Narrative:

Aircraft Y (FL270) was above aircraft X (FL250). Aircraft Y keyed up and said he was declaring a fuel [shortage] and would like to divert to ZZZ. My trainee keyed up and assigned heading 080 vectors for descent. I did not like that heading so I reassigned heading 110. Aircraft Y read that back; then we proceeded to gather more info. The next update; aircraft Y had descended to FL262 and the next update we lost separation. He was not assigned a descent; nor did he report out of FL270. As soon as we noticed the altitude change; I advised aircraft X of the traffic who at this point was diverging and not a factor. I believe the closest the two aircraft got was 300 feet and 3 miles diverging.pilot needs to be more informed on what he is responsible to say if he needs an altitude change; or decides he needs to change altitude without assignment.

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Original NASA ASRS Text

Title: Center Controller reported that an aircraft declaring Minimum Fuel departed his assigned altitude without notification resulting in a conflict with another aircraft.

Narrative: Aircraft Y (FL270) was above Aircraft X (FL250). Aircraft Y keyed up and said he was declaring a fuel [shortage] and would like to divert to ZZZ. My Trainee keyed up and assigned heading 080 vectors for descent. I did not like that heading so I reassigned heading 110. Aircraft Y read that back; then we proceeded to gather more info. The next update; Aircraft Y had descended to FL262 and the next update we lost separation. He was not assigned a descent; nor did he report out of FL270. As soon as we noticed the altitude change; I advised Aircraft X of the traffic who at this point was diverging and not a factor. I believe the closest the two aircraft got was 300 feet and 3 miles diverging.Pilot needs to be more informed on what he is responsible to say if he needs an altitude change; or decides he needs to change altitude without assignment.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.