  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 modeling, this study adopted the denoising diffusion
probability 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 successfully 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 is extended to
three-dimensional framework and integrates 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 Boltzmann method.
