Existing cell instance segmentation pipelines typically combine deterministic predictions with post-processing, which imposes limited explicit constraints on the global structure of instance masks. In this work, we propose a multi-task image-to-image Schr\"odinger Bridge framework that formulates instance segmentation as a distribution-based image-to-image generation problem. Boundary-aware supervision is integrated through a reverse distance map, and deterministic inference is employed to produce stable predictions. Experimental results on the PanNuke dataset demonstrate that the proposed method achieves competitive or superior performance without relying on SAM pre-training or additional post-processing. Additional results on the MoNuSeg dataset show robustness under limited training data. These findings indicate that Schr\"odinger Bridge-based image-to-image generation provides an effective framework for cell instance segmentation.