Property-Constrained 3D Porous Media Reconstruction from 2D Images via Conditional Generative Adversarial Networks

Obtaining truly representative pore-scale images that match bulk formation properties remains a fundamental challenge in subsurface characterization, as natural spatial heterogeneity causes extracted sub-images to deviate significantly from core-measured values. This challenge is compounded by data scarcity, where physical samples are only available at sparse well locations. This study presents a multi-conditional Generative Adversarial Network (cGAN) framework that generates representative pore-scale images with precisely controlled properties. The framework was trained on thin section samples from four depths (1879.50-1943.50 m) of a carbonate formation, simultaneously conditioning on porosity and depth within a single model. It processes RGB thin section images that preserve critical mineralogical information (anhydrite-dolomite differentiation, grain boundaries, porosity distinctions) lost in conventional grayscale representations, capturing characteristics from grainstone fabrics to crystalline textures with anhydrite inclusions. The model achieved strong porosity control (R^2 = 0.95) across all formations with mean absolute errors of 0.0099-0.0197. Morphological validation confirmed preservation of average pore radius, specific surface area, and tortuosity within acceptable tolerances. Two-point correlation (S2) analysis confirmed that generated images preserve the spatial continuity and characteristic length scales of natural pore networks, with results consistent across the imaging resolutions tested (1.8-3.0 micron/pixel). Validated against core sample properties, generated images showed higher property fidelity with dual-constraint errors of 1.9-12.4% compared to 37.5-713.6% for randomly extracted real sub-images. This capability provides practical tools for subsurface characterization, particularly valuable for carbon storage, geothermal energy, and groundwater management.

Inverse design of three-dimensional porous media is central to applications in filtration, catalysis, energy storage, fuel cells, thermal management, and biomedical scaffolds, but remains challenging because many distinct pore geometries can share similar porosity or permeability while small structural changes can strongly affect transport behaviour. This paper proposes a physics-guided generative AI framework for property-targeted porous media design, combining a property-aware variational autoencoder, a conditional latent diffusion model, and an independently trained differentiable structure-to-property surrogate. The framework learns a compact, physically informative latent design space, generates porous structures conditioned on target porosity and directional permeability, and refines generated samples using property-level feedback during denoising and decoding. Experiments on procedurally generated structures and real micro-CT porous-media datasets show improved target-property matching, directional permeability control, and property correlation compared with representative property-aware variational-autoencoder and latent-diffusion baselines. The results demonstrate a scalable route towards controllable inverse design of complex porous geometries and establish a foundation for simulation-informed generative AI tools in engineering and advanced materials discovery.

Conditional medical image generation plays an important role in many clinically relevant imaging tasks. However, existing methods still face a fundamental challenge in balancing inference efficiency, patient-specific fidelity, and distribution-level plausibility, particularly in high-dimensional 3D medical imaging. In this work, we propose GDM, a generative drifting framework that reformulates deterministic medical image prediction as a multi-objective learning problem to jointly promote distribution-level plausibility and patient-specific fidelity while retaining one-step inference. GDM extends drifting to 3D medical imaging through an attractive-repulsive drift that minimizes the discrepancy between the generator pushforward and the target distribution. To enable stable drifting-based learning in 3D volumetric data, GDM constructs a multi-level feature bank from a medical foundation encoder to support reliable affinity estimation and drifting field computation across complementary global, local, and spatial representations. In addition, a gradient coordination strategy in the shared output space improves optimization balance under competing distribution-level and fidelity-oriented objectives. We evaluate the proposed framework on two representative tasks, MRI-to-CT synthesis and sparse-view CT reconstruction. Experimental results show that GDM consistently outperforms a wide range of baselines, including GAN-based, flow-matching-based, and SDE-based generative models, as well as supervised regression methods, while improving the balance among anatomical fidelity, quantitative reliability, perceptual realism, and inference efficiency. These findings suggest that GDM provides a practical and effective framework for conditional 3D medical image generation.