According to the student pilot, he was fast on the approach and touched down on the main landing gear, bounced, then released back pressure on the yoke. The airplane started to porpoise uncontrollably and the nose landing gear broke off. The airplane departed the runway to the right and came to rest inverted in the grass. Examination of the airplane by an FAA inspector revealed that the airplane sustained substantial damage to the firewall, vertical stabilizer, and to the rudder. The pilot reported no preaccident mechanical malfunctions or failures with the airplane that would have precluded normal operation.