Infants are sensitive to the distributional characteristics of the speech they hear, and perception can be altered by the distributional properties of language input. Infants listening to languages with distinct distributional properties show altered perception at the age of 6 months based on learning from ambient language input. Perception can also be altered in the laboratory by manipulating the distributional characteristics of speech in a 2-min exposure. However, the brain mechanisms underlying this learning are not well understood. Here we used MEG to explore the neural processes involved in on-line distributional learning. We examined brain responses to ambiguous speech sounds that straddle a /ba-wa/ speech continuum. Infants were tested longitudinally at 2 and 6 months of age not only to assess whether effects of experience can be documented between 2 and 6 months, but also to determine whether individual differences in brain response can predict future language growth. Our results show that differences in the magnitude of the brain response to ambiguous speech sounds in brain regions involved in auditory speech processing, motor planning, and attention change from 2- to 6-months-of- age. Moreover, we found that individual differences in these regions predict language growth up to 27 months of age.