In the case of S 3 , these bijectors serve as robust flow architectures for modeling distributions on the rotation manifold (SO3). Alternative ways of learning normalized distributions of rotations that do not rely on flows can also be found in the literature and retain the unit-vector representation. All quaternions are assigned to a specific hemisphere and then globally parametrized using standard hyper-spherical coordinates despite the presence of singularities. This choice was implemented to provide model H with sufficient representational power while minimizing computational costs.