  We derive an adiabatic theory for a stochastic differential equation, $
\varepsilon\, \mathrm{d} X(s) = L_1(s) X(s)\, \mathrm{d} s + \sqrt{\varepsilon}
L_2(s) X(s) \, \mathrm{d} B_s, $ under a condition that instantaneous
stationary states of $L_1(s)$ are also stationary states of $L_2(s)$. We use
our results to derive the full statistics of tunneling for a driven stochastic
Schr\"{o}dinger equation describing a dephasing process.
