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Transitions between different inflationary slow-roll scenarios are known to provide short non-slow-roll periods with non-trivial consequences. We consider the effect of quantum diffusion on the inflationary dynamics in a transition process. Using the stochastic δN formalism, we follow the detailed evolution of noises through a sharp transition modeled by the Starobinsky potential, although some of our results apply to any sharp transition. We find how the stochastic noise induced by the transition affects the coarse-grained fields. We then consider the special case that the potential is flat after the transition. It is found that the particular noise we obtain cannot drive the inflaton past the classically unreachable field values. By deriving the characteristic function, we also study the tail behavior for the distribution of curvature perturbations ζ, which we find to decay faster than e^(-3ζ).