Controlled Latent Diffusion Models for 3D Porous Media Reconstruction

Controlled Latent Diffusion Models for 3D Porous Media Reconstruction

Predicting fluid flow through natural rocks requires 3D images that resolve micron-scale pores while spanning a representative elementary volume—an enduring challenge of scale in porous media science. We bridge this gap by coupling a variational autoencoder (VAE) with an Elucidated Diffusion Model (EDM). The VAE first compresses complex rock geometries into a compact latent grid, drastically reducing the memory footprint. The EDM then generates new structures within this efficient latent space, enabling the synthesis of volumes up to 256³ voxels — four times larger than typical pixel-space diffusion methods.

To ensure physical realism, we employ a simple yet powerful conditioning strategy: we first sample a target feature, such as porosity or the two-point correlation function, from its empirical distribution and then use it to guide the latent diffusion process. We validated this approach across four diverse lithologies (sandstone, carbonate, shale, and volcanic tuff). Without being explicitly trained on them, the generated samples faithfully reproduce key experimental metrics, including permeability and pore-size distributions.

The result is a fast, computationally light pipeline that delivers statistically accurate digital rocks ready for direct use in numerical simulations, such as the lattice Boltzmann method. This work sets a new benchmark for data-driven upscaling and generative modeling in porous systems.