TempoBridge: Source-Conditioned Flow Matching with Optimal Transport Couplings for Single-Cell Population Transitions

Single-cell RNA sequencing (scRNA-seq) provides high-dimensional profiles of cellular states, enabling data-driven modeling of cellular dynamics over time. In practice, time-resolved scRNA-seq is collected at only a few discrete time points as unpaired snapshot populations, leaving substantial temporal gaps. This motivates trajectory inference at unmeasured time points. Existing methods mainly follow two directions, optimal-transport (OT) alignment provides distribution-level matching between observed snapshots, while continuous-time generative models support forecasting via learned dynamics. However, two challenges remain: (i) unpaired snapshots render local transitions between adjacent time points ambiguous, leading to unstable supervision; and (ii) long-horizon prediction relies on repeated integration, where small modeling errors compound and cause distribution drift. To address these challenges, we propose single-cell Flow Matching (scFM), a latent generative framework based on coupling-conditioned flow matching. First, we compute entropically regularized OT couplings between adjacent snapshots and use them to construct soft, weighted flow-matching targets for learning time-dependent velocity fields. Second, we learn bidirectional velocity fields and leverage their consistency to refine couplings and improve temporal coherence under sparse supervision. Third, we introduce distribution-level alignment and latent dynamic regularization to anchor long rollouts and mitigate drift. Experiments on real-world time-series scRNA-seq datasets show that scFM consistently improves distributional prediction performance for both temporal interpolation and extrapolation. Moreover, scFM yields more accurate trajectory reconstruction and temporally coherent visualizations where intermediate time points are absent, indicating a more faithful recovery of underlying temporal gene expression dynamics.

Single-cell RNA sequencing provides insights into gene expression at single-cell resolution, yet inferring temporal processes from these static snapshot measurements remains a fundamental challenge. Current approaches utilizing neural differential equations and flows are sensitive to overfitting and lack careful considerations of biological variability. In this work, we propose a generative framework that models population trends using a latent heteroscedastic Gaussian process (GP) approximated by Hilbert space methods. To address the absence of genuine cell trajectories, we leverage an optimal transport (OT) objective that aligns generated and observed population distributions. Our method explicitly captures biological heterogeneity by incorporating cell-specific latent time and cell type conditioning to disentangle temporal asynchrony and trajectories to different cell types. We demonstrate state-of-the-art performance on complex interpolation and extrapolation benchmarks and introduce a novel gradient-based strategy for inferring perturbation trajectories.

Inferring dynamics from population snapshots is a fundamental challenge in machine learning and biology. In scRNA-sequencing (scRNA-seq), destructive measurements preclude direct tracking of individual cells across time, making trajectory inference underdetermined. Optimal Transport (OT) provides a principled framework for snapshot alignment, but a long-standing modeling question is which cost functions yield biologically meaningful couplings. Standard OT approaches rely on gene-expression distances, implicitly treating cells as independent points and neglecting structured cell-cell communication mediated by ligand-receptor signaling. We introduce CellBRIDGE (Cell-Based Regularized Interaction-Driven Gene Expression), which augments feature-based OT with a directed, typed interaction cost derived from ligand-receptor activity. By explicitly modeling cell-cell communication, CellBRIDGE improves cross-snapshot couplings and downstream trajectory estimates across synthetic and real scRNA-seq datasets relative to feature-only baselines. Notably, CellBRIDGE enables mechanistically interpretable in silico perturbations: on lung cancer data, silencing specific ligand-receptor pairs induces trajectory shifts that recapitulate expected effects of targeted pathway inhibition.