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 called ‘Micro3Diff’ for 2D-to-3D reconstruction of microstructures 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 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 or 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.

获取可靠的微观结构数据集是借助集成计算材料工程（ICME）方法进行材料系统设计的关键一步。然而，由于高昂的实验成本或技术限制，获取三维（3D）微观结构数据集通常具有挑战性，而获取二维（2D）显微照片相对容易。为了解决这个问题，本研究提出了一种名为“Micro3Diff”的新颖框架，用于使用基于扩散的生成模型 (DGM) 对微观结构进行 2D 到 3D 重建。具体来说，这种方法仅需要预先训练的 DGM 来生成 2D 样本，并且仅在生成过程（即反向扩散过程）期间进行维度扩展（2D 到 3D）。所提出的框架纳入了称为“多平面去噪扩散”的概念，它将来自不同平面的噪声样本（即潜在变量）转换为数据结构，同时保持 3D 空间中的空间连接性。此外，还开发了协调采样过程，以解决维数扩展期间 DGM 逆马尔可夫链可能出现的偏差。结合起来，我们证明了 Micro3Diff 在重建具有与原始 2D 图像形态等效的连接切片的 3D 样本方面的可行性。为了验证 Micro3Diff 的性能，重建了各种类型的微观结构（合成的或实验观察到的），并定性和定量地评估了生成的样本的质量。成功的重建结果激发了 Micro3Diff 在即将到来的 ICME 应用中的潜在利用，同时在理解和操纵 DGM 的潜在空间方面取得了突破。