We use Wasserstein Generative Adversarial Networks to learn and
integrate multi-scale features in segmented three-dimensional images of
porous materials, enabling the dependable generation of large-scale
representations of complex porous media. A Laplacian pyramid generator
is introduced which creates pore-space features with a hierarchy of
spatial scales. Feature statistics mixing regularization enhances the
ability of the model generation to reliably maintain multi-scale
pore-space features of images by increasing diversity. The method is
tested on a variety of X-ray images of porous rocks. The generated
images can be of any size -- cm-scale ten-billion-cell images are
generated to demonstrate the power of the approach -- which have
two-point correlation functions, porosity, permeability, Euler
characteristic, curvature, and specific surface area close to the
training datasets. The images demonstrate a considerable improvement
over previously- published studies using generative adversarial
networks.