This paper concerns a relaxation of the assumption of uniform mixture composition in the interior of sonoluminescence bubbles. Intense temperature and pressure gradients within the bubble drive relative mass diffusion which overwhelms diffusion driven by concentration gradients. This thermal and pressure diffusion results in a robust compositional inhomogeneity in the bubble which lasts several orders of magnitude longer than the temperature peak or light pulse at the main collapse of the bubble. This effect has important consequences for control of sonoluminescence, gas dynamics, sonochemistry, and the physics of light production.