Infinite rhymes with:
definite, indefinite, affectionate, baronet, bicarbonate, cabinet, compassionate, coordinate, definite, diaconate, dispassionate, extortionate, fortunate, geminate, indefinite, indiscriminate, innominate, laminate, nominate, nondiscriminate, obstinate, passionate, proportionate, sultanate, unfortunate
Infinite sounds like:
impend, impound, impounded, impunity, inabinet, inbound, infant, infante, infiniti, infinity, invent, invented