Diffusion-based models, such as the Stable Diffusion model, have revolutionized text-to-image synthesis with their ability to produce high-quality, high-resolution images. These advancements have prompted significant progress in image generation and editing tasks. However, these models also raise concerns due to their tendency to memorize and potentially replicate exact training samples, posing privacy risks and enabling adversarial attacks. Duplication in training datasets is recognized as a major factor contributing to memorization, and various forms of memorization have been studied so far. This paper focuses on two distinct and underexplored types of duplication that lead to replication during inference in diffusion-based models, particularly in the Stable Diffusion model. We delve into these lesser-studied duplication phenomena and their implications through two case studies, aiming to contribute to the safer and more responsible use of generative models in various applications.