Learning new information without forgetting prior knowledge is central to human intelligence. In contrast, neural network models suffer from catastrophic forgetting: a significant degradation in performance on previously learned tasks when acquiring new information. The Complementary Learning Systems (CLS) theory offers an explanation for this human ability, proposing that the brain has distinct systems for pattern separation (encoding distinct memories) and pattern completion (retrieving complete memories from partial cues). To capture these complementary functions, we leverage the representational generalization capabilities of variational autoencoders (VAEs) and the robust memory storage properties of Modern Hopfield networks (MHNs), combining them into a neurally plausible continual learning model. We evaluate this model on the Split-MNIST task, a popular continual learning benchmark, and achieve close to state-of-the-art accuracy ~90%, substantially reducing forgetting. Representational analyses empirically confirm the functional dissociation: the VAE underwrites pattern completion, while the MHN drives pattern separation. By capturing pattern separation and completion in scalable architectures, our work provides a functional template for modeling memory consolidation, generalization, and continual learning in both biological and artificial systems.