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

2025-02-18

AI Summary

To address the poor scalability and complex trajectory learning of equivariant optimal transport (OT)-based flow models in large-scale 3D point cloud generation, this paper introduces a novel “non-strictly-optimal transport flow” paradigm. It decouples OT computation from flow learning: approximate OT pairings are precomputed offline, and a hybrid training objective—combining independent coupling and OT-aware coupling—is designed to significantly reduce early-stage flow trajectory complexity. The method builds upon an equivariant flow model, inherently supporting permutation-invariant modeling without requiring online OT optimization. Evaluated on ShapeNet, it outperforms state-of-the-art diffusion and flow-based models in both unconditional generation and shape completion, achieving a 12.7% reduction in FID and a 9.3% improvement in Chamfer distance. Notably, it is the first approach to enable efficient, high-fidelity generation of large point clouds (>4K points).

Technology Category

• Computer Vision: Diffusion Models for Vision
• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Deep Generative Models & Autoencoders

Application Category

• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

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.

Problem

• Improving 3D point cloud generation efficiency
• Addressing scalability in large point clouds
• Simplifying learning of equivariant OT flows

Innovation

• Approximate OT precomputation
• Hybrid coupling construction
• Enhanced flow model efficiency