# Hierarchical Flow Matching for 3D Point Cloud Generation

arXiv: https://arxiv.org/abs/2608.05557 · HTML: https://mlsanity.com/paper/2608.05557/

## 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 34 of its 40 references that are in the map.
- First posted on arXiv 6 Aug 2026.

## 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 34)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [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)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [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)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [LION: Latent Point Diffusion Models for 3D Shape Generation](https://mlsanity.com/paper/2210.06978/) (2022)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [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)
- [GET3D: A Generative Model of High Quality 3D Textured Shapes Learned from Images](https://mlsanity.com/paper/2209.11163/) (2022)
- [Multisample Flow Matching: Straightening Flows with Minibatch Couplings](https://mlsanity.com/paper/2304.14772/) (2023)
- [PointGPT: Auto-regressively Generative Pre-training from Point Clouds](https://mlsanity.com/paper/2305.11487/) (2023)
- [DiT-3D: Exploring Plain Diffusion Transformers for 3D Shape Generation](https://mlsanity.com/paper/2307.01831/) (2023)
- [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)
- [SALAD: Part-Level Latent Diffusion for 3D Shape Generation and Manipulation](https://mlsanity.com/paper/2303.12236/) (2023)
- [Fast Point Cloud Generation with Straight Flows](https://mlsanity.com/paper/2212.01747/) (2022)
- [LT3SD: Latent Trees for 3D Scene Diffusion](https://mlsanity.com/paper/2409.08215/) (2024)

## Abstract (arXiv)

Generating high-quality 3D point clouds requires capturing both global shape topology and local geometric details. Existing flow-based methods rely on continuous normalizing flows (CNFs) that demand expensive ODE solving and trace estimation during training, while diffusion models require hundreds of iterative denoising steps. Moreover, most approaches adopt single-level generation directly in point space, disregarding the hierarchical structure natural to 3D shapes. We propose Hierarchical Flow Matching (HFM) that extends flow matching to bilevel structure for unconditional 3D point cloud generation. HFM decomposes the task into two levels via optimal-transport flow matching: a textitLatent Flow Matching models the global shape manifold in a compact latent space, and a textitConditional Point Flow Matching reconstructs detailed point clouds conditioned on the latent code. Both flows are trained with simple MSE regression losses. The resulting straight OT paths enable efficient sampling with as few as 15 Euler steps per flow, while the structured latent space supports downstream tasks including classification. Extensive experiments on ShapeNet and ModelNet benchmarks demonstrate that HFM achieves competitive or even best performance compared with prior state-of-the-art methods.