*

CuInP₂S₆ (CIPS) is a van der Waals (vdW) layered system exhibiting a variety of intriguing properties. Among these properties is the presence of a strain-induced quadruple-well potential for Cu displacements, which features two low-polarization and two high-polarization states, with the latter corresponding to the presence of a second stable Cu position just inside the vdW gap. The mechanism for polarization switching has been experimentally shown to include the possibility of migration of Cu ions across the vdW gap (instead of solely  through the layers), but the detailed pathway taken by the Cu ions in doing so remains poorly understood. Using density functional theory calculations, we investigate the various possible low-energy switching paths involving coherent Cu ion motion, and characterize the sequence of Cu coordination environments visited along the path. Finally, we argue that a such a coherent migration of the Cu sublattice from one vdW layer to the next may be regarded as a realization of quantized adiabatic transport.