# PolycubeNet: A Dual-latent Diffusion Model for Polycube-Based Hexahedral Mesh Generation

arXiv: https://arxiv.org/abs/2605.20274 · HTML: https://mlsanity.com/paper/2605.20274/

## 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 23 of its 49 references that are in the map.
- First posted on arXiv 19 May 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, 23 of 23)

- [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)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Wan: Open and Advanced Large-Scale Video Generative Models](https://mlsanity.com/paper/2503.20314/) (2025)
- [Stable Video Diffusion: Scaling Latent Video Diffusion Models to Large Datasets](https://mlsanity.com/paper/2311.15127/) (2023)
- [Zero-1-to-3: Zero-shot One Image to 3D Object](https://mlsanity.com/paper/2303.11328/) (2023)
- [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)
- [Wonder3D: Single Image to 3D using Cross-Domain Diffusion](https://mlsanity.com/paper/2310.15008/) (2023)
- [ABC: A Big CAD Model Dataset For Geometric Deep Learning](https://mlsanity.com/paper/1812.06216/) (2018)
- [Thingi10K: A Dataset of 10,000 3D-Printing Models](https://mlsanity.com/paper/1605.04797/) (2016)
- [DiffusionNet: Discretization Agnostic Learning on Surfaces](https://mlsanity.com/paper/2012.00888/) (2020)
- [MVDiffusion++: A Dense High-resolution Multi-view Diffusion Model for Single or Sparse-view 3D Object Reconstruction](https://mlsanity.com/paper/2402.12712/) (2024)
- [PointTriNet: Learned Triangulation of 3D Point Sets](https://mlsanity.com/paper/2005.02138/) (2020)
- [PointInfinity: Resolution-Invariant Point Diffusion Models](https://mlsanity.com/paper/2404.03566/) (2024)
- [SRL-Assisted AFM: Generating Planar Unstructured Quadrilateral Meshes with Supervised and Reinforcement Learning-Assisted Advancing Front Method](https://mlsanity.com/paper/2305.00540/) (2023)
- [Hex-Mesh Generation and Processing: a Survey](https://mlsanity.com/paper/2202.12670/) (2022)
- [HexaLab.net: an online viewer for hexahedral meshes](https://mlsanity.com/paper/1806.06639/) (2018)
- [Interactive All-Hex Meshing via Cuboid Decomposition](https://mlsanity.com/paper/2109.06279/) (2021)
- [Evocube: a Genetic Labeling Framework for Polycube-Maps](https://mlsanity.com/paper/2205.00738/) (2022)
- [Fast and Robust Hexahedral Mesh Optimization via Augmented Lagrangian, L-BFGS, and Line Search](https://mlsanity.com/paper/2410.11656/) (2024)
- [DDPM-Polycube: A Denoising Diffusion Probabilistic Model for Polycube-Based Hexahedral Mesh Generation and Volumetric Spline Construction](https://mlsanity.com/paper/2503.13541/) (2025)

## Abstract (arXiv)

Hexahedral meshes are widely used in simulation pipelines, yet automatic generation remains challenging for complex CAD geometries. Polycube-based hexahedral meshing is a representative approach due to its regular, parameterization-friendly structure, but existing polycube construction methods often rely on intricate surface segmentation and local heuristics, which can produce artifacts or fail on difficult shapes. In this paper, we propose an end-to-end framework for polycube generation based on conditional diffusion models. Given an input geometry represented as a point cloud, our method directly produces a corresponding polycube point cloud, eliminating the need for explicit surface segmentation or predefined polycube templates. At the core of our approach is a dual-latent conditional diffusion architecture that confines computationally expensive self-attention operations to a fixed-capacity, low-dimensional latent space. This design effectively decouples computational complexity from the resolution of both the input geometry and the output polycube, thereby avoiding the quadratic cost typical of point cloud self-attention mechanisms while supporting flexible input and output resolutions. To obtain a hexahedral mesh, the generated polycube is aligned to the input shape via rigid and non-rigid point cloud registration to establish surface correspondence, followed by a polycube-to-hex pipeline. We additionally create and release a paired dataset of CAD meshes and their corresponding polycube meshes, together with the core implementation of our model. Experiments show that PolycubeNet generalizes to complex CAD models with arbitrary genus and produces high-quality polycube structures within seconds, improving robustness and efficiency over prior learning-based approaches.