Latent Diffusion Modeling of Two- and Three-dimensional Fracture Networks with Sparse Observation Conditioning

Abstract

Characterizing subsurface fracture networks is challenging because geometry and connectivity are sparsely observed and uncertain away from measurements. We develop a latent diffusion framework for unconditional and observation-conditioned generation of two-dimensional (2D) and three-dimensional (3D) fracture networks. Fractures and the surrounding matrix are represented as binary fields and compressed by a variational autoencoder into compact spatial latent representations, where an Elucidated Diffusion Model learns their distribution. The 3D model operates on native volumetric fields, with a reconstruction objective designed to preserve sparse, thin fracture structures. Sparse borehole observations are incorporated through a conditioning encoder, classifier-free guidance, and diffusion posterior sampling. Generated ensembles reproduce key fracture-network statistics, including fracture area/volume fraction, two-point correlation, and chord-length distributions. Reconstructed fracture counts and gas-production responses are comparable to those of the reference networks under the considered multiphase flow scenarios. Conditional generation satisfies 99.6% of prescribed well observations in 2D. In 3D, where vertical boreholes constrain full voxel columns, conditional realizations satisfy 84.2% of observed well voxels while maintaining fracture volume and geometry comparable to the reference ensemble. These results demonstrate the potential of latent diffusion models as compact probabilistic representations for fracture-network characterization, ensemble generation, and sparse-observation conditioning.