A method of actuating a valve in a well can include storing energy as a result of a differential pressure across a closed closure device of the valve, and releasing at least a portion of the stored energy while opening the closure device. A valve for use in a well can include a closure device, a biasing device, and an actuator which stores energy in the biasing device in response to a pressure differential across the closure device. A well system can include a tubular string, and a valve which controls fluid flow through the tubular string. The valve may include a closure device and an actuator which actuates the valve at least partially in response to a pressure differential across the closure device.