The 1081st Kokutai was organized on April 1st, 1944 when it's parent unit the 1001Ku, an airplane transport unit, became too big. 1081Ku was also an airplane transport unit and originally had Mitsubishi G3M "Nell" and G4M "Betty", 24 escort fighters and 24 carrier bombers. The unit's home base was Miho aifield in Totori Prefecture but it was also based in Atsugi. Originally belonged to the Yokosuka Chinjufu (Yokosuka Naval District, here) but from September 15, 1944 became part of the 101 Koku Sentai (Combined Fleet).
From July 15, 1945 survivors from the Philippines of the 1021Ku joined 1081Ku but at the time there were no airplanes available for them.
Tokumu shoi (special ensign ) Oota Shoichi, who first conceived the "Ohka" flying bomb in June 1944, was a navigator with the 1081Ku. (Wikipedia's Ohka part needs correcting).