Prolonged exposure to a moving stimulus can substantially alter the perceived velocity (both speed and direction) of subsequently presented stimuli. Here, we show that these changes can be parsimoniously explained with a model that combines the effects of two isomorphic mechanisms, one non-directional and one directional. Each produces a pattern of velocity biases that serves as an observable "signature" of the corresponding mechanism. The net effect on perceived velocity is a superposition of these two signatures. By examining human velocity judgments in the context of different adaptor velocities, we are able to separate these two signatures. The model fits the data well, successfully predicts subjects' behavior in an additional experiment using a non-directional adaptor, and is in agreement with a variety of previous experimental results. As such, the model provides a unifying explanation for the diversity of motion aftereffects.