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We propose a novel monocular scene flow method that yields competitive accuracy and real-time performance. By taking an inverse problem view, we design a single convolutional neural network (CNN) that successfully estimates depth and 3D motion simultaneously from a classical optical flow cost volume. We adopt self-supervised learning with 3D loss functions and occlusion reasoning to leverage unlabeled data. We validate our design choices, including the proxy loss and augmentation setup. Our model achieves state-of-the-art accuracy among unsupervised/self-supervised learning approaches to monocular scene flow, and yields competitive results for the optical flow and monocular depth estimation sub-tasks. 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