# DDPM-Polycube: A Denoising Diffusion Probabilistic Model for Polycube-Based Hexahedral Mesh Generation and Volumetric Spline Construction

arXiv: https://arxiv.org/abs/2503.13541 · HTML: https://mlsanity.com/paper/2503.13541/

## Key facts

- Cited by 2 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 17 of its 64 references that are in the map.
- First posted on arXiv 16 Mar 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, 17 of 17)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [MeshGPT: Generating Triangle Meshes with Decoder-Only Transformers](https://mlsanity.com/paper/2311.15475/) (2023)
- [MeshAnything: Artist-Created Mesh Generation with Autoregressive Transformers](https://mlsanity.com/paper/2406.10163/) (2024)
- [Learning Deformable Tetrahedral Meshes for 3D Reconstruction](https://mlsanity.com/paper/2011.01437/) (2020)
- [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)
- [A Large Language Model and Denoising Diffusion Framework for Targeted Design of Microstructures with Commands in Natural Language](https://mlsanity.com/paper/2409.14473/) (2024)
- [Interactive All-Hex Meshing via Cuboid Decomposition](https://mlsanity.com/paper/2109.06279/) (2021)
- [HybridOctree_Hex: Hybrid Octree-Based Adaptive All-Hexahedral Mesh Generation with Jacobian Control](https://mlsanity.com/paper/2401.05984/) (2024)
- [Fast and Robust Hexahedral Mesh Optimization via Augmented Lagrangian, L-BFGS, and Line Search](https://mlsanity.com/paper/2410.11656/) (2024)
- [DL-Polycube: Deep learning enhanced polycube method for high-quality hexahedral mesh generation and volumetric spline construction](https://mlsanity.com/paper/2410.18852/) (2024)

## Built on by (most cited first, 2 of 2)

- [A Survey of AI Methods for Geometry Preparation and Mesh Generation in Engineering Simulation](https://mlsanity.com/paper/2512.23719/) (2025)
- [PolycubeNet: A Dual-latent Diffusion Model for Polycube-Based Hexahedral Mesh Generation](https://mlsanity.com/paper/2605.20274/) (2026)

## Abstract (arXiv)

In this paper, we propose DDPM-Polycube, a generative polycube creation approach based on denoising diffusion probabilistic models (DDPM) for generating high-quality hexahedral (hex) meshes and constructing volumetric splines. Unlike DL-Polycube methods that rely on predefined polycube structure templates, DDPM-Polycube models the deformation from input geometry to its corresponding polycube structures as a denoising task. By learning the deformation characteristics of simple geometric primitives (a cube and a cube with a hole), the DDPM-Polycube model progressively reconstructs polycube structures from input geometry by removing non-standard Gaussian noise. Once valid polycube structures are generated, they are used for surface segmentation and parametric mapping to generate high-quality hex meshes. Truncated hierarchical B-splines are then applied to construct volumetric splines that satisfy the requirements of isogeometric analysis (IGA). Experimental results demonstrate that DDPM-Polycube model can directly generate polycube structures from input geometries, even when the topology of these geometries falls outside its trained range. This provides greater generalization and adaptability for diverse engineering geometries. Overall, this research shows the potential of diffusion models in advancing mesh generation and IGA applications.