GeoTopoDiff: Learning Geometry--Topology Graph Priors through Boundary-Constrained Mixed Diffusion for Sparse-Slice 3D Porous Reconstruction

2026-05-05

AI Summary

This work addresses the challenge of reconstructing three-dimensional porous media from sparse CT slices, where preserving both pore geometric continuity and pore-throat topological discreteness remains difficult. To this end, the authors propose GeoTopoDiff, a novel framework that shifts diffusion prior learning from voxel space to a hybrid graph state space encoding both geometric and topological information. The method innovatively constructs a topology-aware graph prior and incorporates a boundary constraint mechanism to guide the reverse denoising process. Experiments on PTFE and Fontainebleau sandstone datasets demonstrate that GeoTopoDiff reduces morphological error by 19.8% and topology-sensitive transport error by 36.5% on average, substantially improving 3D reconstruction accuracy under sparse observational conditions.

Abstract

Diffusion-based voxel prior modelling is challenging for the reconstruction of large-scale 3D porous microstructures. Due to the demanding requirements for simultaneously modelling both the continuous pore morphology and the discrete pore-throat topology, the diffusion models require fully observed CT scans to provide topology-faithful priors, which results in an inherent trade-off among throughput, topological fidelity, and field of view in practical industrial applications. We propose GeoTopoDiff, a graph diffusion-based framework for reconstructing 3D porous microstructures from sparse CT slices. GeoTopoDiff transfers the learning of diffusion priors from a voxel-based space to a mixed graph state space, which simultaneously encompasses continuous pore geometry and discrete pore-throat topology. A topology-aware partial graph prior from sparsely observed CT slices is introduced to constrain the reverse denoising process. Experiments on anisotropic PTFE and Fontainebleau sandstone show that GeoTopoDiff reduces morphology-related errors by 19.8% and topology-sensitive transport errors by 36.5% on average. Our findings suggest that the mixed graph state space promotes the diffusion denoising process to reduce posterior uncertainty under a sparse observations. All models and code have been made publicly available to facilitate the exploration of diffusion models in the field of 3D porous microstructures simulation.

Problem

• 3D porous reconstruction
• diffusion models
• pore-throat topology
• sparse CT slices
• voxel prior modelling

Innovation

• graph diffusion
• mixed graph state space
• topology-aware prior
• sparse-slice reconstruction
• 3D porous microstructure