mlsanityData to 14 Oct 2026

Integrating Dynamical Systems Modeling with Spatiotemporal scRNA-seq Data Analysis

arXiv 2503.11347 ↗First posted 14 Mar 2025q-bio.QM cs.LG physics.bio-phcited by 9

Not on the map. Why?

Abstract (arXiv)

Understanding the dynamic nature of biological systems is fundamental to deciphering cellular behavior, developmental processes, and disease progression. Single-cell RNA sequencing (scRNA-seq) has provided static snapshots of gene expression, offering valuable insights into cellular states at a single time point. Recent advancements in temporally resolved scRNA-seq, spatial transcriptomics (ST), and time-series spatial transcriptomics (temporal-ST) have further revolutionized our ability to study the spatiotemporal dynamics of individual cells. These technologies, when combined with computational frameworks such as Markov chains, stochastic differential equations (SDEs), and generative models like optimal transport and Schr"odinger bridges, enable the reconstruction of dynamic cellular trajectories and cell fate decisions. This review discusses how these dynamical system approaches offer new opportunities to model and infer cellular dynamics from a systematic perspective.

Key facts. Cited by 9 papers in the map (data through 14 Oct 2026). Builds on 52 of its 207 references that are in the map. First posted on arXiv 14 Mar 2025.

Builds on

52 of 207 references.

References · 52

  1. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  2. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  3. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  4. 2022Flow Matching for Generative Modelingcited by 5,702
  5. 2018Neural Ordinary Differential Equationscited by 3,779
  6. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flowcited by 3,700
  7. 2022Building Normalizing Flows with Stochastic Interpolantscited by 995
  8. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 939
  9. 2023Improving and generalizing flow-based generative models with minibatch optimal transportcited by 879
  10. 2018Computational Optimal Transportcited by 780
  11. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modelingcited by 602
  12. 2013A survey of the Schr"odinger problem and some of its connections with optimal transportcited by 292
38 more
  1. 2021Likelihood Training of Schr"odinger Bridge using Forward-Backward SDEs Theorycited by 219
  2. 2023I2SB: Image-to-Image Schr"odinger Bridgecited by 218
  3. 2023Denoising Diffusion Bridge Modelscited by 178
  4. 2018Optimal Transport for structured data with application on graphscited by 172
  5. 2020TrajectoryNet: A Dynamic Optimal Transport Network for Modeling Cellular Dynamicscited by 160
  6. 2023Diffusion Schr"odinger Bridge Matchingcited by 153
  7. 2021Deep Generative Learning via Schr"odinger Bridgecited by 104
  8. 2014On the relation between optimal transport and Schr"odinger bridges: A stochastic control viewpointcited by 99
  9. 2022Action Matching: Learning Stochastic Dynamics from Samplescited by 98
  10. 2019A Machine Learning Framework for Solving High-Dimensional Mean Field Game and Mean Field Control Problemscited by 97
  11. 2023Simulation-free Schr"odinger bridges via score and flow matchingcited by 83
  12. 2022Manifold Interpolating Optimal-Transport Flows for Trajectory Inferencecited by 64
  13. 2022The Schr"odinger Bridge between Gaussian Measures has a Closed Formcited by 63
  14. 2022Deep Generalized Schr"odinger Bridgecited by 47
  15. 2023A Computational Framework for Solving Wasserstein Lagrangian Flowscited by 46
  16. 2023Convergence of flow-based generative models via proximal gradient descent in Wasserstein spacecited by 34
  17. 2023Unbalancedness in Neural Monge Maps Improves Unpaired Domain Translationcited by 33
  18. 2024Learning stochastic dynamics from snapshots through regularized unbalanced optimal transportcited by 33
  19. 2022Trajectory Inference via Mean-field Langevin in Path Spacecited by 30
  20. 2024Convergence of Continuous Normalizing Flows for Learning Probability Distributionscited by 26
  21. 2024Convergence Analysis of Flow Matching in Latent Space with Transformerscited by 16
  22. 2024Neural Optimal Transport with Lagrangian Costscited by 16
  23. 2019Unnormalized Optimal Transportcited by 15
  24. 2021The most likely evolution of diffusing and vanishing particles: Schrodinger Bridges with unbalanced marginalscited by 14
  25. 2024Partially Observed Trajectory Inference using Optimal Transport and a Dynamics Priorcited by 13
  26. 2021Learning High Dimensional Wasserstein Geodesicscited by 10
  27. 2021Regularized unbalanced optimal transport as entropy minimization with respect to branching Brownian motioncited by 10
  28. 2024Latent Schr"odinger Bridge Diffusion Model for Generative Learningcited by 10
  29. 2023Unbalanced Diffusion Schr"odinger Bridgecited by 9
  30. 2024Inferring biological processes with intrinsic noise from cross-sectional datacited by 9
  31. 2024Plug-in estimation of Schr"odinger bridgescited by 8
  32. 2024Score-based Neural Ordinary Differential Equations for Computing Mean Field Control Problemscited by 7
  33. 2024Joint trajectory and network inference via reference fittingcited by 6
  34. 2024Governing equation discovery of a complex system from snapshotscited by 6
  35. 2022A scalable deep learning approach for solving high-dimensional dynamic optimal transportcited by 5
  36. 2025Half-order Fine-Tuning for Diffusion Model: A Recursive Likelihood Ratio Optimizercited by 5
  37. 2023EPR-Net: Constructing non-equilibrium potential landscape via a variational force projection formulationcited by 3
  38. 2023Entropic regularisation of unbalanced optimal transportation problemscited by 3

50 most cited of 52 All 52 (JSON)

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 6; 2026: 3.

9 papers.

  1. 2025Joint Velocity-Growth Flow Matching for Single-Cell Dynamics Modelingcited by 20
  2. 2025Modeling Cell Dynamics and Interactions with Unbalanced Mean Field Schr"odinger Bridgecited by 12
  3. 2025Variational Regularized Unbalanced Optimal Transport: Single Network, Least Actioncited by 11
  4. 2025Learning of Population Dynamics: Inverse Optimization Meets JKO Schemecited by 9
  5. 2026WFR-FM: Simulation-Free Dynamic Unbalanced Optimal Transportcited by 6
  6. 2025CellStream: Dynamical Optimal Transport Informed Embeddings for Reconstructing Cellular Trajectories from Snapshots Datacited by 2
  7. 2026TracingFlow: A Simulation-Free Trajectory Inference Framework Based on Second-Order Dynamicscited by 1
  8. 2025Cell-cell Communication Inference and Analysis: Biological Mechanisms, Computational Approaches, and Future Opportunitiescited by 0
  9. 2026Multiscale Supervised Unbalanced Optimal Transport Flow Matchingcited by 0