# OT-MeanFlow3D: Bridging Optimal Transport and Meanflow for Efficient 3D Point Cloud Generation

arXiv: https://arxiv.org/abs/2509.22592 · HTML: https://mlsanity.com/paper/2509.22592/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in 3D, point cloud and scene generation, one of 14 directions in Diffusion models.
- Builds on 32 of its 46 references that are in the map.
- First posted on arXiv 26 Sep 2025.

## Placed in

- Diffusion models / [3D, point cloud and scene generation](https://mlsanity.com/diffusion/3d-point-cloud-and-scene-generation/)

## Builds on (most cited first, 30 of 32)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Diffusion Probabilistic Models for 3D Point Cloud Generation](https://mlsanity.com/paper/2103.01458/) (2021)
- [Mean Flows for One-step Generative Modeling](https://mlsanity.com/paper/2505.13447/) (2025)
- [Deep Learning for 3D Point Clouds: A Survey](https://mlsanity.com/paper/1912.12033/) (2019)
- [LION: Latent Point Diffusion Models for 3D Shape Generation](https://mlsanity.com/paper/2210.06978/) (2022)
- [3D Shape Generation and Completion through Point-Voxel Diffusion](https://mlsanity.com/paper/2104.03670/) (2021)
- [PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flows](https://mlsanity.com/paper/1906.12320/) (2019)
- [Multisample Flow Matching: Straightening Flows with Minibatch Couplings](https://mlsanity.com/paper/2304.14772/) (2023)
- [Learning Gradient Fields for Shape Generation](https://mlsanity.com/paper/2008.06520/) (2020)
- [3D Point Cloud Generative Adversarial Network Based on Tree Structured Graph Convolutions](https://mlsanity.com/paper/1905.06292/) (2019)
- [PointGrow: Autoregressively Learned Point Cloud Generation with Self-Attention](https://mlsanity.com/paper/1810.05591/) (2018)
- [SoftFlow: Probabilistic Framework for Normalizing Flow on Manifolds](https://mlsanity.com/paper/2006.04604/) (2020)
- [Discrete Point Flow Networks for Efficient Point Cloud Generation](https://mlsanity.com/paper/2007.10170/) (2020)
- [SetVAE: Learning Hierarchical Composition for Generative Modeling of Set-Structured Data](https://mlsanity.com/paper/2103.15619/) (2021)
- [Optimal Flow Matching: Learning Straight Trajectories in Just One Step](https://mlsanity.com/paper/2403.13117/) (2024)
- [Learning to Reconstruct Shapes from Unseen Classes](https://mlsanity.com/paper/1812.11166/) (2018)
- [Fast Point Cloud Generation with Straight Flows](https://mlsanity.com/paper/2212.01747/) (2022)
- [Simple ReFlow: Improved Techniques for Fast Flow Models](https://mlsanity.com/paper/2410.07815/) (2024)
- [Not-So-Optimal Transport Flows for 3D Point Cloud Generation](https://mlsanity.com/paper/2502.12456/) (2025)
- [Beyond Optimal Transport: Model-Aligned Coupling for Flow Matching](https://mlsanity.com/paper/2505.23346/) (2025)

## Abstract (arXiv)

Flow-matching models have recently emerged as a powerful framework for continuous generative modeling, including 3D point cloud synthesis. However, their deployment is limited by the need for multiple sequential sampling steps at inference time. MeanFlow enables single-step generation and significantly accelerates inference, but often struggles to approximate the trajectories of the original multi-step flow, leading to degraded sample quality. In this work, we propose an Optimal Transport-enhanced MeanFlow framework (OT-MF3D) for efficient and accurate 3D point cloud generation and completion. By incorporating optimal transport-based sampling, our method better preserves the geometric and distributional structure of the underlying multi-step flow while retaining single-step inference. Experiments on ShapeNet show improved generation and completion quality compared to recent baselines, while reducing training and inference costs relative to conventional diffusion and flow-based models.