An exact formula has been presented to correlate the bending curvature variation ratio, Omega, of any given bilayer structure comprising a solvent-swellable polymer layer with diffusion time, t, under case II diffusion. The formula can be used to determine the diffusion front velocity, upsilon, for layered structures comprising a thick polymer film on a thin substrate or vice versa when subjected to solvent diffusion. According to this formula, there is little effect from plasticization or swelling in the transverse direction on the diffusion curve of Omega vs. t if the polymer layer to be investigated is relatively thin and its intrinsic hygroscopic strain ratio is less than unity. By using this model, the diffusion of N-methyl pyrollidinone (NMP) in a 18-mu m rodlike pyromellitic dianhydride p-phenylene-diamine (PMDA-PDA) polyimide film, coated on a 75-mu m silicon substrate, is found to be case II with a diffusion front velocity of 1.84 x 10(-7) cm/s.