We report on the formation of hollow structures driven by a phase transition that proceeds via diffusion through a membrane. The mechanism is demonstrated for Mg/MgO core/shell nanoparticles: When they undergo successive metal-hydride transitions at sufficiently high temperature, the core material progressively diffuses outward and evaporates, leaving a hollow shell with the original shape and thickness. This phenomenon might become a general approach to the design of materials with controlled porosity.