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We introduce DiffPhy, a differentiable physics-based model for articulated 3d human motion reconstruction from video. Applications of physics-based reasoning in human motion analysis have so far been limited, both by the complexity of constructing adequate physical models of articulated human motion, and by the formidable challenges of performing stable and efficient inference with physics in the loop. We jointly address such modeling and inference challenges by proposing an approach that combines a physically plausible body representation with anatomical joint limits, a differentiable physics simulator, and optimization techniques that ensure good performance and robustness to suboptimal local optima. In contrast to several recent methods, our approach readily supports full-body contact including interactions with objects in the scene. Most importantly, our model connects end-to-end with images, thus supporting direct gradient-based physics optimization by means of image-based loss functions. We validate the model by demonstrating that it can accurately reconstruct physically plausible 3d human motion from monocular video, both on public benchmarks with available 3d ground-truth, and on videos from the internet.