The flight instructor reported that he was conducting primary flight training in a complex, high-performance airplane. On final approach during daylight hours, the runway's precision approach path indicator (PAPI) indicated the airplane was low on the approach path. He advised the student pilot to reduce the rate of descent. He further reported that the student pilot "relaxed his white knuckle grip" and the airplane pitched down "significantly". The flight instructor grabbed the control yoke and applied full throttle, but the airplane struck the runway approach lights during the low altitude recovery. The flight instructor landed the airplane without further incident. A postaccident examination of the airplane, by the flight instructor, revealed the airplane was trimmed nose down and that the right wing had sustained substantial damage. The flight instructor reported no preaccident mechanical malfunctions or failures with the airplane that would have precluded normal operation.