SoftFlow: Probabilistic Framework for Normalizing Flow on Manifolds

TL;DR

SoftFlow introduces a probabilistic framework that enables flow-based generative models to effectively learn on manifold data by estimating conditional distributions, leading to high-quality sample generation and state-of-the-art results in 3D point cloud synthesis.

Contribution

It proposes SoftFlow, a novel approach for training normalizing flows on manifolds by estimating conditional distributions, overcoming dimension mismatch issues.

Findings

SoftFlow captures manifold structures effectively.

SoftPointFlow achieves state-of-the-art 3D point cloud generation.

The framework improves sample quality over traditional flow models.

Abstract

Flow-based generative models are composed of invertible transformations between two random variables of the same dimension. Therefore, flow-based models cannot be adequately trained if the dimension of the data distribution does not match that of the underlying target distribution. In this paper, we propose SoftFlow, a probabilistic framework for training normalizing flows on manifolds. To sidestep the dimension mismatch problem, SoftFlow estimates a conditional distribution of the perturbed input data instead of learning the data distribution directly. We experimentally show that SoftFlow can capture the innate structure of the manifold data and generate high-quality samples unlike the conventional flow-based models. Furthermore, we apply the proposed framework to 3D point clouds to alleviate the difficulty of forming thin structures for flow-based models. The proposed model for 3D point clouds, namely SoftPointFlow, can estimate the distribution of various shapes more accurately and achieves state-of-the-art performance in point cloud generation.