  We demonstrate a close connection between the decoherent histories (DH)
approach to quantum mechanics and the quantum state diffusion (QSD) picture,
for open quantum systems described by a master equation of Lindblad form. The
(physically unique) set of variables that localize in the QSD picture also
define an approximately decoherent set of histories in the DH approach. The
degree of localization is related to the degree of decoherence, and the
probabilities for histories prescribed by each approach are essentially the
same.
