  We present embedding procedures for the non-Markovian stochastic
Schr\"{o}dinger equations, arising from studies of quantum systems coupled with
bath environments. By introducing auxiliary wave functions, it is demonstrated
that the non-Markovian dynamics can be embedded in extended, but Markovian,
stochastic models. Two embedding procedures are presented. The first method
leads to nonlinear stochastic equations, the implementation of which is much
more efficient than the non-Markovian stochastic Schr\"{o}dinger equations.
  The stochastic Schr\"{o}dinger equations obtained from the second procedure
involve more auxiliary wave functions, but the equations are linear, and we
derive the corresponding generalized quantum master equation for the
density-matrix. The accuracy of the embedded models is ensured by fitting to
the power spectrum. The stochastic force is represented using a linear
superposition of Ornstein-Uhlenbeck processes, which are incorporated as
multiplicative noise in the auxiliary Schr\"{o}dinger equations. The asymptotic
behavior of the spectral density in the low frequency regime is preserved by
using correlated stochastic processes.
  The approximations are verified by using a spin-boson system as a test
example.
