Refill units for foam dispensers include a container for holding foamable liquid, a foam pump secured to the container, a foaming cartridge, an outlet and an actuation mechanism. The foam pump includes a housing, a liquid pump diaphragm, a plurality of air pump diaphragms, and a mixing chamber. An actuation mechanism releasably connects to a drive system in the dispenser. The actuation mechanism sequentially activates the liquid pump diaphragm and the air pump diaphragms when the refill unit is connected to the dispenser and the drive system. Sequential activation of the liquid pump diaphragm and air pump diaphragms causes the liquid pump diaphragm to pump at least a partial dose of liquid into the mixing chamber and the air pump diaphragms to pump at least a partial dose of air into the mixing chamber.