# MeshFlow: Mesh Generation with Equivariant Flow Matching

arXiv: https://arxiv.org/abs/2606.23489 · HTML: https://mlsanity.com/paper/2606.23489/

## Key facts

- Cited by 4 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 67 of its 97 references that are in the map.
- First posted on arXiv 22 Jun 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 67)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [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)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Objaverse-XL: A Universe of 10M+ 3D Objects](https://mlsanity.com/paper/2307.05663/) (2023)
- [Structured 3D Latents for Scalable and Versatile 3D Generation](https://mlsanity.com/paper/2412.01506/) (2024)
- [Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution](https://mlsanity.com/paper/2310.16834/) (2023)
- [SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformers](https://mlsanity.com/paper/2401.08740/) (2024)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [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)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [All are Worth Words: A ViT Backbone for Diffusion Models](https://mlsanity.com/paper/2209.12152/) (2022)
- [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, 4 of 4)

- [Meshy T2: Fast Native Mesh Generation with Flow Matching](https://mlsanity.com/paper/2607.28675/) (2026)
- [An overview of 3D Vision-Language Models](https://mlsanity.com/paper/2609.05583/) (2026)
- [Flow Matching Reinforcement for 3D Mesh Generation via Dynamic Homing Optimization](https://mlsanity.com/paper/2610.01233/) (2026)
- [OuroReward: Sequential Reward Scheduling for Reinforcement Learning in Text-to-3D Generation](https://mlsanity.com/paper/2610.03423/) (2026)

## Abstract (arXiv)

Meshes are among the most common 3D scene representations, but directly generating meshes is challenging because the representation contains important symmetries, including permutation invariance of faces and vertices. MeshFlow learns to generate triangle meshes directly as triangle soups, avoiding the need to serialize meshes into long autoregressive sequences. We adopt equivariant optimal-transport flow matching models that respect the key symmetries of triangle soups: arbitrary permutations of faces and permutations of the vertices within each face. Toward this goal, we propose a simple yet effective modification to the Diffusion Transformer architecture, resulting in a scalable network capable of modeling a velocity field while maintaining the desired equivariance. We further introduce an optimal-transport-based training objective that improves convergence by eliminating supervision signals that violate these symmetries. MeshFlow achieves mesh quality comparable to state-of-the-art autoregressive mesh generators while providing about an 18× speedup during inference. Project page is at https://qiisun.github.io/MeshFlow/.