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Noisy labels collected with limited annotation cost prevent medical image segmentation algorithms from learning precise semantic correlations. Previous segmentation arts of learning with noisy labels merely perform a pixel-wise manner to preserve semantics, such as pixel-wise label correction, but neglect the pair-wise manner. In fact, we observe that the pair-wise manner capturing affinity relations between pixels can greatly reduce the label noise rate. Motivated by this observation, we present a novel perspective for noisy mitigation by incorporating both pixel-wise and pair-wise manners, where supervisions are derived from noisy class and affinity labels, respectively. Unifying the pixel-wise and pair-wise manners, we propose a robust Joint Class-Affinity Segmentation (JCAS) framework to combat label noise issues in medical image segmentation. Considering the affinity in pair-wise manner incorporates contextual dependencies, a differentiated affinity reasoning (DAR) module is devised to rectify the pixel-wise segmentation prediction by reasoning about intra-class and inter-class affinity relations. To further enhance the noise resistance, a class-affinity loss correction (CALC) strategy is designed to correct supervision signals via the modeled noise label distributions in class and affinity labels. Meanwhile, CALC strategy interacts the pixel-wise and pair-wise manners through the theoretically derived consistency regularization. Extensive experiments under both synthetic and real-world noisy labels corroborate the efficacy of the proposed JCAS framework with a minimum gap towards the upper bound performance. The source code is available at \url{https://github.com/CityU-AIM-Group/JCAS}.