Abstract
In this article, we prove that the quantum f-divergence between two normal states on a semifinite von~Neumann algebra is equal to the classical f-divergence between two corresponding classical states, which are called Nussbaum-Szko{\l}a distributions. This result has been proved by the second named author and T.C.~John for normal states on the von~Neumann algebra B(H) of all bounded operators on a Hilbert space H. We extend their result for normal states on any semifinite von~Neumann algebra, not only B(H).