We present a method to estimate depth of a dynamic scene, containing arbitrary moving objects, from an ordinary video captured with a moving camera. We seek a geometrically and temporally consistent solution to this underconstrained problem: the depth predictions of corresponding points across frames should induce plausible, smooth motion in 3D. We formulate this objective in a new test-time training framework where a depth-prediction CNN is trained in tandem with an auxiliary scene-flow

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... ion MLP over the entire input video. By recursively unrolling the scene-flow prediction MLP over varying time steps, we compute both short-range scene flow to impose local smooth motion priors directly in 3D, and long-range scene flow to impose multi-view consistency constraints with wide baselines. We demonstrate accurate and temporally coherent results on a variety of challenging videos containing diverse moving objects (pets, people, cars), as well as camera motion. Our depth maps give rise to a number of depth-and-motion aware video editing effects such as object and lighting insertion.