ABSTRACT Circadian rhythms are remarkably widespread across most organisms, regulating hormonal, metabolic, physiological, and behavioral oscillations through molecular clocks that orchestrate the rhythmic expression of thousands of genes. Here, we generate single-nucleus RNA and ATAC multiomics data to simultaneously characterize gene expression and chromatin accessibility of mouse liver cells across the 24-hour day. We interrogate multimodal circadian rhythmicity in both discretized cell types and transient sub-lobule cell states, capturing space-time omics profiles. We delve beyond mean cyclic patterns to characterize stochastic transcriptional bursting and infer spatiotemporal gene regulatory networks that control circadian rhythmicity and liver physiology. Our findings apply to existing single-cell data of mouse and Drosophila brains and are validated by time-series single-molecule fluorescence in situ hybridization and vast amounts of orthogonal omics data. Altogether, our study constructs a comprehensive map of the time-series transcriptomic and epigenomic landscapes that elucidate the function and mechanism of the liver peripheral clocks.