  We show that any free product of finite-dimensional von Neumann algebras
equipped with non-tracial states is isomorphic to a free Araki-Woods factor
with its free quasi-free state possibly direct sum a finite-dimensional von
Neumann algebra. This gives a complete answer to questions posed by Dykema and
Shlyakhtenko, which had been partially answered by work of Houdayer and work of
Ueda. We also extend this to suitable infinite-dimensional von Neumann algebras
with almost periodic states.
