SoftFlow: Probabilistic Framework for Normalizing Flow on Manifolds
This addresses a fundamental limitation in flow-based models for researchers working with manifold-structured data like 3D point clouds.
The paper tackles the dimension mismatch problem in flow-based generative models when data lies on manifolds, proposing SoftFlow which estimates conditional distributions of perturbed data instead of learning data distributions directly. The method achieves state-of-the-art performance in 3D point cloud generation with SoftPointFlow.
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.