Unsupervised visible-infrared person re-identification (UVI-ReID) has recently gained great attention due to its potential for enhancing human detection in diverse environments without labeling. Previous methods utilize intra-modality clustering and cross-modality feature matching to achieve UVI-ReID. However, there exist two challenges: 1) noisy pseudo labels might be generated in the clustering process, and 2) the cross-modality feature alignment via matching the marginal distribution of visible and infrared modalities may misalign the different identities from two modalities. In this paper, we first conduct a theoretic analysis where an interpretable generalization upper bound is introduced. Based on the analysis, we then propose a novel unsupervised cross-modality person re-identification framework (PRAISE). Specifically, to address the first challenge, we propose a pseudo-label correction strategy that utilizes a Beta Mixture Model to predict the probability of mis-clustering based network's memory effect and rectifies the correspondence by adding a perceptual term to contrastive learning. Next, we introduce a modality-level alignment strategy that generates paired visible-infrared latent features and reduces the modality gap by aligning the labeling function of visible and infrared features to learn identity discriminative and modality-invariant features. Experimental results on two benchmark datasets demonstrate that our method achieves state-of-the-art performance than the unsupervised visible-ReID methods.