We present a methodology for the generative reconstruction of 3D microstructures from 2D cross-sectional electron backscatter diffraction micrographs. The method is applied to Ti-6Al-4V processed by laser powder bed fusion, where a high amount of basketweave morphology is observed, which arises from the solid-state β→α-transition upon cooling. Prior-β-grain reconstruction is performed and the out-of-plane orientation of the observed grains is obtained leveraging Burgers orientation relationship. Microstructural descriptors related to convolutional neural networks are extracted from the 2D micrographs, and used for cross-section-based optimization of pixel values in a 3D volume. In order to reconstruct crystallographic orientations, the orientation distribution of the basketweave microstructure is reduced to a discrete set of characteristic orientations, which are sequentially reconstructed as separate components. Our reconstructions capture the characteristic lath morphology that is typically observed in powder bed fusion-processed Ti-6Al-4V and perform well in comparisons of chord length, as well as grain size, aspect ratio, and axis orientation distributions.