Abstract: Reasoning about uncertain orientations is one of the core problems in many perception tasks such as object pose estimation or motion estimation. In these scenarios, poor illumination conditions, sensor limitations, or appearance invariance may result in highly uncertain estimates. In this work, we propose a novel learning-based representation for orientation uncertainty. By characterizing uncertainty over unit quaternions with the Bingham distribution, we formulate a loss that naturally captures the antipodal symmetry of the representation. We discuss the interpretability of the learned distribution parameters and demonstrate the feasibility of our approach on several challenging real-world pose estimation tasks involving uncertain orientations.