Born in Brooklyn, New York in 1938 to Hungarian immigrant parents, Kuhn first became interested in music at a young age while listening to his father's jazz record collection on 78s. Starting piano lessons at age five, he quickly displayed his gift for perfect pitch. After moving to Boston with his family, Kuhn began taking lessons with the legendary Boston-area pedagogue Margaret Chaloff, whom he credits with engendering his strong classical piano technique. Also during this time, he befriended Chaloff's son, saxophonist Serge Chaloff, who encouraged his interest in jazz.
In the late '60s, Kuhn relocated to Stockholm, Sweden, where he lived and performed until 1971. Ironically, it wasn't until returning to the States that Kuhn signed with Manfred Eicher's then-fledgling European jazz label ECM. Notably, Kuhn's work on The October Suite had been one of Eicher's early inspirations in founding the label. With ECM, Kuhn released several probing and atmospheric albums including Ecstasy (1974), Trance (1974), Motility (1977), Non-Fiction (1978), Playground, featuring vocalist Sheila Jordan (1979), and Last Year's Waltz (1981).
While the trio remained Kuhn's preferred format, his 1995 album Seasons of Romance found him working in an all-star quintet with tenor saxophonist Bob Mintzer and trumpeter Tom Harrell. Even more expansive was his 2004 return to ECM, Promises Kept, which found him backed by a small string orchestra. Kuhn also retained his exploratory edge, returning to his love of classical composers like Debussy and Ravel on 2006's Pavane for a Dead Princess. Jazz reworkings of classical compositions were featured on his 2008 trio album, Baubles, Bangles and Beads.