The production of behavioral diversity – producing a diversity of effects – is an essential strategy for robots exploring the world when facing situations where interaction possibilities are unknown or non-obvious. It allows to discover new aspects of the environment that cannot be inferred or deduced from available knowledge. However, creating behavioral diversity in situations where it is most crucial – new and unknown ones – is far from trivial. In particular in large and redundant sensorimotor spaces, only small areas are interesting to explore for any practical purpose. When the environment does not provide clues or gradient toward those areas, trying to discover those areas relies on chance. To address this problem, we introduce a method to create behavioral diversity in a new sensorimotor task by re-enacting actions that allowed to produce behavioral diversity in a previous task, along with a measure that quantifies this diversity. We show that our method can learn how to interact with an object by reusing experience from another, that it adapts to instances of morphological changes and of dissimilarity between tasks, and how scaffolding behaviors can emerge by simply switching the attention of the robot to different parts of the environment. Finally, we show that the method can robustly use simulated experiences and crude cognitive models to generate behavioral diversity in real robots.