Delving into Discrete Normalizing Flows on SO(3) Manifold for Probabilistic Rotation Modeling

Yulin Liu, Haoran Liu, Yingda Yin, Yang Wang, Baoquan Chen, He Wang

Abstract: Normalizing flows (NFs) provide a powerful tool to construct an expressive distribution by a sequence of trackable transformations of a base distribution and form a probabilistic model of underlying data. Rotation, as an important quantity in computer vision, graphics and robotics, can exhibit many ambiguities when occlusion and symmetry occur and thus demands such probabilistic models. Though various NFs in Euclidean space have been proposed, there are no normalizing flows tailored for SO(3) manifold. Given the unique non-Euclidean properties of the rotation manifold, adapting the existing NFs to SO(3) manifold is non-trivial. In this paper, we propose a novel normalizing flow on SO(3) by combining a Möbius transformation-based layer and a quaternion affine transformation. With our proposed rotation normalizing flows, one can not only effectively express arbitrary distributions on SO(3), but also conditionally build the target distribution given input observations. Extensive experiments show that our rotation normalizing flows significantly outperform the baselines on both unconditional and conditional tasks.

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