Generating and navigating single cell dynamics via a geodesic bridge between nonlinear transcriptional and linear latent manifolds

Time-series single-cell RNA sequencing (scRNA-seq) captures cellular processes as sparse and unpaired snapshots, limiting our ability not only to reconstruct continuous cell state transitions, but also to navigate between states in a controlled and interpretable manner. Here we present GeoBridge, a framework modeling cellular dynamics as geodesic trajectories on the transcriptional manifold based on isometric geodesic theory. By learning the geodesic bridge mapping, the method theoretically and computationally transforms time-varying nonlinear transcriptional geodesics (original nonlinear manifold) into constant-velocity straight-line geodesics (latent linear manifold). In the learned geodesic space, continuous interpolation becomes biologically meaningful, enabling reconstruction of unobserved intermediate states and efficient navigation between distinct cellular phenotypes at a single-cell resolution. By mapping interpolated trajectories back to the original gene expression space, GeoBridge recovers smooth transcriptional programs that are robust to noise and snapshot sparsity. Leveraging the derived geodesic potentials, GeoBridge further infers pseudo-temporal trajectories with superior fidelity compared to mainstream approaches from single-snapshot scRNA-seq data without temporal annotation, and directly identifies genes that drive progression along transition paths. We demonstrate the utility of GeoBridge across diverse systems, where GeoBridge resolves EMT-MET progression in cancer stem cells and identifies stage-specific modules as well as the branching cell-fate dynamics in human pluripotent stem cells with higher reconstruction accuracy than state-of-art methods. More importantly, GeoBridge supports single-cell fate navigation in multi-target hematopoietic lineages, allowing neutrophil-biased cells to be virtually guided toward mast-cell fates along biologically plausible paths. Together, GeoBridge establishes a principled method that transforms sparse single-cell measurements into a continuous, controllable landscape for the reconstruction, navigation and manipulation of cellular state transitions.