A fast-acting, pneumatic diaphragm valve includes a diaphragm valve closure member, a pneumatic piston that provides a closure force on the closure member, and a solenoid pilot valve that controls pressurized air to the piston to cause the piston to move in a reciprocal manner so that the closure member opens and closes the valve. The valve seat seal can be elastomer for enhancing speed, and the solenoid pilot valve can be positioned and configured with air flow longitudinally through or past the solenoid armature to enhance speed.