An exhalation valve includes a body and a cantilevered diaphragm having a clamped region and a valve face. The diaphragm's clamped region is clamped at the valve's body but the valve face deforms in response to the exhalation pressure. A valve seat on the valve body faces the valve face. The vanes cause a pressure field that results from the exhalation pressure. Its average pressure gradient points toward the valve seat and the region of the valve face that defines the longest moment arm. Normally, the valve face contacts the valve seat and closes the exhalation valve. In response to exhalation-induced torque above the threshold, it lifts off the valve seat and opens the exhalation valve.