There is a paradoxical dissociation between recognizing that two stimuli are different and recognizing how they are different. We show that this dissociation can be captured by modeling perceptual similarity as a species of analogical processes. Using SME to model comparison, we show that the dissociation arises naturally from different stages in the analogical mapping process. Rather than relying on hand-coded input representations, our model uses an automatic, incremental encoding process to generate representations from the same stimuli as given to human participants.