Current weakly-supervised semantic segmentation (WSSS) techniques concentrate on enhancing class activation maps (CAMs) with image-level annotations. Yet, the emphasis on producing these pseudo-labels often overshadows the pivotal role of training the segmentation model itself. This paper underscores the significant influence of noisy pseudo-labels on segmentation network performance, particularly in boundary region. To address above issues, we introduce a novel paradigm: Weak to Partial Supervision (W2P). At its core, W2P categorizes the pseudo-labels from WSSS into two unique supervisions: trustworthy clean labels and uncertain noisy labels. Next, our proposed partially-supervised framework adeptly employs these clean labels to rectify the noisy ones, thereby promoting the continuous enhancement of the segmentation model. To further optimize boundary segmentation, we incorporate a noise detection mechanism that specifically preserves boundary regions while eliminating noise. During the noise refinement phase, we adopt a boundary-conscious noise correction technique to extract comprehensive boundaries from noisy areas. Furthermore, we devise a boundary generation approach that assists in predicting intricate boundary zones. Evaluations on the PASCAL VOC 2012 and MS COCO 2014 datasets confirm our method's impressive segmentation capabilities across various pseudo-labels.