Pilot reported a near mid-air collision in cruise when another aircraft climbed rapidly from below and after passing behind turned directly facing the pilot. The reporter made an immediate diving turn to avoid collision.

Narrative

IFR Flight: I was just passing by Pullman airport. Level at 7000 feet heading direct to ZZZ airport. I noticed on foreflight that there was a plane Aircraft X that was approaching from the left side of the plane. I started looking out for the airplane. ATC advised that there was a plane that was flying up like a rocket. It was showing that the plane was climbing at appt 1500 feet per minute. I watched closely for the airplane on ADS-B and noticed the track would pass under the airplane. ATC advised again the path and that the plane was still climbing. I advised that the plane was not in sight and would pass behind the airplane. ATC communicated that the traffic was a non factor. But I noticed that the plane began to do a left 180. I kept following the airplane on foreflight and the plane levels at 7000 and was now directly in my forward flight path. The target turned yellow on foreflight. 2o'clock and getting closer. I looked outside and there the plane was directly facing me. I immediately dropped the power. Kicked off the autopilot and began a dive. In the dive I radioed ATC to advised the immediate dive. I was in a 1900 feet per minute diving right turn diving below the traffic. When I reached 6000 I started to level off. ATC was not aware that the plane did a left 180 and leveled off at 7000. They advised me to level off at 6000 and we shared a dialogue of him being unaware of the traffic and me being glad that I had ADS-B on the flight to keep an eye on traffic.