# Generating 3D structures from a 2D slice with GAN-based dimensionality expansion

arXiv: https://arxiv.org/abs/2102.07708 · HTML: https://mlsanity.com/paper/2102.07708/

## Key facts

- Cited by 29 papers in the map (data through 7 Oct 2026).
- Builds on 9 of its 35 references that are in the map.
- First posted on arXiv 10 Feb 2021.

## Builds on (most cited first, 9 of 9)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Wasserstein GAN](https://mlsanity.com/paper/1701.07875/) (2017)
- [Generative Adversarial Networks: An Overview](https://mlsanity.com/paper/1710.07035/) (2017)
- [Learning a Probabilistic Latent Space of Object Shapes via 3D Generative-Adversarial Modeling](https://mlsanity.com/paper/1610.07584/) (2016)
- [Semi-Supervised Learning with Generative Adversarial Networks](https://mlsanity.com/paper/1606.01583/) (2016)
- [Reconstruction of three-dimensional porous media using generative adversarial neural networks](https://mlsanity.com/paper/1704.03225/) (2017)
- [Pores for thought: The use of generative adversarial networks for the stochastic reconstruction of 3D multi-phase electrode microstructures with periodic boundaries](https://mlsanity.com/paper/2003.11632/) (2020)

## Built on by (most cited first, 29 of 29)

- [Aligning Optimization Trajectories with Diffusion Models for Constrained Design Generation](https://mlsanity.com/paper/2305.18470/) (2023)
- [Materials science in the era of large language models: a perspective](https://mlsanity.com/paper/2403.06949/) (2024)
- [Deep Learning in Deterministic Computational Mechanics](https://mlsanity.com/paper/2309.15421/) (2023)
- [Recent Advances and Applications of Machine Learning in Experimental Solid Mechanics: A Review](https://mlsanity.com/paper/2303.07647/) (2023)
- [FakeNews: GAN-based generation of realistic 3D volumetric data -- A systematic review and taxonomy](https://mlsanity.com/paper/2207.01390/) (2022)
- [Diffusing the Optimal Topology: A Generative Optimization Approach](https://mlsanity.com/paper/2303.09760/) (2023)
- [Semi-Supervised Disease Classification based on Limited Medical Image Data](https://mlsanity.com/paper/2405.04295/) (2024)
- [Multi-plane denoising diffusion-based dimensionality expansion for 2D-to-3D reconstruction of microstructures with harmonized sampling](https://mlsanity.com/paper/2308.14035/) (2023)
- [MicroLib: A library of 3D microstructures generated from 2D micrographs using SliceGAN](https://mlsanity.com/paper/2210.06541/) (2022)
- [DA-VEGAN: Differentiably Augmenting VAE-GAN for microstructure reconstruction from extremely small data sets](https://mlsanity.com/paper/2303.03403/) (2023)
- [RockGPT: Reconstructing three-dimensional digital rocks from single two-dimensional slice from the perspective of video generation](https://mlsanity.com/paper/2108.03132/) (2021)
- [Fusion of complementary 2D and 3D mesostructural datasets using generative adversarial networks](https://mlsanity.com/paper/2110.11281/) (2021)
- [NITO: Neural Implicit Fields for Resolution-free Topology Optimization](https://mlsanity.com/paper/2402.05073/) (2024)
- [Feature Disentanglement in generating three-dimensional structure from two-dimensional slice with sliceGAN](https://mlsanity.com/paper/2105.00194/) (2021)
- [Using convolutional neural networks for stereological characterization of 3D hetero-aggregates based on synthetic STEM data](https://mlsanity.com/paper/2310.18523/) (2023)
- [Prediction of microstructural representativity from a single image](https://mlsanity.com/paper/2410.19568/) (2024)
- [PolyMicros: Bootstrapping a Foundation Model for Polycrystalline Material Structure](https://mlsanity.com/paper/2506.11055/) (2025)
- [3D microstructural generation from 2D images of cement paste using generative adversarial networks](https://mlsanity.com/paper/2204.01645/) (2022)
- [Two approaches to inpainting microstructure with deep convolutional generative adversarial networks](https://mlsanity.com/paper/2210.06997/) (2022)
- [FluxGAN: A Physics-Aware Generative Adversarial Network Model for Generating Microstructures That Maintain Target Heat Flux](https://mlsanity.com/paper/2310.04622/) (2023)
- [Denoising diffusion-based synthetic generation of three-dimensional (3D) anisotropic microstructures from two-dimensional (2D) micrographs](https://mlsanity.com/paper/2312.07832/) (2023)
- [Generating multi-scale NMC particles with radial grain architectures using spatial stochastics and GANs](https://mlsanity.com/paper/2407.05333/) (2024)
- [Constrained Transformer-Based Porous Media Generation to Spatial Distribution of Rock Properties](https://mlsanity.com/paper/2410.21462/) (2024)
- [Generative adversarial framework to calibrate excursion set models for the 3D morphology of all-solid-state battery cathodes](https://mlsanity.com/paper/2503.17171/) (2025)
- [evoxels: A differentiable physics framework for voxel-based microstructure simulations](https://mlsanity.com/paper/2507.21748/) (2025)
- [MicroLad: 2D-to-3D Microstructure Reconstruction and Generation via Latent Diffusion and Score Distillation](https://mlsanity.com/paper/2508.20138/) (2025)
- [Well Log-Guided Synthesis of Subsurface Images from Sparse Petrography Data Using cGANs](https://mlsanity.com/paper/2603.09651/) (2026)
- [GeoTopoDiff: Learning Geometry--Topology Graph Priors through Boundary-Constrained Mixed Diffusion for Sparse-Slice 3D Porous Reconstruction](https://mlsanity.com/paper/2605.03764/) (2026)
- [Generating Heterogeneous 3D Geological Microstructures from 2D Images via a Stable Diffusion-Adversarial Model](https://mlsanity.com/paper/2609.20358/) (2026)

## Abstract (arXiv)

Generative adversarial networks (GANs) can be trained to generate 3D image data, which is useful for design optimisation. However, this conventionally requires 3D training data, which is challenging to obtain. 2D imaging techniques tend to be faster, higher resolution, better at phase identification and more widely available. Here, we introduce a generative adversarial network architecture, SliceGAN, which is able to synthesise high fidelity 3D datasets using a single representative 2D image. This is especially relevant for the task of material microstructure generation, as a cross-sectional micrograph can contain sufficient information to statistically reconstruct 3D samples. Our architecture implements the concept of uniform information density, which both ensures that generated volumes are equally high quality at all points in space, and that arbitrarily large volumes can be generated. SliceGAN has been successfully trained on a diverse set of materials, demonstrating the widespread applicability of this tool. The quality of generated micrographs is shown through a statistical comparison of synthetic and real datasets of a battery electrode in terms of key microstructural metrics. Finally, we find that the generation time for a 108 voxel volume is on the order of a few seconds, yielding a path for future studies into high-throughput microstructural optimisation.