Although visual statistical learning (VSL) has been established as a method for testing implicit knowledge gained through observation, little is known about the mechanisms underlying this type of learning. We examined the role of sleep in stabilization and consolidation of learning in a typical VSL task, where subjects observed scenes composed of simple shape combinations according to specific rules, and then demonstrated their gained familiarity of the underlying statistical regularities. We asked 1) whether there would be interference between learning regularities in multiple VSL tasks within close spatial and temporal proximity even if the shapes used in the tasks were different, and 2) whether sleep between interfering conditions could stabilize and consolidate the learning rules, improving performance. Subjects completed four separate VSL learning blocks, each containing scenes composed of different shapes: Learning A and B were presented sequentially, Learning B and C were separated temporally by two hours, and Learning C and D were separated by a period of similar length in which subjects either took a nap which included or excluded REM sleep, or remained awake, either quietly or actively. Familiarity tests with the four structures were conducted following Learning D. If sleep blocks interference, we would expect to see interference between Learning A and B, and not between Learning C and D. If sleep increases learning, performance would be best on the test of Learning D. We found indications of interference between Learning A and B, but only in the non-REM nap group. Also, a significantly improved performance on the Learning D familiarity test was found, but only in the REM nap group. Thus, knowledge gained by VSL does interfere despite segregation in shape identity across tasks, a period of stabilization can eliminate this effect, and REM sleep enhances acquisition of new learning.