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

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.