The transduction of sound into light by a pulsating bubble in water occurs when its maximum radius is about ten times greater than its ambient radius. For such high-amplitude motion, the steady-state balance of mass flow between the bubble and gas dissolved in the surrounding fluid can be maintained by diffusion only at low partial pressures, about 3 Torr. The observation of sonoluminescence (SL) from bubbles in 200 Torr solutions of air in water requires the action of some as yet unknown mass flow mechanism. On the other hand, gas solutions prepared at low partial pressures, in the diffusion-controlled regime, enable one to achieve SL in gases that do not emit light at higher partial pressures. These include hydrogenic gases and gases with a ratio of specific heats close to unity, which hardly heat up upon adiabatic compression. Experiments that probe the role of mass transfer in SL are presented along with the implications of their comparison to a multiple-time-scale analysis of mass diffusion.