Controlled latent diffusion models for 3D porous media reconstruction

Abstract

Three-dimensional digital reconstruction of porous media presents a fundamental challenge in geosciences, requiring simultaneous resolution of fine-scale pore structures while capturing representative elementary volumes. This work introduces a computational framework that addresses this challenge through latent diffusion models operating within the Elucidated Diffusion Models (EDM) framework. The proposed approach reduces dimensionality via a custom Variational Autoencoder trained in binary geological volumes, improving efficiency and also enabling the generation of larger volumes than previously possible with diffusion models. A key innovation is the controlled unconditional sampling methodology, which enhances distribution coverage by first sampling target statistics from their empirical distributions, and then generating samples conditioned on these values. Extensive testing on four distinct rock types demonstrates that conditioning on porosity – a readily computable statistic – is sufficient to ensure a consistent representation of multiple complex properties, including permeability, two-point correlation functions, and pore size distributions. The framework achieves better generation quality than pixel-space diffusion while enabling significantly larger volume reconstruction ($256^3$ voxels) with substantially reduced computational requirements, establishing a new state-of-the-art for digital rock physics applications.