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

TL;DR

GeoTopoDiff introduces a graph diffusion framework that effectively reconstructs 3D porous microstructures from sparse CT slices by modeling both geometry and topology, improving accuracy and reducing errors.

Contribution

It transfers diffusion prior learning to a mixed graph space and incorporates topology-aware priors, enhancing reconstruction from sparse data.

Findings

Reduces morphology-related errors by 19.8%.

Decreases topology-sensitive transport errors by 36.5%.

Promotes denoising under sparse observations.

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.