Learning biophysical models of gene regulation with probability flow matching

TL;DR

This paper introduces Probability Flow Matching (PFM), a scalable method for learning biophysical gene regulation models from single-cell data, capturing mechanisms of cell differentiation and responses.

Contribution

PFM is a novel framework that infers mechanistically interpretable stochastic gene regulation models directly from time-resolved single-cell measurements.

Findings

PFM accurately captures lineage transitions and fate decisions.

Models with similar interpolation accuracy can encode different dynamics.

PFM handles unbalanced populations, inferring proliferation and death rates.

Abstract

Cellular differentiation is governed by gene regulatory networks, the high-dimensional stochastic biochemical systems that determine the transcriptional landscape and mediate cellular responses to signals and perturbations. Although single-cell RNA sequencing provides quantitative snapshots of the transcriptome, current methods for inferring gene-regulatory dynamics often lack mechanistic interpretability and fail to generalize to unseen conditions. Here we introduce Probability Flow Matching (PFM), a scalable framework for learning biophysically consistent stochastic processes directly from time-resolved single-cell measurements. Applying PFM to three hematopoiesis datasets, we show that models with similar interpolation accuracy can encode fundamentally different dynamics, with only biophysically consistent formulations accurately capturing mechanisms of lineage transitions, fate specification, and gene perturbation responses. We further demonstrate that PFM accommodates unbalanced populations, enabling simultaneous inference of cellular proliferation and death dynamics. Together, these results establish PFM as a flexible, scalable framework for integrating mechanistic modeling with single-cell omics.