In the case of S 3 , these bijectors serve as robust flow architectures for modelling distributions on the rotation manifold (SO3). Alternative ways of learning normalised distributions of rotations that do not rely on flows can also be found in the literature and retain the unit-vector representation. For the sake of providing sufficient representational power to the model while minimising the computational cost associated with evaluating the inverse mappings, in this work, all quaternions are simply assigned to a specific hemisphere and then globally parameterised using standard hyper-spherical coordinates, despite the presence of singularities.