Distributionally robust memory evolution is a continual learning technique that dynamically modifies the data distribution within an experience replay buffer using distributionally robust optimization to prevent catastrophic forgetting. Rather than keeping stored memory samples static, which risks model overfitting and poorly captures the broader distribution of past data streams, this approach evolves the buffered samples toward a worst-case probability distribution. By optimizing the learning model against these progressively more challenging, evolved representations—often navigated through continuous measure-space dynamics such as Wasserstein gradient flows—the method narrows the gap between the memory buffer and previously observed data, discourages trivial memorization, and promotes the acquisition of robust, transferable features across continuous learning tasks.