# ReGDiff: Guided Diffusion in Regulated Latent Space for Exploring Metamaterial Voxel Geometry

arXiv: https://arxiv.org/abs/2609.34231 · HTML: https://mlsanity.com/paper/2609.34231/

## 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 17 of its 35 references that are in the map.
- First posted on arXiv 28 Sep 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, 17 of 17)

- [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)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Structured 3D Latents for Scalable and Versatile 3D Generation](https://mlsanity.com/paper/2412.01506/) (2024)
- [Learning a Probabilistic Latent Space of Object Shapes via 3D Generative-Adversarial Modeling](https://mlsanity.com/paper/1610.07584/) (2016)
- [A Theoretical Analysis of Contrastive Unsupervised Representation Learning](https://mlsanity.com/paper/1902.09229/) (2019)
- [PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flows](https://mlsanity.com/paper/1906.12320/) (2019)
- [MeshDiffusion: Score-based Generative 3D Mesh Modeling](https://mlsanity.com/paper/2303.08133/) (2023)
- [XCube: Large-Scale 3D Generative Modeling using Sparse Voxel Hierarchies](https://mlsanity.com/paper/2312.03806/) (2023)
- [Geometric Latent Diffusion Models for 3D Molecule Generation](https://mlsanity.com/paper/2305.01140/) (2023)
- [3D Equivariant Diffusion for Target-Aware Molecule Generation and Affinity Prediction](https://mlsanity.com/paper/2303.03543/) (2023)
- [Generative and Discriminative Voxel Modeling with Convolutional Neural Networks](https://mlsanity.com/paper/1608.04236/) (2016)
- [DiT-3D: Exploring Plain Diffusion Transformers for 3D Shape Generation](https://mlsanity.com/paper/2307.01831/) (2023)
- [Unifying the design space and optimizing linear and nonlinear truss metamaterials by generative modeling](https://mlsanity.com/paper/2306.14773/) (2023)
- [Guided Diffusion for Fast Inverse Design of Density-based Mechanical Metamaterials](https://mlsanity.com/paper/2401.13570/) (2024)
- [MetamatBench: Integrating Heterogeneous Data, Computational Tools, and Visual Interface for Metamaterial Discovery](https://mlsanity.com/paper/2505.20299/) (2025)
- [UniMate: A Unified Model for Mechanical Metamaterial Generation, Property Prediction, and Condition Confirmation](https://mlsanity.com/paper/2506.15722/) (2025)

## Abstract (arXiv)

Metamaterials are artificially engineered structures whose mechanical and physical behaviors are strongly shaped by geometry rather than composition. Voxel representation provides a unified format for metamaterial geometry generation, as it can express diverse classes such as truss, shell, and porous structures within a single cubic discretization. However, voxel-based generation faces a plausibility-novelty trade-off: staying close to known geometries helps preserve geometric regularities, while moving away from them is necessary for novelty but may produce degenerate geometries. To address this challenge, we propose REGDIFF, a generative framework that couples voxel representation with latent space regulation and guided diffusion. REGDIFF introduces a repel-and-sink (RAS) mechanism to smooth the latent distribution of plausible geometries, and short-range repulsion (SRR) guidance to discourage generation overly close to known samples while maintaining geometric plausibility. We further contribute a voxel-based benchmark covering truss- and shell-type metamaterial geometries, together with an evaluation module for geometric plausibility, novelty, and diversity. Experiments show that REGDIFF outperforms voxel-based generative baselines, achieving +8.9% in geometric plausibility, +46.4% in novelty, and +128.6% in diversity on average across two datasets. These results suggest that REGDIFF is a strong geometry candidate generator for downstream evaluation. Our code is provided at https://github.com/wzhan24/ReGDiff.