Microstructure reconstruction of 2D/3D random materials via diffusion-based deep generative models

Microstructure reconstruction serves as a crucial foundation for establishing process–structure–property (PSP) relationship in material design. Confronting the limitations of variational autoencoder and generative adversarial network within generative models, this study adopted the denoising diffusion probabilistic model (DDPM) to learn the probability distribution of high-dimensional raw data and successfully reconstructed the microstructures of various composite materials, such as inclusion materials, spinodal decomposition materials, chessboard materials, fractal noise materials, and so on. The quality of generated microstructure was evaluated using quantitative measures like spatial correlation functions and Fourier descriptor. On this basis, this study also achieved the regulation of microstructure randomness and the generation of gradient materials through continuous interpolation in latent space using denoising diffusion implicit model (DDIM). Furthermore, the two-dimensional microstructure reconstruction was extended to three-dimensional framework and integrated permeability as a feature encoding embedding. This enables the conditional generation of three-dimensional microstructures for random porous materials within a defined permeability range. The permeabilities of these generated microstructures were further validated through the application of the lattice Boltzmann method. The above methods provide new ideas and references for material reverse design.