Instructor pilot reported while in cruise the aircraft lost airspeed and the autopilot began to push the nose over in an attempt to regain airspeed. The instructor reported taking the controls from the student and pulling the autopilot circuit breaker. After diverting; maintenance found a large bug in the air intake vane.

Narrative

I was flying with a commercial pilot student for his 100NM Day Cross Country; the plan was to go from ZZZ-ZZZ1-ZZZ. The flight was uneventful until we were about halfway between ZZZ1-ZZZ; about 7-8 NM south/southwest of ZZZ2. We were cruising at 3;500 feet at about 105 KTS when all of a sudden the airspeed indicator dropped down to about 30-35 KIAS and the PFD alert for low airspeed started to sound; a few seconds after the alert; the autopilot ESP (electronic stability protection) took over and pitch the nose of the plane down in an effort to recover airspeed. My student attempted to disconnect the autopilot but it would just kick back in; knowing it was the ESP; I decided to pull the autopilot circuit breaker because that is the quickest way to disable the ESP. I asked for the controls from my student and advice ATC that we would like to divert to ZZZ2 and requested Runway XX (which is the closest one to us). We landed at ZZZ2 safely without a working airspeed indicator. When we pulled into the FBO to inspect the problem; we found a massive bug covering our ram air inlet. This aircraft is equipped with the Garmin G3X PFD/MFD and GFC 500 autopilot. While the ESP has good intent to protect pilots from getting into bad situations; on this flight it did the opposite. Since the ESP relies on a single source of data (in this case the ram air inlet of the pitot static system) it has no way of knowing whether the data it is receiving is good or bad. In this instance it took a perfectly good airplane into a significant nose down attitude because a bug caused to system to generate bad data. This situation is eerily similar to the another situation where the MCAS was tied to a single (Aircraft Operations Area) AOA vane which ultimately led to the two crashes of that aircraft.