Generative modeling of three-dimensional multiphase flow in porous media

Understanding multiphase flow in porous media requires models that capture complex pore geometries and reproduce realistic fluid distributions under diverse boundary conditions. In this paper, we propose a generative framework that combines variational machine learning with a denoising diffusion approach to build 3D multiphase pore structures directly from micro-CT images. The model is trained on small subvolumes to balance resolution with computational feasibility, enabling efficient training and rapid generation of new realizations. Quantitative comparisons show good agreement between generated and experimental samples across morphological metrics and statistical functions, while permeability distributions are reproduced within the range of variability. The variational component of the proposed method provides a compact latent representation that accelerates sampling and also increases the diversity of multiphase configurations that the model can generate, capturing a wider range of pore-scale fluid distributions. The framework allows tiling strategies to produce larger domains that remain consistent with pore-scale data, to scale from local heterogeneity to larger representative volumes. This method generates ensembles of realistic multiphase structures that can be used as input for sampling, conditioning, and optimization workflows in porous media applications.