We present FlowHMR, a framework for recovering physically plausible global 3D human motion from monocular video. Previous learning-based methods typically regress human motion directly from video and train the network with geometric supervision. However, recovering human motion from monocular video is inherently ambiguous in depth, and direct regression tends to collapse toward an averaged solution. Moreover, the recovered motions are not guaranteed to be physically plausible, so physics-based tracking of them often fails. To address these challenges, we formulate video motion capture as a video-conditioned motion generation problem and first pretrain a flow matching model for this task. Given an input video, the pretrained model generates diverse motion candidates, but not all of them are faithful to the video or physically trackable. We therefore post-train the model using Group Relative Policy Optimization (GRPO) with two rewards. A fidelity reward encourages consistency with the input video. A tracking reward favors motions that a physics-based controller can track successfully. Together, these rewards shift the model's output preference, so the post-trained model stays faithful to the input video while producing more physically plausible motion. We further introduce Wild-4K, a large and diverse dataset of about 4K internet videos, for evaluating human motion recovery in the wild. Qualitative and quantitative experiments on Wild-4K show that our method outperforms state-of-the-art methods in overall motion fidelity and achieves a physical tracking success rate of 82.47%, compared with 62.82% for the strongest baseline, GVHMR.

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