The Skinned Multi-Person Linear (SMPL) model represents human bodies by mapping pose and shape parameters to body meshes. However, not all pose and shape parameter values yield physically-plausible or even realistic body meshes. In other words, SMPL is under-constrained and may yield invalid results. We propose learning a prior that restricts the SMPL parameters to values that produce realistic poses via adversarial training. We show that our learned prior covers the diversity of the real-data distribution, facilitates optimization for 3D reconstruction from 2D keypoints, and yields better pose estimates when used for regression from images. For all these tasks, it outperforms the state-of-the-art VAE-based approach to constraining the SMPL parameters. The code will be made available at https://github.com/cvlab epfl/adv_param_pose_prior.