We intend to determine the nature of ionic conductivity and the pathways of thermally-induced diffusion in the inverse cubic perovskites BaLiX3 (X = H, D, F). To this end, neutron powder measurements at high temperatures followed by careful Rietveld analysis of the Debye–Waller factors including anharmonic contributions is necessary. Reconstruction of the scattering-length density using the maximum-entropy method (MEM) and derivation of probability-density functions (PDFs) allows mapping of the actual ion pathways. The associated effective one-particle potentials (OPPs) give access to the energy barriers for migration. The outcome of our study will be compared to additional high-temperature NMR investigations (Prof. Wilkening, Graz) and quantum-chemical computations (Prof. Bredow, Bonn). Combining all these results, we hope to acquire a fundamental understanding of mobility in potential two-ion conductors and lay a foundation for further experiments with mixed anion sets.