With the rapid development in advanced bioimaging techniques, numerous image data has been generated for various high-throughput applications, which pose big challenges to efficient storage, transmission and sharing of these data. Traditional compression techniques and current deep learning-based compression methods lack the elimination of semantic redundancy on multidimensional biomedical data containing high dynamic range and complex structural features. Here, we propose compression with implicit function correlation (SWIFT) approach based on the first-proved high correlation of biomedical data in the implicit function domain. Through reducing the extra-compression of data correlation, SWIFT approach shows compression ratios and processing speed higher than existing implicit neural representation-based approaches. With further combination of residual entropy coding and attention mechanism, SWIFT achieves compression of various biological data with high time continuity and structure fidelity, for example, yielding 1500-fold, effective compression of live-cell 3D super-resolution data to enables downstream tasks and quantitative analyses at notably improved efficiency.