Adaptation is the holy grail of intelligence, but even the best AI models lack the adaptability of toddlers. In spite of great progress, little is known about the mechanisms by which machines can learn to adapt as fast as humans and animals. Here, we cast adaptation as `correction' of old posteriors and show that a wide-variety of existing adaptation methods follow this very principle, including those used for continual learning, federated learning, unlearning, and model merging. In all these settings, more accurate posteriors often lead to smaller corrections and can enable faster adaptation. Posterior correction is derived by using the dual representation of the Bayesian Learning Rule of Khan and Rue (2023), where the interference between the old representation and new information is quantified by using the natural-gradient mismatch. We present many examples demonstrating how machines can learn to adapt quickly by using posterior correction.