The key of visible-infrared person re-identification (VIReID) lies in how to minimize the modality discrepancy between visible and infrared images. Existing methods mainly exploit the spatial information while ignoring the discriminative frequency information. To address this issue, this paper aims to reduce the modality discrepancy from the frequency domain perspective. Specifically, we propose a novel Frequency Domain Nuances Mining (FDNM) method to explore the cross-modality frequency domain information, which mainly includes an amplitude guided phase (AGP) module and an amplitude nuances mining (ANM) module. These two modules are mutually beneficial to jointly explore frequency domain visible-infrared nuances, thereby effectively reducing the modality discrepancy in the frequency domain. Besides, we propose a center-guided nuances mining loss to encourage the ANM module to preserve discriminative identity information while discovering diverse cross-modality nuances. Extensive experiments show that the proposed FDNM has significant advantages in improving the performance of VIReID. Specifically, our method outperforms the second-best method by 5.2\% in Rank-1 accuracy and 5.8\% in mAP on the SYSU-MM01 dataset under the indoor search mode, respectively. Besides, we also validate the effectiveness and generalization of our method on the challenging visible-infrared face recognition task. \textcolor{magenta}{The code will be available.}

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