Center Controller reported descending an IFR aircraft 1;000 feet below the MIA to get the aircraft to VFR conditions and below icing.

Narrative

When event happened; I was training an R-side trainee on their first two sectors. IFR and icing conditions existed throughout the airspace and traffic volume was low. We were just talking through an icing situation that happened; so while traffic was low; we were discussing an event that just took place. We noticed Aircraft X not climbing; and since we knew icing conditions were out there; we solicited why pilot was [not] climbing the aircraft. Pilot stated he was experiencing moderate rime icing; but wanted to continue on his flight path. We further pushed the pilot to make sure he was able to maintain altitude and asked him to state intentions. We gave him a slight turn to the south and assigned a block altitude to help him stay between layers. After a few minutes; the pilot came back and said he was unable to maintain altitude and wanted to change destinations. At this point; he was below the terrain; but was still in moderate icing and unable to maintain altitude. I gave him the minimum IFR altitude and asked the pilot to maintain a SW heading towards lower terrain. Pilot was able to fly southwest; but still could not maintain altitude. At that point; I gave the pilot a 260 heading and asked if he could see the ground. Pilot stated he was able to get ground contact; but it was choppy and was in the bases. I asked the pilot if 'another thousand feet would get him out of the icing'. He stated it would. I then descended the aircraft 1;000 feet below the MIA to get him out of the icing; but to also keep him at a safe altitude. MIA's in mountainous terrain are 2;000 feet above the highest point of terrain; so I felt comfortable that the altitude I assigned would both keep him safe and get him out of the icing. Pilot stated he was VFR as soon as he descended the extra 1;000 feet and the icing was burning off the aircraft. Pilot stated he wanted to cancel his IFR and maintain VFR to ZZZ1.