# 3D Shape Tokenization via Latent Flow Matching

arXiv: https://arxiv.org/abs/2412.15618 · HTML: https://mlsanity.com/paper/2412.15618/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Placed in 3D, point cloud and scene generation, one of 14 directions in Diffusion models.
- Builds on 65 of its 106 references that are in the map.
- First posted on arXiv 20 Dec 2024.

## 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 65)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [Objaverse: A Universe of Annotated 3D Objects](https://mlsanity.com/paper/2212.08051/) (2022)
- [Zero-1-to-3: Zero-shot One Image to 3D Object](https://mlsanity.com/paper/2303.11328/) (2023)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [LRM: Large Reconstruction Model for Single Image to 3D](https://mlsanity.com/paper/2311.04400/) (2023)
- [Structured 3D Latents for Scalable and Versatile 3D Generation](https://mlsanity.com/paper/2412.01506/) (2024)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [LGM: Large Multi-View Gaussian Model for High-Resolution 3D Content Creation](https://mlsanity.com/paper/2402.05054/) (2024)
- [SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformers](https://mlsanity.com/paper/2401.08740/) (2024)
- [Diffusion Probabilistic Models for 3D Point Cloud Generation](https://mlsanity.com/paper/2103.01458/) (2021)
- [Point-E: A System for Generating 3D Point Clouds from Complex Prompts](https://mlsanity.com/paper/2212.08751/) (2022)
- [Perceiver IO: A General Architecture for Structured Inputs & Outputs](https://mlsanity.com/paper/2107.14795/) (2021)
- [Google Scanned Objects: A High-Quality Dataset of 3D Scanned Household Items](https://mlsanity.com/paper/2204.11918/) (2022)
- [Habitat-Matterport 3D Dataset (HM3D): 1000 Large-scale 3D Environments for Embodied AI](https://mlsanity.com/paper/2109.08238/) (2021)
- [LION: Latent Point Diffusion Models for 3D Shape Generation](https://mlsanity.com/paper/2210.06978/) (2022)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flows](https://mlsanity.com/paper/1906.12320/) (2019)
- [3DShape2VecSet: A 3D Shape Representation for Neural Fields and Generative Diffusion Models](https://mlsanity.com/paper/2301.11445/) (2023)

## Built on by (most cited first, 10 of 10)

- [MeshRipple: Structured Autoregressive Generation of Artist-Meshes](https://mlsanity.com/paper/2512.07514/) (2025)
- [NOVA3R: Non-pixel-aligned Visual Transformer for Amodal 3D Reconstruction](https://mlsanity.com/paper/2603.04179/) (2026)
- [LiTo: Surface Light Field Tokenization](https://mlsanity.com/paper/2603.11047/) (2026)
- [VesselTok: Tokenizing Vessel-like 3D Biomedical Graph Representations for Reconstruction and Generation](https://mlsanity.com/paper/2603.18797/) (2026)
- [ELSA3D: Elastic Semantic Anchoring for Unified 3D Understanding and Generation](https://mlsanity.com/paper/2607.06565/) (2026)
- [ZipTok3D: High-Fidelity 3D Tokenization with Compact Token Prefixes](https://mlsanity.com/paper/2609.01740/) (2026)
- [Squeeze3D: Extreme Neural Compression with Latent Space Bridging](https://mlsanity.com/paper/2506.07932/) (2025)
- [Velox: Learning Representations of 4D Geometry and Appearance](https://mlsanity.com/paper/2605.04527/) (2026)
- [DynaTok: Token-Based 4D Reconstruction from Partial Point Clouds](https://mlsanity.com/paper/2606.12189/) (2026)
- [FILIGREE3D: Scaling Sparse Latent Flow Matching for Ultra-High-Resolution Image-to-3D Generation](https://mlsanity.com/paper/2609.34900/) (2026)

## Abstract (arXiv)

We introduce a latent 3D representation that models 3D surfaces as probability density functions in 3D, i.e., p(x,y,z), with flow-matching. Our representation is specifically designed for consumption by machine learning models, offering continuity and compactness by construction while requiring only point clouds and minimal data preprocessing. Despite being a data-driven method, our use of flow matching in the 3D space enables interesting geometry properties, including the capabilities to perform zero-shot estimation of surface normal and deformation field. We evaluate with several machine learning tasks, including 3D-CLIP, unconditional generative models, single-image conditioned generative model, and intersection-point estimation. Across all experiments, our models achieve competitive performance to existing baselines, while requiring less preprocessing and auxiliary information from training data.