  We consider the Cauchy problem for the defocusing stochastic nonlinear
Schr\"odinger equations (SNLS) with an additive noise in the mass-critical and
energy-critical settings. By adapting the probabilistic perturbation argument
employed in the context of the random data Cauchy theory by the first author
with B\'enyi and Pocovnicu (2015) to the current stochastic PDE setting, we
present a concise argument to establish global well-posedness of the
mass-critical and energy-critical SNLS.
