<p>Single-cell assay for transposase-accessible chromatin using sequencing (scATAC-seq) deciphers genome-wide chromatin accessibility, providing profound insights into gene regulation mechanisms. With the rapid advance of sequencing technologies, scATAC-seq data typically encompass numerous samples from various conditions, resulting in complex batch effects, thus necessitating reliable integration tools. While numerous batch integration tools exist for single-cell RNA sequencing data, inherent data characteristic differences limit their effectiveness on scATAC-seq data. Existing integration methods for scATAC-seq data suffer from several fundamental limitations, such as disrupting the biological heterogeneity and focusing solely on low-dimensional correction, which may distort data and hinder downstream analysis. Here we propose Fountain, a deep learning framework for scATAC-seq data integration via rigorous barycentric mapping. Barycentric mapping transforms one data distribution to another in a principled and effective manner through optimal transport. By regularizing barycentric mapping with geometric data information, Fountain achieves accurate batch alignment while preserving biological heterogeneity. Comprehensive experiments across diverse real-world datasets demonstrate the advantages of Fountain over existing methods in batch correction and biological conservation. In addition, the trained Fountain model can integrate data from new batches alongside already integrated data without retraining, enabling continuous online data integration. Moreover, Fountain’s reconstruction strategy generates batch-corrected ATAC profiles, improving the capture of cellular heterogeneity and revealing cell-type-specific implications such as expression enrichment analysis and partitioned heritability analysis.</p>