  Acquiring reliable microstructure datasets is a pivotal step toward the
systematic design of materials with the aid of integrated computational
materials engineering (ICME) approaches. However, obtaining three-dimensional
(3D) microstructure datasets is often challenging due to high experimental
costs or technical limitations, while acquiring two-dimensional (2D)
micrographs is comparatively easier. To deal with this issue, this study
proposes a novel framework for 2D-to-3D reconstruction of microstructures
called Micro3Diff using diffusion-based generative models (DGMs). Specifically,
this approach solely requires pre-trained DGMs for the generation of 2D
samples, and dimensionality expansion (2D-to-3D) takes place only during the
generation process (i.e., reverse diffusion process). The proposed framework
incorporates a new concept referred to as multi-plane denoising diffusion,
which transforms noisy samples (i.e., latent variables) from different planes
into the data structure while maintaining spatial connectivity in 3D space.
Furthermore, a harmonized sampling process is developed to address possible
deviations from the reverse Markov chain of DGMs during the dimensionality
expansion. Combined, we demonstrate the feasibility of Micro3Diff in
reconstructing 3D samples with connected slices that maintain morphologically
equivalence to the original 2D images. To validate the performance of
Micro3Diff, various types of microstructures (synthetic and experimentally
observed) are reconstructed, and the quality of the generated samples is
assessed both qualitatively and quantitatively. The successful reconstruction
outcomes inspire the potential utilization of Micro3Diff in upcoming ICME
applications while achieving a breakthrough in comprehending and manipulating
the latent space of DGMs.
