# QEMesh: Employing A Quadric Error Metrics-Based Representation for Mesh Generation

arXiv: https://arxiv.org/abs/2504.05720 · HTML: https://mlsanity.com/paper/2504.05720/

## 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 28 of its 40 references that are in the map.
- First posted on arXiv 8 Apr 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, 28 of 28)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [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 Probabilistic Models for 3D Point Cloud Generation](https://mlsanity.com/paper/2103.01458/) (2021)
- [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)
- [VoxFormer: Sparse Voxel Transformer for Camera-based 3D Semantic Scene Completion](https://mlsanity.com/paper/2302.12251/) (2023)
- [GRM: Large Gaussian Reconstruction Model for Efficient 3D Reconstruction and Generation](https://mlsanity.com/paper/2403.14621/) (2024)
- [Text-to-3D using Gaussian Splatting](https://mlsanity.com/paper/2309.16585/) (2023)
- [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)
- [GaussianDreamer: Fast Generation from Text to 3D Gaussians by Bridging 2D and 3D Diffusion Models](https://mlsanity.com/paper/2310.08529/) (2023)
- [AutoSDF: Shape Priors for 3D Completion, Reconstruction and Generation](https://mlsanity.com/paper/2203.09516/) (2022)
- [MeshDiffusion: Score-based Generative 3D Mesh Modeling](https://mlsanity.com/paper/2303.08133/) (2023)
- [Shape As Points: A Differentiable Poisson Solver](https://mlsanity.com/paper/2106.03452/) (2021)
- [Locally Attentional SDF Diffusion for Controllable 3D Shape Generation](https://mlsanity.com/paper/2305.04461/) (2023)
- [MeshXL: Neural Coordinate Field for Generative 3D Foundation Models](https://mlsanity.com/paper/2405.20853/) (2024)
- [SDF-StyleGAN: Implicit SDF-Based StyleGAN for 3D Shape Generation](https://mlsanity.com/paper/2206.12055/) (2022)
- [SALAD: Part-Level Latent Diffusion for 3D Shape Generation and Manipulation](https://mlsanity.com/paper/2303.12236/) (2023)
- [PolyDiff: Generating 3D Polygonal Meshes with Diffusion Models](https://mlsanity.com/paper/2312.11417/) (2023)
- [Controllable Mesh Generation Through Sparse Latent Point Diffusion Models](https://mlsanity.com/paper/2303.07938/) (2023)
- [PoNQ: a Neural QEM-based Mesh Representation](https://mlsanity.com/paper/2403.12870/) (2024)
- [GetMesh: A Controllable Model for High-quality Mesh Generation and Manipulation](https://mlsanity.com/paper/2403.11990/) (2024)
- [GenUDC: High Quality 3D Mesh Generation with Unsigned Dual Contouring Representation](https://mlsanity.com/paper/2410.17802/) (2024)

## Abstract (arXiv)

Mesh generation plays a crucial role in 3D content creation, as mesh is widely used in various industrial applications. Recent works have achieved impressive results but still face several issues, such as unrealistic patterns or pits on surfaces, thin parts missing, and incomplete structures. Most of these problems stem from the choice of shape representation or the capabilities of the generative network. To alleviate these, we extend PoNQ, a Quadric Error Metrics (QEM)-based representation, and propose a novel model, QEMesh, for high-quality mesh generation. PoNQ divides the shape surface into tiny patches, each represented by a point with its normal and QEM matrix, which preserves fine local geometry information. In our QEMesh, we regard these elements as generable parameters and design a unique latent diffusion model containing a novel multi-decoder VAE for PoNQ parameters generation. Given the latent code generated by the diffusion model, three parameter decoders produce several PoNQ parameters within each voxel cell, and an occupancy decoder predicts which voxel cells containing parameters to form the final shape. Extensive evaluations demonstrate that our method generates results with watertight surfaces and is comparable to state-of-the-art methods in several main metrics.