  We prove a Wong-Zakai theorem for the defocusing mass-critical stochastic
nonlinear Schr\"odinger equation (NLS) on $\mathbb{R}$. The main ingredient are
careful mixtures of bootstrapping arguments at both deterministic and
stochastic levels. Several subtleties arising from the proof mark the
difference between the dispersive case and corresponding situations in SDEs and
parabolic stochastic PDEs, as well as the difference between the large-$n$ case
and the limiting ($n=\infty$) case.
