Recently, One-stage Weakly Supervised Semantic Segmentation (WSSS) with image-level labels has gained increasing interest due to simplification over its cumbersome multi-stage counterpart. Limited by the inherent ambiguity of Class Activation Map (CAM), we observe that one-stage pipelines often encounter confirmation bias caused by incorrect CAM pseudo-labels, impairing their final segmentation performance. Although recent works discard many unreliable pseudo-labels to implicitly alleviate this issue, they fail to exploit sufficient supervision for their models. To this end, we propose a dual student framework with trustworthy progressive learning (DuPL). Specifically, we propose a dual student network with a discrepancy loss to yield diverse CAMs for each sub-net. The two sub-nets generate supervision for each other, mitigating the confirmation bias caused by learning their own incorrect pseudo-labels. In this process, we progressively introduce more trustworthy pseudo-labels to be involved in the supervision through dynamic threshold adjustment with an adaptive noise filtering strategy. Moreover, we believe that every pixel, even discarded from supervision due to its unreliability, is important for WSSS. Thus, we develop consistency regularization on these discarded regions, providing supervision of every pixel. Experiment results demonstrate the superiority of the proposed DuPL over the recent state-of-the-art alternatives on PASCAL VOC 2012 and MS COCO datasets.