mlsanityData to 14 Oct 2026

Modeling Cell Dynamics and Interactions with Unbalanced Mean Field Schr"odinger Bridge

arXiv 2505.11197 ↗First posted 16 May 2025cs.LG math.OC q-bio.QMcited by 12

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Abstract (arXiv)

Modeling the dynamics from sparsely time-resolved snapshot data is crucial for understanding complex cellular processes and behavior. Existing methods leverage optimal transport, Schr"odinger bridge theory, or their variants to simultaneously infer stochastic, unbalanced dynamics from snapshot data. However, these approaches remain limited in their ability to account for cell-cell interactions. This integration is essential in real-world scenarios since intercellular communications are fundamental life processes and can influence cell state-transition dynamics. To address this challenge, we formulate the Unbalanced Mean-Field Schr"odinger Bridge (UMFSB) framework to model unbalanced stochastic interaction dynamics from snapshot data. Inspired by this framework, we further propose CytoBridge, a deep learning algorithm designed to approximate the UMFSB problem. By explicitly modeling cellular transitions, proliferation, and interactions through neural networks, CytoBridge offers the flexibility to learn these processes directly from data. The effectiveness of our method has been extensively validated using both synthetic gene regulatory data and real scRNA-seq datasets. Compared to existing methods, CytoBridge identifies growth, transition, and interaction patterns, eliminates false transitions, and reconstructs the developmental landscape with greater accuracy. Code is available at: https://github.com/zhenyiizhang/CytoBridge-NeurIPS.

Key facts. Cited by 12 papers in the map (data through 14 Oct 2026). Builds on 51 of its 110 references that are in the map. First posted on arXiv 16 May 2025.

Builds on

51 of 110 references.

References · 51

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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. 2020TrajectoryNet: A Dynamic Optimal Transport Network for Modeling Cellular Dynamicscited by 160
  5. 2023Diffusion Schr"odinger Bridge Matchingcited by 153
  6. 2022Action Matching: Learning Stochastic Dynamics from Samplescited by 98
  7. 2019A Machine Learning Framework for Solving High-Dimensional Mean Field Game and Mean Field Control Problemscited by 97
  8. 2023Simulation-free Schr"odinger bridges via score and flow matchingcited by 83
  9. 2024Metric Flow Matching for Smooth Interpolations on the Data Manifoldcited by 77
  10. 2022Manifold Interpolating Optimal-Transport Flows for Trajectory Inferencecited by 64
  11. 2022The Schr"odinger Bridge between Gaussian Measures has a Closed Formcited by 63
  12. 2022Deep Generalized Schr"odinger Bridgecited by 47
  13. 2023A Computational Framework for Solving Wasserstein Lagrangian Flowscited by 46
  14. 2024Meta Flow Matching: Integrating Vector Fields on the Wasserstein Manifoldcited by 43
  15. 2023Generalized Schr"odinger Bridge Matchingcited by 40
  16. 2023Unbalancedness in Neural Monge Maps Improves Unpaired Domain Translationcited by 33
  17. 2024Learning stochastic dynamics from snapshots through regularized unbalanced optimal transportcited by 33
  18. 2022Trajectory Inference via Mean-field Langevin in Path Spacecited by 30
  19. 2023Causal machine learning for single-cell genomicscited by 23
  20. 2022Self-Consistency of the Fokker-Planck Equationcited by 18
  21. 2023Self-Consistent Velocity Matching of Probability Flowscited by 17
  22. 2021The most likely evolution of diffusing and vanishing particles: Schrodinger Bridges with unbalanced marginalscited by 14
  23. 2023Score-based Transport Modeling for Mean-Field Fokker-Planck Equationscited by 14
  24. 2022Learning High-Dimensional McKean-Vlasov Forward-Backward Stochastic Differential Equations with General Distribution Dependencecited by 13
  25. 2024Partially Observed Trajectory Inference using Optimal Transport and a Dynamics Priorcited by 13
  26. 2024Multi-Modal and Multi-Attribute Generation of Single Cells with CFGencited by 12
  27. 2021Regularized unbalanced optimal transport as entropy minimization with respect to branching Brownian motioncited by 10
  28. 2023Unbalanced Diffusion Schr"odinger Bridgecited by 9
  29. 2024Inferring biological processes with intrinsic noise from cross-sectional datacited by 9
  30. 2025Integrating Dynamical Systems Modeling with Spatiotemporal scRNA-seq Data Analysiscited by 9
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50 most cited of 51 All 51 (JSON)

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 8; 2026: 4.

12 papers.

  1. 2025Joint Velocity-Growth Flow Matching for Single-Cell Dynamics Modelingcited by 20
  2. 2025Variational Regularized Unbalanced Optimal Transport: Single Network, Least Actioncited by 11
  3. 2025Learning of Population Dynamics: Inverse Optimization Meets JKO Schemecited by 9
  4. 2025Branched Schr"odinger Bridge Matchingcited by 5
  5. 2025ContextFlow: Context-Aware Flow Matching For Trajectory Inference From Spatial Omics Datacited by 2
  6. 2025CellStream: Dynamical Optimal Transport Informed Embeddings for Reconstructing Cellular Trajectories from Snapshots Datacited by 2
  7. 2025Entangled Schr"odinger Bridge Matchingcited by 1
  8. 2026Leveraging Gauge Freedom for Learning Non-Gradient Population Dynamics of Stochastic Systemscited by 1
  9. 2026CellBRIDGE: Learning Cellular Trajectories via Interaction-Aware Alignmentcited by 1
  10. 2026Nonlocal Mean Field Schr"odinger Bridge with Learned Interactionscited by 1
  11. 2025Cell-cell Communication Inference and Analysis: Biological Mechanisms, Computational Approaches, and Future Opportunitiescited by 0
  12. 2026Dynamic Generalized Gromov-Wasserstein Optimal Transportcited by 0