Set Flow: A Permutation Invariant Normalizing Flow

TL;DR

Set Flow introduces a permutation-invariant normalizing flow model capable of learning complex, non-i.i.d. set data distributions, with applications demonstrated on 3D point clouds achieving state-of-the-art likelihoods.

Contribution

The paper extends RealNVPs to handle finite, exchangeable set data, enabling learning of dependencies and variable set sizes efficiently.

Findings

Achieves state-of-the-art likelihoods on 3D point clouds

Learns statistical dependencies within set data

Handles variable set sizes efficiently

Abstract

We present a generative model that is defined on finite sets of exchangeable, potentially high dimensional, data. As the architecture is an extension of RealNVPs, it inherits all its favorable properties, such as being invertible and allowing for exact log-likelihood evaluation. We show that this architecture is able to learn finite non-i.i.d. set data distributions, learn statistical dependencies between entities of the set and is able to train and sample with variable set sizes in a computationally efficient manner. Experiments on 3D point clouds show state-of-the art likelihoods.