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.
Related
- Broadband Ground-Motion Synthesis by Conditioning Denoising Diffusion Models on Low-Frequency Waveforms
- An AI-assisted conditioning and geological interpretation workflow for usage in implicit geological modeling
- Modeling of fracture intensity by integrating geostatistical and neural network methods: The asmari reservoir, Rag-e-Sefid Oilfield, SW Iran
- Modelling wide-swath altimeter observation-error correlations with a regularised diffusion operator
- Cutting and shuffling control mixing in three-dimensional discrete fracture networks
BibTeX
@misc{shen2026latent,
title = {{Latent Diffusion Modeling of Two- and Three-dimensional Fracture Networks with Sparse Observation Conditioning}},
author = {Jiawei Shen and Hongkyu Yoon and Jonghyun Lee},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.14412},
eprint = {2610.14412},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.14412},
}
RIS
TY - UNPB
TI - Latent Diffusion Modeling of Two- and Three-dimensional Fracture Networks with Sparse Observation Conditioning
AU - Jiawei Shen
AU - Hongkyu Yoon
AU - Jonghyun Lee
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2610.14412
UR - https://arxiv.org/abs/2610.14412
AB - 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.
ER -