  Microstructure reconstruction has been an essential part of computational
material engineering to reveal the relationship between microstructures and
material properties. However, finding a general solution for microstructure
characterization and reconstruction (MCR) tasks is still challenging, although
there have been many attempts such as the descriptor-based MCR methods. To
address this generality problem, the denoising diffusion models are first
employed for the microstructure reconstruction task in this study. The
applicability of the diffusion-based models is validated with several types of
microstructures (e.g., polycrystalline alloy, carbonate, ceramics, copolymer,
fiber composite, etc.) that have different morphological characteristics. The
quality of the generated images is assessed with the quantitative evaluation
metrics (FID score, precision, and recall) and the conventional statistical
microstructure descriptors. Furthermore, the formulation of implicit
probabilistic models (which yields non-Markovian diffusion processes) is
adopted to accelerate the sampling process, thereby controlling the
computational cost considering the practicability and reliability. The results
show that the denoising diffusion models are well applicable to the
reconstruction of various types of microstructures with different spatial
distributions and morphological features. The diffusion-based approach provides
a stable training process with simple implementation for generating visually
similar and statistically equivalent microstructures. In these regards, the
diffusion model has great potential to be used as a universal microstructure
reconstruction method for handling complex microstructures for materials
science.
