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

Wangzhi Zhan; Jianpeng Chen; Dongqi Fu; Dawei Zhou

cs.CVSep 28, 2026

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

Authors: Wangzhi Zhan, Jianpeng Chen, Dongqi Fu, Dawei Zhou

Organizations: Department of Computer Science Virginia Tech Blacksburg, VA 24061 · Meta Menlo Park, CA 94025

Abstract

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.

Figures & tables

Panel of Figure 1 — Figure 1 : Overview of metamaterials and benchmark development.

Figure 2 : An overview of the proposed framework ReGDiff . It encodes voxel geometries into latent space, applies RAS for latent regulation, and employs SRR-guided diffusion to generate novel yet geometrically plausible metamaterial geometry candidates.

Figure 3 : Illustration of the effect of RAS and its components.

Approaches	Geometric Plausibility Scores				Novelty Score	Diversity Score
Approaches	$S_{\mathrm{sym}}$ $\uparrow$	$S_{\mathrm{per}}$ $\uparrow$	$S_{\mathrm{con}}$ $\uparrow$	Mean $\uparrow$	$S_{\mathrm{nov}}$ $\uparrow$	$S_{\mathrm{div}}$ $\uparrow$
MetaTruss (ours)
DiT-3D ( Mo et al. (2023) )	0.358	0.248	0.500	0.369	0.003	0.010
Y. Yang et al. ( Yang et al. (2024) )	0.800	0.585	0.494	0.626	0.163	0.158
XCube ( Ren et al. (2024) )	0.506	0.525	0.522	0.518	0.000	0.004
Trellis ( Xiang et al. (2025) )	0.081	0.063	0.133	0.092	0.000	0.001

Table 1 : Performance evaluation of different approaches.

Panel of Table 2 — Table 2 : Latent distribution visualization and generated samples with RAS regulation, contrastive regulation, or no regulation. Reg. denotes regulation, and Contra. denotes contrastive.

Approaches	Geometric Plausibility Scores				Novelty Score	Diversity Score
Approaches	$S_{\mathrm{sym}}$ $\uparrow$	$S_{\mathrm{per}}$ $\uparrow$	$S_{\mathrm{con}}$ $\uparrow$	Mean $\uparrow$	$S_{\mathrm{nov}}$ $\uparrow$	$S_{\mathrm{div}}$ $\uparrow$
Case 1 (RAS + vanilla DDPM)	0.753	0.632	0.885	0.757	0.208	0.336
Case 2 (w/o reg + SRR Diff.)	0.873	0.801	0.295	0.656	0.014	0.011
Case 3 (full framework)	0.718	0.487	0.969	0.725	0.296	0.420

Table 3 : Ablation on RAS regulation and SRR diffusion.

Approaches	Geometric Plausibility Scores				Novelty Score	Diversity Score
Approaches	$S_{\mathrm{sym}}$ $\uparrow$	$S_{\mathrm{per}}$ $\uparrow$	$S_{\mathrm{con}}$ $\uparrow$	Mean $\uparrow$	$S_{\mathrm{nov}}$ $\uparrow$	$S_{\mathrm{div}}$ $\uparrow$
Increase AE Param. Num.	0.753	0.471	0.977	0.734	0.308	0.411
Decrease AE Param. Num.	0.688	0.479	0.953	0.707	0.280	0.413
Increase diff. Param. Num.	0.705	0.474	0.936	0.705	0.330	0.444
Decrease diff. Param. Num.	0.722	0.493	0.955	0.723	0.286	0.409
Original setting	0.718	0.487	0.969	0.725	0.296	0.420

Table 4 : Ablation on model capacity. Param. Num. denotes parameter number.

Appendix figures & tables6 assets

Supplementary material from the paper’s appendix.

Appendix

Panel of Figure 4 — Figure 4 : Generated samples on MetaTruss with different models.

Panel of Figure 5 — Figure 5 : Generated samples on MetaShell with different models.

Approaches	Geometric Plausibility Scores				Novelty Score	Diversity Score
Approaches	$S_{\mathrm{sym}}$ $\uparrow$	$S_{\mathrm{per}}$ $\uparrow$	$S_{\mathrm{con}}$ $\uparrow$	Mean $\uparrow$	$S_{\mathrm{nov}}$ $\uparrow$	$S_{\mathrm{div}}$ $\uparrow$
Case 1 (RAS + vanilla DDPM)	0.935	0.884	0.930	0.916	0.305	0.625
Case 2 (w/o reg + SRR Diff.)	0.910	0.795	0.842	0.849	0.237	0.477
Case 3 (full framework)	0.923	0.856	0.978	0.919	0.380	0.783

Appendix

Table 5 : Ablation on RAS regulation and SRR diffusion.

Approaches	Geometric Plausibility Scores				Novelty Score	Diversity Score
Approaches	$S_{\mathrm{sym}}$ $\uparrow$	$S_{\mathrm{per}}$ $\uparrow$	$S_{\mathrm{con}}$ $\uparrow$	Mean $\uparrow$	$S_{\mathrm{nov}}$ $\uparrow$	$S_{\mathrm{div}}$ $\uparrow$
Increase AE Param. Num.	0.915	0.858	0.985	0.919	0.362	0.711
Decrease AE Param. Num.	0.894	0.823	0.963	0.893	0.363	0.742
Increase diff. Param. Num.	0.920	0.810	0.953	0.894	0.389	0.781
Decrease diff. Param. Num.	0.907	0.852	0.956	0.905	0.359	0.775
Original setting	0.923	0.856	0.978	0.919	0.380	0.783

Appendix

Table 6 : Ablation on model capacity. Param. Num. denotes parameter number.

Approaches	Time (s)
DiT-3D ( Mo et al. (2023) )	326
Y. Yang et al. ( Yang et al. (2024) )	28
XCube ( Ren et al. (2024) )	94
Trellis ( Xiang et al. (2025) )	5
3D-CDM ( Zheng et al. (2025) )	813
ReGDiff (ours)	31

Appendix

Table 7 : Time efficiency comparison.

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