A tire having a tire cavity is disclosed, wherein the tire has a bi-directional pump assembly including a pump passageway having an inlet end and an outlet end, and being operative to allow a portion of the pump passageway near a tire footprint to substantially close and open the pump passageway. The tire includes a valve assembly having a valve housing, wherein a diaphragm is mounted in the valve housing forming an interior chamber, and wherein the diaphragm is responsive to the pressure of the tire cavity. The interior chamber has an inlet in fluid communication with outside air, and an outlet in fluid communication with inlet and outlet of the pump passageway. The valve assembly further includes an inlet control valve having a valve bottom positioned over the outlet and operative to open and close the outlet. The inlet control valve has a first end connected to the diaphragm, and a resilient member biases the inlet control valve into the open position.