  Non-Markovian stochastic Schr\"odinger equations (NMSSE) are important tools
in quantum mechanics, from the theory of open systems to foundations. Yet, in
general, they are but formal objects: their solution can be computed
numerically only in some specific cases or perturbatively. This article is
focused on the NMSSE themselves rather than on the open-system evolution they
unravel and aims at making them less abstract. Namely, we propose to write the
stochastic realizations of linear NMSSE as averages over the solutions of an
auxiliary equation with an additional random field. Our method yields a
non-perturbative numerical simulation algorithm for generic linear NMSSE that
can be made arbitrarily accurate for reasonably short times. For isotropic
complex noises, the method extends from linear to non-linear NMSSE and allows
to sample the solutions of norm-preserving NMSSE directly.
