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Advances in next-generation sequencing technologies have vastly expanded the availability of diverse genomic, epigenomic and transcriptomic data, presenting the opportunity to develop a general AI model that integrates comprehensive genomic knowledge into a unified model. Unlike previous predictive models, which are typically specialized to certain tasks, our general AI model unifies a wide range of genomic modalities, such as nascent RNA and ultra-high-resolution chromatin organization, within a multi-task architecture. Using ATAC-seq and DNA sequences as inputs, we incorporated diverse genomic modalities as output, and the model exhibits strong generalizability across different cell types and tissues in all tasks we trained. It accurately predicts gene-level transcription measured by various nascent RNA assays, and effectively captures enhancer-associated transcription. Additionally, it also accurately captures the potential functions of non-coding genetic variants and regulatory elements. Additionally, we extended the model trained on human data to a mouse general model, achieving accurate predictions of genomic modalities, such as high resolution chromatin contact maps with limited data availability, which are further validated using an established mouse inner-ear study. This comprehensive approach offers a powerful tool for understanding genome regulation in both human and mouse species.