The student pilot entered downwind for the runway and performed a normal touch-and-go landing. On the second landing, the airplane bounced and the right wing lifted quickly. The student pilot applied right aileron and left rudder; the airplane landed back onto the runway on the right main landing gear and nosewheel. The pilot still had full left rudder in on the second touchdown and the airplane suddenly veered to the left and exited the runway. During the landing roll, the nosewheel dug into the soft ground and subsequently the airplane nosed over. The pilot stated that there were no preimpact mechanical malfunctions or failures with the airplane.