A319 pilot reported loss of control due to severe turbulence in cruise flight. Flight crew regained control and landed uneventfully.

Narrative

On Day 0; while operating Flight XXXX; we encountered severe turbulence with updrafts that led the aircraft to an overspeed state. The flight was assigned to fly directly to the ZZZ VOR at FL350. There was no significant weather painted on the radar until we would reach the ZZZ VOR. The flight started to experience light occasional turbulence; so I decided to turn on the fasten seatbelt sign. About 38 NM east of ZZZ1 VOR; the aircraft altitude and airspeed began increasing rather quickly. I selected Mach 0.76 using selected airspeed knob to help reduce the airspeed increasing trend. Even through the aircraft engines were spooling back to attain Mach 0.76; the aircraft airspeed and altitude kept increasing; which led to the first overspeed warning. As we started to recover from the first upset; the aircraft entered another updraft and overspeed once again. I disconnected the autopilot and autothrust and rode the updraft upwards until it subsided at FL364. The event duration was about 20-30 seconds long. We immediately notified ZZZ Center of the upset event; which the controller began warning other aircrafts of the event in that area. We then contacted the flight attendants to learn about the status of the cabin. FA (Flight Attendant) A reported that no one was injured; none of the overhead bins ejected any of its contents; nor did any O2 masks drop from their PSUs. Since no one was injured and the flight was less than 200 NM from ZZZ; I did not find it necessary to declare an inflight emergency and continued to ZZZ where a safe landing was made.