Geometric phases acquired randomly can give rise to coherence dephasing in nuclear spin systems, equivalent to spin relaxation. We calculate the form and extent of this geometric dephasing in a number of model systems involving the motion of Xe-131 nuclei in shaped containers. The dephasing is calculated in two ways : first, using an analytical treatment of the diffusive motion of individual nuclei, and second, using ensemble averaged propagators. The effects of applying additional magnetic fields to these systems are discussed briefly.