Accurate segmentation of medical images is challenging due to unclear lesion boundaries and mask variability. We introduce \emph{Segmentation Schödinger Bridge (SSB)}, the first application of Schödinger Bridge for ambiguous medical image segmentation, modelling joint image-mask dynamics to enhance performance. SSB preserves structural integrity, delineates unclear boundaries without additional guidance, and maintains diversity using a novel loss function. We further propose the \emph{Diversity Divergence Index} ($D_{DDI}$) to quantify inter-rater variability, capturing both diversity and consensus. SSB achieves state-of-the-art performance on LIDC-IDRI, COCA, and RACER (in-house) datasets.