Roman Kunsman was born in 1941 in Kuibyshev (now Samara), where his family had been evacuated during the war, and grew up back in Leningrad from 1945. He trained on clarinet as a child, moved to saxophone in his teens, and by 1962 was lead saxophonist in Anatoly Kroll's big band in Tula. Back in Leningrad in 1963 he formed a modern-jazz quartet with pianist Yuri Vikharev, bassist Eduard Moskalev and drummer Valery Mysovsky, working the "White Nights" café and the "Vostok" club and touring the Baltic festival circuit. In 1965 the quartet won the Leningrad Jazz Festival, and his composition "Loneliness" took a special prize from the USSR Union of Composers. In 1967, after a piece of his was performed in Moscow under Oleg Lundstrem, he joined Lundstrem's state jazz orchestra as a soloist and section leader — one of the few ways a Soviet musician could play jazz professionally and legally at the time. He is reported to have shared a bill with the American saxophonist Charles Lloyd at the Tallinn Jazz Festival in 1967 or 1968 (sources disagree on the year).

He emigrated to Israel around 1970–71 — sources differ on the exact year and on whether Jerusalem or Holon was his first home — and was discovered playing at the Sormelo jazz club in Jerusalem by drummer Aharon "Arale" Kaminsky, who had been asked by singer Arik Einstein to put together a backing band. Kaminsky and Kunsman co-founded that band, Platina, in 1971; Einstein is credited with naming it. Kunsman became its musical director, writing nearly all of its original material and arrangements, alongside guitarist Yitzhak "Churchill" Klepter, keyboardist Alona Turel, keyboardist Nahum Perferkovich, and a rotating bass chair that later included Alon Oleartchik. Once Einstein moved on, the band pushed into original jazz-rock and fusion territory of its own, releasing Live at the "Bar Barim" (1973) and Freedom (1974) and backing Chava Alberstein on her 1974 album with the group. In 1974 Platina played Avery Fisher Hall in New York as part of the Newport Jazz Festival's New York edition — a booking real enough to be independently documented, though not the 1972 date sometimes given for it.

In 1976 Kunsman became religiously observant, and the change broke up the band; a final session of Debussy arrangements, The Girl with the Flaxen Hair, was recorded that year, shelved, and released only posthumously in 2003 after the surviving tapes turned up. Kunsman relocated to New York around 1978 and in August–September 1979 recorded a solo album, Heavy Skies, at Downtown Sound with producers George Avakian and Hank O'Neal, liner notes by Nat Hentoff, and a band including bassist Alex Blake and tabla player Badal Roy — it too went unreleased until 2003. He returned to Israel, and from the 1980s moved into klezmer and Hasidic music, recording and performing for years alongside clarinetist Moshe "Musa" Berlin as part of the group Sulam, often billed in this period as Rafael Kunsman. Platina itself reunited briefly in the mid-1990s for the live album Live '95.

He died on November 6, 2002, at his rented home on Moshav Beit Gamliel, where he had lived alone for a little over a year; Haaretz reported he was last seen walking home from a Talmud class that Saturday afternoon. In April 2025, three private citizens in St. Petersburg installed unofficial memorial plaques at his two former Leningrad addresses.

Kunsman's writing for Platina sits at the point where late-1960s Soviet big-band jazz meets the jazz-rock idiom that Israeli pop was absorbing in the early 1970s — tight horn-and-organ arrangements built for a working band rather than a solo showcase, with Kunsman's own alto and flute out front. Heavy Skies, cut in New York five years later with Badal Roy's tabla in the band, shows the more exploratory, fusion-facing side of his playing that Platina's pop-adjacent context didn't always have room for. His late-career turn to klezmer with Sulam is a real stylistic break, not a footnote — by his own account it followed directly from the 1976 religious change that ended Platina.