# TrajectoryNet: A Dynamic Optimal Transport Network for Modeling Cellular Dynamics

arXiv: https://arxiv.org/abs/2002.04461 · HTML: https://mlsanity.com/paper/2002.04461/

## Key facts

- Cited by 160 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Feb 2020.

## Built on by (most cited first, 30 of 160)

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
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- [SE(3)-Stochastic Flow Matching for Protein Backbone Generation](https://mlsanity.com/paper/2310.02391/) (2023)
- [Solving Schr"odinger Bridges via Maximum Likelihood](https://mlsanity.com/paper/2106.02081/) (2021)
- [Equivariant flow matching](https://mlsanity.com/paper/2306.15030/) (2023)
- [Action Matching: Learning Stochastic Dynamics from Samples](https://mlsanity.com/paper/2210.06662/) (2022)
- [Proximal Optimal Transport Modeling of Population Dynamics](https://mlsanity.com/paper/2106.06345/) (2021)
- [Simulation-free Schr"odinger bridges via score and flow matching](https://mlsanity.com/paper/2307.03672/) (2023)
- [Metric Flow Matching for Smooth Interpolations on the Data Manifold](https://mlsanity.com/paper/2405.14780/) (2024)
- [Neural Conservation Laws: A Divergence-Free Perspective](https://mlsanity.com/paper/2210.01741/) (2022)
- [Low-Rank Sinkhorn Factorization](https://mlsanity.com/paper/2103.04737/) (2021)
- [Manifold Interpolating Optimal-Transport Flows for Trajectory Inference](https://mlsanity.com/paper/2206.14928/) (2022)
- [The Schr"odinger Bridge between Gaussian Measures has a Closed Form](https://mlsanity.com/paper/2202.05722/) (2022)
- [A Computational Framework for Solving Wasserstein Lagrangian Flows](https://mlsanity.com/paper/2310.10649/) (2023)
- [Meta Flow Matching: Integrating Vector Fields on the Wasserstein Manifold](https://mlsanity.com/paper/2408.14608/) (2024)
- [Deep Momentum Multi-Marginal Schr"odinger Bridge](https://mlsanity.com/paper/2303.01751/) (2023)
- [Aligned Diffusion Schr"odinger Bridges](https://mlsanity.com/paper/2302.11419/) (2023)
- [Unbalancedness in Neural Monge Maps Improves Unpaired Domain Translation](https://mlsanity.com/paper/2311.15100/) (2023)
- [Learning stochastic dynamics from snapshots through regularized unbalanced optimal transport](https://mlsanity.com/paper/2410.00844/) (2024)
- [Towards a mathematical theory of trajectory inference](https://mlsanity.com/paper/2102.09204/) (2021)
- [Trajectory Inference via Mean-field Langevin in Path Space](https://mlsanity.com/paper/2205.07146/) (2022)
- [GENOT: Entropic (Gromov) Wasserstein Flow Matching with Applications to Single-Cell Genomics](https://mlsanity.com/paper/2310.09254/) (2023)
- [DynGFN: Towards Bayesian Inference of Gene Regulatory Networks with GFlowNets](https://mlsanity.com/paper/2302.04178/) (2023)
- [Multi-marginal Schr"odinger Bridges with Iterative Reference Refinement](https://mlsanity.com/paper/2408.06277/) (2024)
- [Dynamic Conditional Optimal Transport through Simulation-Free Flows](https://mlsanity.com/paper/2404.04240/) (2024)
- [Learning diffusion at lightspeed](https://mlsanity.com/paper/2406.12616/) (2024)
- [Riemannian Metric Learning via Optimal Transport](https://mlsanity.com/paper/2205.09244/) (2022)
- [Joint Velocity-Growth Flow Matching for Single-Cell Dynamics Modeling](https://mlsanity.com/paper/2505.13413/) (2025)

## 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.