Chest X-ray imaging is essential for diagnosing thoracic diseases, with multi-label classification playing a critical role in identifying multiple conditions from a single image. Despite deep neural networks significantly advancing this field, noisy labels extracted from clinical reports pose a significant challenge, undermining the performance of deep models. Several research attempts have been made to address this issue but fail to consider the critical inter-class correlations prevalent in chest X-ray diagnostics. To this end, we propose a Global and Local Noise Correction framework. Our framework comprises a classification backbone and two primary components: a global noise correction module and a local noise correction module. The global noise correction module calculates the noise transition matrix based on the label co-occurrence frequencies and uses the estimated noise transition matrix to reduce the impact of the noisy labels. The local noise correction module treats the temporal ensembling of samples’ historical predictions as the instance-specific pseudo labels, which also serve as the supervision. The proposed framework addresses the shortcomings of existing techniques, i.e., the unreliability of noise transition matrices in the presence of class imbalances and zero co-occurrence frequencies. Comprehensive experimental results demonstrate that our framework surpasses competing methods, showcasing its superior ability to combat label noise and improve multi-label chest X-ray classification accuracy.