mlsanityData to 7 Oct 2026

TrajectoryNet: A Dynamic Optimal Transport Network for Modeling Cellular Dynamics

arXiv 2002.04461 ↗First posted 9 Feb 2020stat.ML cs.CV cs.LGcited by 155

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Cited by 32 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

It is increasingly common to encounter data from dynamic processes captured by static cross-sectional measurements over time, particularly in biomedical settings. Recent attempts to model individual trajectories from this data use optimal transport to create pairwise matchings between time points. However, these methods cannot model continuous dynamics and non-linear paths that entities can take in these systems. To address this issue, we establish a link between continuous normalizing flows and dynamic optimal transport, that allows us to model the expected paths of points over time. Continuous normalizing flows are generally under constrained, as they are allowed to take an arbitrary path from the source to the target distribution. We present TrajectoryNet, which controls the continuous paths taken between distributions to produce dynamic optimal transport. We show how this is particularly applicable for studying cellular dynamics in data from single-cell RNA sequencing (scRNA-seq) technologies, and that TrajectoryNet improves upon recently proposed static optimal transport-based models that can be used for interpolating cellular distributions.

Key facts. Cited by 155 papers in the map (data through 7 Oct 2026). First posted on arXiv 9 Feb 2020.

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Citing papers per year: 2021: 5; 2022: 13; 2023: 28; 2024: 24; 2025: 41; 2026: 44.

155 papers.

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  1. 2022Flow Matching for Generative Modelingcited by 5,426
  2. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 897
  3. 2023Improving and generalizing flow-based generative models with minibatch optimal transportcited by 835
  4. 2023Multisample Flow Matching: Straightening Flows with Minibatch Couplingscited by 267
  5. 2023SE(3)-Stochastic Flow Matching for Protein Backbone Generationcited by 147
  6. 2021Solving Schr"odinger Bridges via Maximum Likelihoodcited by 140
  7. 2023Equivariant flow matchingcited by 131
  8. 2022Action Matching: Learning Stochastic Dynamics from Samplescited by 94
  9. 2021Proximal Optimal Transport Modeling of Population Dynamicscited by 91
  10. 2023Simulation-free Schr"odinger bridges via score and flow matchingcited by 81
  11. 2024Metric Flow Matching for Smooth Interpolations on the Data Manifoldcited by 74
  12. 2022Neural Conservation Laws: A Divergence-Free Perspectivecited by 67
38 more
  1. 2021Low-Rank Sinkhorn Factorizationcited by 66
  2. 2022The Schr"odinger Bridge between Gaussian Measures has a Closed Formcited by 63
  3. 2022Manifold Interpolating Optimal-Transport Flows for Trajectory Inferencecited by 63
  4. 2023A Computational Framework for Solving Wasserstein Lagrangian Flowscited by 43
  5. 2024Meta Flow Matching: Integrating Vector Fields on the Wasserstein Manifoldcited by 41
  6. 2023Deep Momentum Multi-Marginal Schr"odinger Bridgecited by 40
  7. 2023Aligned Diffusion Schr"odinger Bridgescited by 38
  8. 2023Unbalancedness in Neural Monge Maps Improves Unpaired Domain Translationcited by 32
  9. 2021Towards a mathematical theory of trajectory inferencecited by 31
  10. 2024Learning stochastic dynamics from snapshots through regularized unbalanced optimal transportcited by 30
  11. 2022Trajectory Inference via Mean-field Langevin in Path Spacecited by 29
  12. 2023DynGFN: Towards Bayesian Inference of Gene Regulatory Networks with GFlowNetscited by 27
  13. 2023GENOT: Entropic (Gromov) Wasserstein Flow Matching with Applications to Single-Cell Genomicscited by 27
  14. 2024Multi-marginal Schr"odinger Bridges with Iterative Reference Refinementcited by 26
  15. 2024Dynamic Conditional Optimal Transport through Simulation-Free Flowscited by 24
  16. 2022Riemannian Metric Learning via Optimal Transportcited by 21
  17. 2024Learning diffusion at lightspeedcited by 21
  18. 2025Joint Velocity-Growth Flow Matching for Single-Cell Dynamics Modelingcited by 20
  19. 2024ImageFlowNet: Forecasting Multiscale Image-Level Trajectories of Disease Progression with Irregularly-Sampled Longitudinal Medical Imagescited by 19
  20. 2021Diffusion Earth Mover's Distance and Distribution Embeddingscited by 18
  21. 2023Light Schr"odinger Bridgecited by 18
  22. 2025Curly Flow Matching for Learning Non-gradient Field Dynamicscited by 17
  23. 2022Neural Unbalanced Optimal Transport via Cycle-Consistent Semi-Couplingscited by 16
  24. 2024Neural Optimal Transport with Lagrangian Costscited by 16
  25. 2024Partially Observed Trajectory Inference using Optimal Transport and a Dynamics Priorcited by 13
  26. 2024Geometry-Aware Generative Autoencoders for Warped Riemannian Metric Learning and Generative Modeling on Data Manifoldscited by 13
  27. 2025Modeling Cell Dynamics and Interactions with Unbalanced Mean Field Schr"odinger Bridgecited by 12
  28. 2023Flow Factorized Representation Learningcited by 11
  29. 2025Multi-Marginal Stochastic Flow Matching for High-Dimensional Snapshot Data at Irregular Time Pointscited by 11
  30. 2022Geodesic Sinkhorn for Fast and Accurate Optimal Transport on Manifoldscited by 10
  31. 2025Trajectory Inference with Smooth Schr"odinger Bridgescited by 10
  32. 2025Variational Regularized Unbalanced Optimal Transport: Single Network, Least Actioncited by 10
  33. 2023Transport with Support: Data-Conditional Diffusion Bridgescited by 9
  34. 2023Inferring dynamic regulatory interaction graphs from time series data with perturbationscited by 9
  35. 2023Unbalanced Diffusion Schr"odinger Bridgecited by 9
  36. 2024Generalized Sobolev Transport for Probability Measures on a Graphcited by 9
  37. 2024Efficient Trajectory Inference in Wasserstein Space Using Consecutive Averagingcited by 9
  38. 2025Integrating Dynamical Systems Modeling with Spatiotemporal scRNA-seq Data Analysiscited by 9

50 most cited of 155 All 155 (JSON)