<p>Visible-Infrared Person Re-Identification (VIReID) is an identity retrieval task between visible and infrared modalities. Existing research aims to capture shared semantic features, which can retrieve the same identity under different modalities. Although the previous methods have achieved excellent performance, they still face critical limitations: (1) Coupled Noisy Problem: Due to the complexity of cross-modality annotation and the variability in crowdsourced labeling reliability, the presence of coupled noisy labels resulting from mismatched visible-infrared pairs is unavoidable. (2) Lack of historical relevance: Current approaches to noisy label learning predominantly focus on identifying potentially noisy samples based on features from the current training step, overlooking the rich semantic information in earlier training stages. These two limitations restrict the adaptability of such methods to scenarios with coupled noisy samples. We propose a Cross-Modality Geometry-Guided Historical Momentum Learning to address these issues. Firstly, we employ a Geometry-Guided Noisy Correspondence Detector to estimate confidence weights from each sample pair. Secondly, we design a historical momentum triplet loss function, which leverages features of early training steps to capture the training trajectory, addressing the historical smoothing issue in the training process. Finally, we utilize these high-confidence samples to learn the discriminative features through an iterative framework. Extensive experiments on the SYSU-MM01 and RegDB datasets demonstrate the effectiveness of our method against the state-of-the-art VIReID methods.</p>