Distillation-based self-supervised learning typically leads to more compressed representations due to its radical clustering process and the implementation of a sharper target distribution. To overcome this limitation and preserve more information from the input, we introduce UDI, conceptualized as Unsqueezed DIstillation-based self-supervised learning (SSL). UDI enriches the learned representation by encouraging multi-modal prediction distilled from a consolidated profile of local predictions that are derived via stratified sampling. Our evaluations show that UDI not only promotes semantically meaningful representations at instance level, delivering superior or competitive results to state-of-the-art SSL methods in image classification, but also effectively preserves the nuisance of input, which yields significant improvement in dense prediction tasks, including object detection and segmentation. Additionally, UDI performs competitively in low-shot image classification, improving the scalability of joint-embedding pipelines. Various visualizations and ablation studies are presented to further elucidate the mechanisms behind UDI.