Perceiving and identifying an object is improved by prior exposure to the object. This perceptual priming phenomenon is accompanied by reduced neural activity. But whether suppression of neuronal activity with priming is responsible for the improvement in perception is unclear. To address this problem, we developed a rate-based network model of visual processing. In the model, decreased neural activity following priming was due to stimulus-specific sharpening of representations taking place in the early visual areas. Representation sharpening led to decreased interference of representations in higher visual areas that facilitated selection of one of the competing representations, thereby improving recognition. The model explained a wide range of psychophysical and physiological data observed in priming experiments, including antipriming phenomena, and predicted two functionally distinct stages of visual processing.