  Among quantum Langevin equations describing the unitary time evolution of a
quantum system in contact with a quantum bath, we completely characterize those
equations which are actually driven by classical noises. The characterization
is purely algebraic, in terms of the coefficients of the equation. In a second
part, we consider general quantum Langevin equations and we prove that they can
always be split into a maximal part driven by classical noises and a purely
quantum one.
