Modeling Temporal scRNA-seq Data with Latent Gaussian Process and Optimal Transport

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.

Understanding how living cells change over time is a fundamental goal of modern biology. The challenge is that the main tool scientists use to measure gene expression, single-cell RNA sequencing, destroys each cell in the process, leaving only population-level snapshots rather than continuous movies of cellular change. We developed a computational framework, LGP-OT, that reconstructs these missing movies from the snapshots. Our approach uses Gaussian processes to model smooth, biologically plausible trajectories over time, while explicitly accounting for the fact that biological variability is not constant. Some developmental moments are simply noisier than others. To link our simulated cells to the real observed ones (despite having no one-to-one correspondence between them), we use optimal transport, a technique that finds the most efficient way to match two populations. We also introduce a gradient-based method to simulate what would happen to a cell population if specific genes were artificially switched on or off. Our model outperforms existing methods at predicting gene expression at unobserved time points, and can help researchers design targeted gene perturbation experiments.