Instructor pilot reported a rough running engine coupled with power loss and elected to divert to make a precautionary landing.

Narrative

I was on an IFR flight with my student to ZZZ. Upon departing ZZZ1 my student mentioned that the aircraft engine didn't sound right. I was unable to detect a distinctive difference to be of any concern; so I decided to continue the flight. At 5;000 feet and roughly 10 NM away from the ZZZ airport on the XXX; there was an audible bang from the engine and a loss of 300 RPM from the engine. I tried exercising the throttle with only 2;300 RPM at full throttle. I reduced the throttle and ran through the engine roughness checklist. None of the items on the checklist remedied the loss of power or engine roughness. The mag check resulted in roughly 1;000 RPM drops for both; but the engine continued to operate; just at reduced power. I made the decision to divert to ZZZ airport. I called Center to cancel IFR and go into ZZZ under VFR. I was able to land the aircraft without further incident. It is important to note that the mag check on the run up was within limits. This event could have been caused by a maintenance issue. I think that it is important to heed the alerts from all of those on board. I could have paid more attention to my student mentioning the noise from the engine. I might have been able to detect an issue before we were enroute.