/magicleap/DELTAS