3D human pose estimation from monocular images is a highly ill-posed problem due to depth ambiguities and occlusions. Nonetheless, most existing works ignore these ambiguities and only estimate a single solution. In contrast, we generate a diverse set of hypotheses that represents the full posterior distribution of feasible 3D poses. To this end, we propose a normalizing flow based method that exploits the deterministic 3D-to-2D mapping to solve the ambiguous inverse 2D-to-3D problem. Additionally, uncertain detections and occlusions are effectively modeled by incorporating uncertainty information of the 2D detector as condition. Further keys to success are a learned 3D pose prior and a generalization of the best-of-M loss. We evaluate our approach on the two benchmark datasets Human3.6M and MPI-INF-3DHP, outperforming all comparable methods in most metrics. The implementation is available on GitHub.