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A stochastic model for migration dynamics of solute molecules from the bulk aqueous phase to the intravesicular water pool is developed with a goal to interpret recent passive permeability measurements of bilayer membranes. Previously neglected fluctuations of the number of solubilized species in the inner water pool of a vesicle are naturally incorporated into the model and each event of the bilayer crossing is taken into account. For a homogeneous one-phase bilayer, the model predicts exponential long-time asymptotics of the migration dynamics with a rate constant given by a sum of the frequencies of exit and entry of a solute molecule from/into the intravesicular water pool into/from the bulk aqueous phase. The long-time constant is directly related to the membrane permeability.