The successful design of new biodegradable, renewable resource plastics as replacements to commodity barrier plastics would benefit from an accurate measurement of sorption and diffusion of liquids. In this study, the diffusion of liquid water in amorphous polylactide [PLA] and a PLA graft copolymer, poly(1,5-cyclooctadiene-co-5-norbornene-2-methanol-graft-dl-lactide) [PCNL], was examined with time-resolved Fourier transform infrared attenuated total reflectance (FTIR-ATR) spectroscopy. Non-Fickian behavior was observed for all experiments, indicated by a slow approach to steady state due to diffusion and polymer relaxation occurring on similar time scales. This non-Fickian behavior highlights the variability of the sorption isotherms reported in the literature, where others have collected nonequilibrium sorption behavior (instead of true steady-state equilibrium sorption) at different time points and film thicknesses. The dynamic infrared data provided direct evidence for both water diffusion and water-induced polymer relaxation, where both were quantified and regressed to a diffusion-relaxation model to determine the diffusion coefficient and the polymer relaxation time constant. In addition to the successful measurement and modeling of the diffusion-relaxation phenomena for diffusion of a liquid in a nonequilibrium state glassy polymer, this study also determined that the diffusivity of water in the PLA graft copolymer (with only 5 wt % rubber) was 3-fold lower than in the PLA homopolymer.