Significant structural evolution occurs during the deposition of CuInSe_{2} solar materials when the Cu content increases. We use in situ heating in a scanning transmission electron microscope to directly observe how grain boundaries migrate during heating, causing nondefected grains to consume highly defected grains. Cu substitutes for In in the near grain boundary regions, turning them into a Cu-Se phase topotactic with the CuInSe_{2} grain interiors. Together with density functional theory and molecular dynamics calculations, we reveal how this Cu-Se phase makes the grain boundaries highly mobile.