  Due to the visual ambiguity, purely kinematic formulations on monocular human
motion capture are often physically incorrect, biomechanically implausible, and
can not reconstruct accurate interactions. In this work, we focus on exploiting
the high-precision and non-differentiable physics simulator to incorporate
dynamical constraints in motion capture. Our key-idea is to use real physical
supervisions to train a target pose distribution prior for sampling-based
motion control to capture physically plausible human motion. To obtain accurate
reference motion with terrain interactions for the sampling, we first introduce
an interaction constraint based on SDF (Signed Distance Field) to enforce
appropriate ground contact modeling. We then design a novel two-branch decoder
to avoid stochastic error from pseudo ground-truth and train a distribution
prior with the non-differentiable physics simulator. Finally, we regress the
sampling distribution from the current state of the physical character with the
trained prior and sample satisfied target poses to track the estimated
reference motion. Qualitative and quantitative results show that we can obtain
physically plausible human motion with complex terrain interactions, human
shape variations, and diverse behaviors. More information can be found
at~\url{https://www.yangangwang.com/papers/HBZ-NM-2022-03.html}
