Training subjects to discriminate fine details of stimuli can improve perceptual capabilities, a phenomenon known as perceptual learning (PL). Experiments have discovered intriguing psychophysical findings despite the simple stimuli (e.g., Gabor patches) and training procedures (e.g., 2AFC task) involved. Finding explanations for these learning effects could shed light on sensory plasticity in adulthood and constraints in sensory processing. A profound feature of (visual) PL is its slow learning speed, which can take days of training and hundreds or thousands of trials for the performance to saturate. This is sometimes attributed to the low signal-to-noise ratio in the sensory activities, which poses a challenging classification problem for decision neurons that readout these activities. How could the decision neurons learn when the signal is so weak? We hypothesize that, rather than relying on the short-lived activities at each trial, the brain may learn according to the distribution of sensory activities summarized by sensory neurons over multiple stimulus presentations. In such a noisy condition, we also assume that the decision neurons combine sensory signals using uncertain readout weights modeled as probabilistic (Bayesian) synapses (e.g. with a mean and sd). During PL, the weights are updated by averaging over the stimulus distribution of the presented category; during perception, the decision neuron acts according to the probability of the perceived category computed by a sample of the posterior weights. This model can explain several behavioral results obtained by Dosher and Lu (1998, 2005). We show that the model replicates the uniform downward shift of threshold-versus-noise contrast (TVC) curves, the power-law decrease of the signal threshold with training, and the asymmetric transfer between noisy and clean displays. This theory thus offers an alternative to the Hebbian reweighting model (Dosher and Lu, 2010) and connects the theoretical literature of probabilistic synapses to visual perceptual learning.