Not-So-Optimal Transport Flows for 3D Point Cloud Generation
This work addresses the problem of efficient 3D point cloud generation for applications in computer vision and graphics, offering an incremental improvement over existing methods.
The paper tackles the challenge of scaling permutation-invariant generative models for 3D point clouds by addressing the inefficiency and complexity of existing equivariant optimal transport flows, proposing a method that uses offline OT precomputation and hybrid coupling to improve training. The result is a model that outperforms prior diffusion- and flow-based approaches on unconditional generation and shape completion tasks on the ShapeNet benchmark.
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.