We compare the classic Ward-Tordai and the microscopic Smoluchowski models for the dynamics of surfactant transport through fluid/fluid interfaces. The Smoluchowski model treats the interface as a free-energy field, whereas the Ward-Tordai model treats the interface as an infinitesimally thin plane exhibiting adsorption and desorption kinetics. Equivalence of the two models is established when the free-energy well underlying surfactant adsorption is flanked by barriers that are larger than thermal energy. When energy barriers are non-existent, however, a finite interfacial width must be introduced into the Ward-Tordai analysis to obtain physically meaningful results, i.e. non-negative desorption rate constants. Recenty, we presented an experimental investigation into the adsorption dynamics of diblock copolymers to a polymer/polymer interface and found them to be well described by the Smoluchowski model. Here, we show that the experimental sorption dynamics are also captured by a finite-interfacial-width extension of the Ward-Tordai model, whereas the classical model fails to predict the observed behavior.