# Mesh BDF: Barycentric Dominance Field for 3D Native Mesh Generation

arXiv: https://arxiv.org/abs/2606.31777 · HTML: https://mlsanity.com/paper/2606.31777/

## Key facts

- Cited by 1 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 32 of its 37 references that are in the map.
- First posted on arXiv 30 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 32)

- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [Point-E: A System for Generating 3D Point Clouds from Complex Prompts](https://mlsanity.com/paper/2212.08751/) (2022)
- [CLAY: A Controllable Large-scale Generative Model for Creating High-quality 3D Assets](https://mlsanity.com/paper/2406.13897/) (2024)
- [Shap-E: Generating Conditional 3D Implicit Functions](https://mlsanity.com/paper/2305.02463/) (2023)
- [Hunyuan3D 2.0: Scaling Diffusion Models for High Resolution Textured 3D Assets Generation](https://mlsanity.com/paper/2501.12202/) (2025)
- [Rodin: A Generative Model for Sculpting 3D Digital Avatars Using Diffusion](https://mlsanity.com/paper/2212.06135/) (2022)
- [PolyGen: An Autoregressive Generative Model of 3D Meshes](https://mlsanity.com/paper/2002.10880/) (2020)
- [MeshGPT: Generating Triangle Meshes with Decoder-Only Transformers](https://mlsanity.com/paper/2311.15475/) (2023)
- [Direct3D: Scalable Image-to-3D Generation via 3D Latent Diffusion Transformer](https://mlsanity.com/paper/2405.14832/) (2024)
- [Native and Compact Structured Latents for 3D Generation](https://mlsanity.com/paper/2512.14692/) (2025)
- [Flexible Isosurface Extraction for Gradient-Based Mesh Optimization](https://mlsanity.com/paper/2308.05371/) (2023)
- [Using Shape to Categorize: Low-Shot Learning with an Explicit Shape Bias](https://mlsanity.com/paper/2101.07296/) (2021)
- [MeshAnything V2: Artist-Created Mesh Generation With Adjacent Mesh Tokenization](https://mlsanity.com/paper/2408.02555/) (2024)
- [3DTopia-XL: Scaling High-quality 3D Asset Generation via Primitive Diffusion](https://mlsanity.com/paper/2409.12957/) (2024)
- [Meshtron: High-Fidelity, Artist-Like 3D Mesh Generation at Scale](https://mlsanity.com/paper/2412.09548/) (2024)
- [Sparc3D: Sparse Representation and Construction for High-Resolution 3D Shapes Modeling](https://mlsanity.com/paper/2505.14521/) (2025)
- [EdgeRunner: Auto-regressive Auto-encoder for Artistic Mesh Generation](https://mlsanity.com/paper/2409.18114/) (2024)
- [Hunyuan3D 1.0: A Unified Framework for Text-to-3D and Image-to-3D Generation](https://mlsanity.com/paper/2411.02293/) (2024)
- [SparseFlex: High-Resolution and Arbitrary-Topology 3D Shape Modeling](https://mlsanity.com/paper/2503.21732/) (2025)
- [Scaling Mesh Generation via Compressive Tokenization](https://mlsanity.com/paper/2411.07025/) (2024)
- [PolyDiff: Generating 3D Polygonal Meshes with Diffusion Models](https://mlsanity.com/paper/2312.11417/) (2023)
- [DeepMesh: Auto-Regressive Artist-mesh Creation with Reinforcement Learning](https://mlsanity.com/paper/2503.15265/) (2025)
- [TexVerse: A Universe of 3D Objects with High-Resolution Textures](https://mlsanity.com/paper/2508.10868/) (2025)
- [MeshCraft: Exploring Efficient and Controllable Mesh Generation with Flow-based DiTs](https://mlsanity.com/paper/2503.23022/) (2025)
- [QuadGPT: Native Quadrilateral Mesh Generation with Autoregressive Models](https://mlsanity.com/paper/2509.21420/) (2025)
- [MeshRipple: Structured Autoregressive Generation of Artist-Meshes](https://mlsanity.com/paper/2512.07514/) (2025)
- [LATO: 3D Mesh Flow Matching with Structured TOpology Preserving LAtents](https://mlsanity.com/paper/2603.06357/) (2026)
- [Topology-Preserved Auto-regressive Mesh Generation in the Manner of Weaving Silk](https://mlsanity.com/paper/2507.02477/) (2025)

## Built on by (most cited first, 1 of 1)

- [MeshOctave: Vertex Split-and-Rewire Cascades for Native Mesh Generation](https://mlsanity.com/paper/2609.38985/) (2026)

## Abstract (arXiv)

Autoregressive (AR) modeling has recently achieved remarkable progress in native 3D mesh generation, largely due to its natural ability to handle variable-length, discrete data structures. However, the inherent constraints of the AR paradigm severely restrict the generated meshes, leading to limited face counts, bounded vertex resolutions, and difficulties in supporting textures. To overcome these bottlenecks, we propose the Barycentric Dominance Field (BDF), a continuous representation defined on triangular mesh surfaces that elegantly encodes vertex topological connectivity. BDF bridges the fundamental gap between discrete mesh topology and continuous diffusion-based generative modeling by transforming connectivity into a continuous surface signal. As an intrinsic mesh property, BDF shares strong similarities with texture maps, enabling its seamless integration into existing 3D diffusion pipelines without requiring architectural modifications. Extensive experiments demonstrate that BDF empowers diffusion models to generate native meshes with significantly higher quality, greater scalability, and stronger robustness compared to state-of-the-art autoregressive methods.