Continual learning (CL) focuses on learning non-stationary data distribution without forgetting previous knowledge. The most widely used memory-replay approaches are often prone to memory overfitting due to the limited memory diversity and hardness. Existing work mitigating memory overfitting either lacks data diversity or hardness or is hard to train. To address the above limitations and release the memory buffer potential, we view the memory buffer transformation from a new dynamic system perspective and propose a continuous and reversible memory transformation method. We introduce an adversarial optimization objective that jointly learns the CL model and memory transformer. Specifically, we present a deterministic continuous memory transformer (DCMT) to generate diverse memory data. Furthermore, we inject uncertainty into the transformation function and develop a stochastic continuous memory transformer (SCMT), which substantially enhances the diversity of the transformed memory buffer. The presented neural transformation approaches have significant advantages over existing ones: (1) they significantly increase the memory buffer diversity and hardness to overfit; (2) they are memory efficient without needing to make a replica of the memory data. Extensive experiments show a significant improvement with our approach compared to strong baselines.