PRIME: scalable, robust inference of mechanistic cell states from multimodal single-cell counts via probability generating functions

Single-cell multiomic technologies can now quantify complementary RNA species within the same cell, creating an opportunity to move beyond descriptive clustering toward mechanistically interpretable cell states. Yet most current methods depend on heuristic integration steps and become computationally burdensome at scale, limiting their ability to robustly detect subtle kinetic differences across heterogeneous populations. Here we introduce PRIME, a scalable framework for mechanistic cell-state discovery from multimodal single-cell count data. PRIME embeds multimodal measurements in a probability generating function (PGF) space, where transcriptional dynamics are encoded compactly and compared efficiently. This representation enables robust inference of latent kinetic structure and supports rapid cell grouping with a power K-means backbone that remains stable under noise, sparsity, and multimodality. Across synthetic benchmarks and experimental multimodal datasets, PRIME consistently recovers cell populations distinguished by transcriptional kinetics, outperforms conventional integration-and-clustering pipelines in robustness, and yields interpretable parameters that link observed variability to underlying regulatory mechanisms. By providing a mathematically principled yet practical route from multimodal counts to kinetic cell states, PRIME empowers biologists to uncover dynamic transcriptional regimes, dissect regulatory heterogeneity, and connect cell identity to mechanism rather than markers.