Latent diffusion modeling of porous media informed by spatial statistics

Accurate modeling and generation of porous media structures are critical for understanding fluid transport, mechanical properties, and multiphysics behavior in natural and engineered materials. In this paper, we develop a generative framework that leverages latent diffusion models (LDMs) trained on porous media generated using stochastic simulation along with experimental data. The utilized stochastic model provides a computationally efficient method to produce high-resolution porous samples that preserve spatial correlation statistics derived from training images. These samples serve as a statistically controlled dataset to train a latent diffusion pipeline, which integrates a variational autoencoder for dimensionality reduction and a UNet denoiser for latent-space generation. The resulting LDM learns a powerful and data-driven prior over porous structures while preserving key statistical properties. We demonstrate that the model can unconditionally generate realistic porous media models that reflect the input spatial statistics while exhibiting improved visual diversity and generative fidelity. This hybrid approach offers a promising pathway for fast, scalable, and controllable porous media generation in data-scarce or simulation-heavy settings.