Go with the Flows: Mixtures of Normalizing Flows for Point Cloud Generation and Reconstruction

Recently normalizing flows (NFs) have demonstrated state-of-the-art performance on modeling 3D point clouds while allowing sampling with arbitrary resolution at inference time. However, these flow-based models still require long training times and large models for representing complicated geometries. This work enhances their representational power by applying mixtures of NFs to point clouds. We show that in this more general framework each component learns to specialize in a particular subregion of an object in a completely unsupervised fashion. By instantiating each mixture component with a comparatively small NF we generate point clouds with improved details compared to single-flow-based models while using fewer parameters and considerably reducing the inference runtime. We further demonstrate that by adding data augmentation, individual mixture components can learn to specialize in a semantically meaningful manner. We evaluate mixtures of NFs on generation, autoencoding and single-view reconstruction based on the ShapeNet dataset.