  Microstructure reconstruction, a major component of inverse computational
materials engineering, is currently advancing at an unprecedented rate. While
various training-based and training-free approaches are developed, the majority
of contributions are based on generative adversarial networks. In contrast,
diffusion models constitute a more stable alternative, which have recently
become the new state of the art and currently attract much attention. The
present work investigates the applicability of diffusion models to the
reconstruction of real-world microstructure data. For this purpose, a highly
diverse and morphologically complex data set is created by combining and
processing databases from the literature, where the reconstruction of realistic
micrographs for a given material class demonstrates the ability of the model to
capture these features. Furthermore, a fiber composite data set is used to
validate the applicability of diffusion models to small data set sizes that can
realistically be created by a single lab. The quality and diversity of the
reconstructed microstructures is quantified by means of descriptor-based error
metrics as well as the Fr\'echet inception distance (FID) score. Although not
present in the training data set, the generated samples are visually
indistinguishable from real data to the untrained eye and various error metrics
are computed. This demonstrates the utility of diffusion models in
microstructure reconstruction and provides a basis for further extensions such
as 2D-to-3D reconstruction or application to multiscale modeling and
structure-property linkages.
