Not-So-Optimal Transport Flows for 3D Point Cloud Generation

TL;DR

This paper introduces not-so-optimal transport flow models for efficient 3D point cloud generation, addressing scalability and learning challenges of existing equivariant OT flows, and demonstrates superior performance on ShapeNet tasks.

Contribution

It proposes approximate OT flows with offline precomputation and hybrid coupling, improving scalability and training ease for permutation-invariant 3D point cloud generation.

Findings

Outperforms prior diffusion and flow models on ShapeNet benchmarks.

Scales better on large point clouds compared to equivariant OT flows.

Enables efficient training through approximate OT and hybrid coupling.

Abstract

Learning generative models of 3D point clouds is one of the fundamental problems in 3D generative learning. One of the key properties of point clouds is their permutation invariance, i.e., changing the order of points in a point cloud does not change the shape they represent. In this paper, we analyze the recently proposed equivariant OT flows that learn permutation invariant generative models for point-based molecular data and we show that these models scale poorly on large point clouds. Also, we observe learning (equivariant) OT flows is generally challenging since straightening flow trajectories makes the learned flow model complex at the beginning of the trajectory. To remedy these, we propose not-so-optimal transport flow models that obtain an approximate OT by an offline OT precomputation, enabling an efficient construction of OT pairs for training. During training, we can additionally construct a hybrid coupling by combining our approximate OT and independent coupling to make the target flow models easier to learn. In an extensive empirical study, we show that our proposed model outperforms prior diffusion- and flow-based approaches on a wide range of unconditional generation and shape completion on the ShapeNet benchmark.