Continual learning -- the ability to acquire knowledge incrementally without forgetting previous skills -- is fundamental to natural intelligence. While the human brain excels at this, artificial neural networks struggle with "catastrophic forgetting," where learning new tasks erases previously acquired knowledge. This challenge is particularly severe for text-to-image diffusion models, which generate images from textual prompts. Additionally, these models face "mode collapse," where their outputs become increasingly repetitive over time. To address these challenges, we apply Latent Replay, a neuroscience-inspired approach, to diffusion models. Traditional replay methods mitigate forgetting by storing and revisiting past examples, typically requiring large collections of images. Latent Replay instead retains only compact, high-level feature representations extracted from the model's internal architecture. This mirrors the hippocampal process of storing neural activity patterns rather than raw sensory inputs, reducing memory usage while preserving critical information. Through experiments with five sequentially learned visual concepts, we demonstrate that Latent Replay significantly outperforms existing methods in maintaining model versatility. After learning all concepts, our approach retained 77.59% Image Alignment (IA) on the earliest concept, 14% higher than baseline methods, while maintaining diverse outputs. Surprisingly, random selection of stored latent examples outperforms similarity-based strategies. Our findings suggest that Latent Replay enables efficient continual learning for generative AI models, paving the way for personalized text-to-image models that evolve with user needs without excessive computational costs.