Cumulative culture requires efficient learning mechanisms that can withstand environmental change across generations. We unify two competing theories of the learning mechanism supporting cumulative culture in a common computational framework, distinguishing model-based from model-free social learning. We describe and analyze evolutionary models that explain when and why model-based and model-free social learning are each optimal, and in particular how environmental volatility determines which strategy succeeds. Strikingly, we find that model-based social learning can succeed even in high-volatility environments. These results yield novel predictions concerning cultural variation in social learning mechanisms