Generating Heterogeneous 3D Geological Microstructures from 2D Images via a Stable Diffusion-Adversarial Model

Accurately characterizing the 3D microstructure of porous media is essential for predicting material properties in fields like geological waste disposal and materials science. However, high-resolution 3D imaging is often costly or technically limited. This paper addresses the challenge of synthesizing representative 3D microstructures from readily available 2D images, aiming to overcome the instability and poor structural fidelity often seen in existing generative models.

The authors propose the Dimensionality Expansion Diffusion Adversarial Model (DimExDAM). Unlike standard diffusion models that require 3D training data, or GAN-based models like SliceGAN that often struggle with training instability in multi-discriminator configurations, DimExDAM uses a hybrid framework. It employs a 3D generator and a single 2D discriminator, replacing the traditional denoising mean-squared-error loss with an adversarial loss. This allows the model to learn complex, non-Gaussian transitions between noise levels using a short diffusion chain (8 steps). To ensure stable convergence, the authors implement several stabilization strategies, including spectral normalization, a low-pass curriculum on real images, and temperature-scaled discriminator activations.

DimExDAM successfully generates 3D volumes that closely match the ground truth across various geological materials, including sandstone, carbonate, and highly heterogeneous Boom Clay. Quantitative evaluations using structural descriptors (chord length, lineal path, and two-point correlation functions) and physics-based transport simulations (gas diffusivity and permeability) demonstrate that DimExDAM outperforms SliceGAN. While SliceGAN often produces visible artifacts and exhibits shifts in transport properties, DimExDAM maintains better structural coherence and directional consistency. The model's ability to produce physically meaningful transport results, even when trained on limited 2D data, highlights its potential for generating synthetic datasets for downstream modeling.