# MicroLad: 2D-to-3D Microstructure Reconstruction and Generation via Latent Diffusion and Score Distillation

arXiv: https://arxiv.org/abs/2508.20138 · HTML: https://mlsanity.com/paper/2508.20138/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 24 of its 76 references that are in the map.
- First posted on arXiv 27 Aug 2025.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 24 of 24)

- [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)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Diffusion Models in Vision: A Survey](https://mlsanity.com/paper/2209.04747/) (2022)
- [MagNet: a Two-Pronged Defense against Adversarial Examples](https://mlsanity.com/paper/1705.09064/) (2017)
- [Text-to-image Diffusion Models in Generative AI: A Survey](https://mlsanity.com/paper/2303.07909/) (2023)
- [A Survey on Generative Diffusion Model](https://mlsanity.com/paper/2209.02646/) (2022)
- [Unsupervised Detection of Lesions in Brain MRI using constrained adversarial auto-encoders](https://mlsanity.com/paper/1806.04972/) (2018)
- [Diffusion Models Beat GANs on Topology Optimization](https://mlsanity.com/paper/2208.09591/) (2022)
- [JAX-FEM: A differentiable GPU-accelerated 3D finite element solver for automatic inverse design and mechanistic data science](https://mlsanity.com/paper/2212.00964/) (2022)
- [Rethinking Score Distillation as a Bridge Between Image Distributions](https://mlsanity.com/paper/2406.09417/) (2024)
- [Generating 3D structures from a 2D slice with GAN-based dimensionality expansion](https://mlsanity.com/paper/2102.07708/) (2021)
- [Overview: Computer vision and machine learning for microstructural characterization and analysis](https://mlsanity.com/paper/2005.14260/) (2020)
- [A numerical method for computing the overall response of nonlinear composites with complex microstructure](https://mlsanity.com/paper/2012.08962/) (2020)
- [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)
- [Three-dimensional microstructure generation using generative adversarial neural networks in the context of continuum micromechanics](https://mlsanity.com/paper/2206.01693/) (2022)
- [Evaluation of pseudo-healthy image reconstruction for anomaly detection with deep generative models: Application to brain FDG PET](https://mlsanity.com/paper/2401.16363/) (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)

## Abstract (arXiv)

A major obstacle to establishing reliable structure-property (SP) linkages in materials engineering is the scarcity of diverse 3D microstructure datasets. Limited dataset availability and insufficient control over the analysis and design space restrict the variety of achievable microstructure morphologies, hindering progress in solving the inverse (property-to-structure) design problem. To address these challenges, we introduce MicroLad, a latent diffusion framework specifically designed for reconstructing 3D microstructures from 2D data. Trained on 2D images and employing multi-plane denoising diffusion sampling in the latent space, the framework reliably generates stable and coherent 3D volumes that remain statistically consistent with the original data. While this reconstruction capability enables dimensionality expansion (2D-to-3D) for generating statistically equivalent 3D samples from 2D data, effective exploration of microstructure design requires methods to guide the generation process toward specific objectives. To achieve this, MicroLad integrates score distillation sampling (SDS), which combines a differentiable score loss with microstructural descriptor-matching and property-alignment terms. This approach updates encoded 2D slices of the 3D volume in the latent space, enabling robust inverse-controlled 2D-to-3D microstructure generation. Consequently, the method facilitates exploration of an expanded 3D microstructure analysis and design space in terms of both microstructural descriptors and material properties.