mlsanityData to 14 Oct 2026

Learning biophysical models of gene regulation with probability flow matching

arXiv 2604.25062 ↗First posted 27 Apr 2026q-bio.MN cs.LG physics.bio-phcited by 0

On the map: Diffusion models → Flow matching, time series and science

Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 16 of its 76 references that are in the map. First posted on arXiv 27 Apr 2026.

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16 of 76 references.

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  1. 2024Flow Matching Guide and Code9 Dec
  2. 2022Flow Matching for Generative Modeling6 Oct

Other references · 14

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  4. 2019Sliced Score Matching: A Scalable Approach to Density and Score Estimationcited by 384
  5. 2020TrajectoryNet: A Dynamic Optimal Transport Network for Modeling Cellular Dynamicscited by 160
  6. 2023Simulation-free Schr"odinger bridges via score and flow matchingcited by 83
  7. 2022The Schr"odinger Bridge between Gaussian Measures has a Closed Formcited by 63
  8. 2021Inverse-Dirichlet Weighting Enables Reliable Training of Physics Informed Neural Networkscited by 43
  9. 2018Scalable Unbalanced Optimal Transport using Generative Adversarial Networkscited by 42
  10. 2021Towards a mathematical theory of trajectory inferencecited by 31
  11. 2022Trajectory Inference via Mean-field Langevin in Path Spacecited by 30
  12. 2023Stochastic force inference via density estimationcited by 5
2 more
  1. 2025Inferring stochastic dynamics with growth from cross-sectional datacited by 4
  2. 2025Random Matrix Theory-guided sparse PCA for single-cell RNA-seq datacited by 1

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  1. 2026From Snapshots to Trajectories: Learning Single-Cell Gene Expression Dynamics via Conditional Flow Matching
  2. 2026Generalizable single-cell perturbation response prediction using energy-guided flow matching
  3. 2026MIOFlow 2.0: A unified framework for inferring cellular stochastic dynamics from single cell and spatial transcriptomics data
  4. 2026TempoBridge: Source-Conditioned Flow Matching with Optimal Transport Couplings for Single-Cell Population Transitions
  5. 2025Joint Velocity-Growth Flow Matching for Single-Cell Dynamics Modeling
  6. 2026WFR-MFM: One-Step Inference for Dynamic Unbalanced Optimal Transport
  7. 2026TracingFlow: A Simulation-Free Trajectory Inference Framework Based on Second-Order Dynamics
  8. 2024Meta Flow Matching: Integrating Vector Fields on the Wasserstein Manifold