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

TL;DR

MicroLad addresses the scarcity of 3D microstructure data by coupling a pretrained VAE with latent diffusion in a low-dimensional manifold to reconstruct 3D volumes from 2D slices using latent multi-plane denoising diffusion. It further enables inverse-controlled generation by applying score-distillation sampling with descriptor- and differentiable-property-based losses, allowing target-guided morphologies and properties without requiring labeled 3D data. The approach achieves descriptor- and property-guided 2D-to-3D generation and efficient reconstruction, validated on binary carbonate and three-phase SOFC morphologies, while offering substantial speedups over pixel-space methods. These capabilities expand the microstructure design space, enabling robust exploration of structure–property linkages and paving the way for manufacturing-aware, physics-informed design workflows, with future directions toward conditional diffusion, multi-physics modeling, and broader material systems.

Abstract

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.

Figures (27)

• Figure 1: MicroLad framework description: (a) acquire a 2D microstructure dataset, (b) encode the data into a latent space, (c) add noise to the latent variables, (d) train a U-Net to predict the noise, (e) initialize stacked 2D latent variables, (f) apply L-MPDD to spatially connect the 2D reverse diffusion processes, (g) generate 3D latent variables, (h) refine the latent representation to produce 3D voxels, (i) decode the final 3D microstructure, and (j) apply SDS for inverse-controlled microstructure generation with different objectives.
• Figure 2: Comparison between (a) conventional computational materials engineering for structure–property (SP) linkage, which relies on experimental microstructure data acquisition, morphological and descriptor analysis, and numerical simulation-based property evaluation and (b) the proposed MicroLad framework, which explores 3D microstructure design spaces through reconstruction and inverse-controlled microstructure generation.
• Figure 3: 2D-to-3D microstructure reconstruction results for binary microstructure: (a) original 2D microstructure images, (b) reconstructed 3D microstructure, (c) random cross-sectional slices of (b), (d) two-point correlation functions of 2D slices from the reconstructed 3D samples in (b) compared to those from the original 2D dataset in (a), (e) reconstructed 3D microstructure guided by target two-point correlation functions, (f) random cross-sectional slices of (e), and (g) two-point correlation functions of 2D slices from the guided reconstruction in (e) compared to the original 2D dataset.
• Figure 4: 2D-to-3D microstructure reconstruction results for three-phase microstructure: (a) original 2D microstructure images, (b) reconstructed 3D microstructure, (c) random cross-sectional slices of (b), (d) two-point correlation functions of 2D slices from the reconstructed 3D samples in (b) compared to those from the original 2D dataset in (a), (e) reconstructed 3D microstructure guided by target two-point correlation functions, (f) random cross-sectional slices of (e), and (g) two-point correlation functions of 2D slices from the guided reconstruction in (e) compared to the original 2D dataset.
• Figure 5: Inverse 2D-to-3D generation of three-phase microstructures with controlled volume fractions for each material phase: (a) generated 3D volumes, (b) variation in 2D cross-sectional images (randomly selected slices) as SDS steps increase, and (c) distribution of variables in the training dataset compared to generated samples with target objectives.