Extensive training on simple tasks such as fine orientation discrimination results in large improvements in performance, a form of learning known as perceptual learning. Previous models have argued that perceptual learning is due to either sharpening and amplification of tuning curves in early visual areas or to improved probabilistic inference in later visual areas (at the decision stage). However, early theories are inconsistent with the conclusions of psychophysical experiments manipulating external noise, whereas late theories cannot explain the changes in neural responses that have been reported in cortical areas V1 and V4. Here we show that we can capture both the neurophysiological and behavioral aspects of perceptual learning by altering only the feedforward connectivity in a recurrent network of spiking neurons so as to improve probabilistic inference in early visual areas. The resulting network shows modest changes in tuning curves, in line with neurophysiological reports, along with a marked reduction in the amplitude of pairwise noise correlations.