Janis Postels, Mengya Liu, Riccardo Spezialetti, Luc Van Gool and Federico Tombari

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 have fundamental limitations on complicated geometries. This work generalizes prior work by introducing additional discrete latent variable, i.e. mixture model. This circumvents limitations of prior approaches, leads to more parameter efficient models and reduces the inference runtime. Moreover, in this more general framework each component learns to specialize in a particular subregion of an object in a completely unsupervised fashion yielding promising clustering properties. 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.