  Normalizing flows have proven their efficacy for density estimation in
Euclidean space, but their application to rotational representations, crucial
in various domains such as robotics or human pose modeling, remains
underexplored. Probabilistic models of the human pose can benefit from
approaches that rigorously consider the rotational nature of human joints. For
this purpose, we introduce HuProSO3, a normalizing flow model that operates on
a high-dimensional product space of SO(3) manifolds, modeling the joint
distribution for human joints with three degrees of freedom. HuProSO3's
advantage over state-of-the-art approaches is demonstrated through its superior
modeling accuracy in three different applications and its capability to
evaluate the exact likelihood. This work not only addresses the technical
challenge of learning densities on SO(3) manifolds, but it also has broader
implications for domains where the probabilistic regression of correlated 3D
rotations is of importance.
