To obtain the solute transport rate, we develop a Langevin equation for the solute transport. It is frequently assumed that the fluctuations of the thermal random force are adequately described by the white noise, i.e. that the correlation time of the random force is much smaller than the characteristic time of the solute transport. We demonstrate that although this assumption is correct when the solute is located sufficiently far from the interface, the correlation time of the random force becomes significant within a very narrow (less than 1 nm wide) region of the interface. We demonstrate that the slow fluctuations of the random force in this narrow region are caused by fluctuations of the interface. Unlike the random collisions of the solute with the solvent molecules in homogeneous fluids, the interface fluctuations change the composition of the solvation shell of the solute. We propose a multi-dimensional Langevin equation which explicitly accounts for the solute interface coupling and validate it for surfactant-free and surfactant-covered interfaces. The strength of the solute-interface coupling is determined by the magnitude of the protrusions of the interface formed when solute is constrained in the vicinity of the interface. Similar phenomena is expected to occur in other interfacial systems such as lipid bilayers.