<p>The early detection and treatment of colorectal cancer depend on accurate polyp identification. However, fully-supervised segmentation methods are limited in clinical practice by the cost of pixel-level annotations. Therefore, we propose BoxSupSeg, a box-supervised polyp segmentation model via multi-loss synergistic optimization. To mitigate morphological bias, insufficient multi-scale sensitivity, and misalignment of geometric constraints inherent in box-supervision, we construct a quadruple loss synergistic optimization framework. First, the consistent prediction loss reduces discrepancies caused by data augmentation and multi-scale inputs. Second, the fore/background edge contrast loss enhances class discrimination by measuring similarity between pixel embeddings. Third, the dual-projection structure alignment loss uses horizontal and vertical projection constraints to correct geometric deviations in rough boxes. Finally, the neighborhood consistency loss ensures connectivity within segmented regions. Experimental results on five public polyp datasets show that BoxSupSeg achieves comparable accuracy with fully-supervised methods only relying on box-supervision.</p>