A conditional denoising diffusion probabilistic model with soft and hard data for microstructure reconstruction of porous materials

The controllable reconstruction of three-dimensional porous microstructures is essential for analyzing and designing porous construction and geomaterials, where pore morphology, connectivity, and pore-size distribution strongly affect transport, insulation, lightweight performance, and mechanical trade-offs. However, existing generative reconstruction methods often struggle to simultaneously preserve spatial pore morphology and satisfy target physical constraints. In this study, we propose a conditional soft- and hard-data-based denoising diffusion probabilistic model (CSHDDPM) for porous microstructure reconstruction. The framework incorporates hard data, including porosity and pore-size statistics, together with soft probabilistic spatial information derived from indicator kriging. A dual-path conditional residual block is designed to separately encode low-dimensional hard conditions and high-dimensional soft probability volumes, enabling their complementary fusion during diffusion-based generation. Experiments on Berea sandstone, Beadpack, and heterogeneous shale datasets demonstrate that CSHDDPM produces reconstructions with improved morphological fidelity, pore connectivity, and agreement with prescribed hard constraints compared with GAN-based baselines and diffusion variants. Ablation studies further show that the combined use of hard and soft data outperforms either condition alone, while robustness tests confirm graceful degradation under noisier or sparser soft data. The results indicate that CSHDDPM provides a flexible framework for controlled reconstruction and virtual characterization of porous microstructures, although its iterative denoising process entails higher computational cost than GAN-based alternatives.