arxiv: 2605.00545 · v1 · submitted 2026-05-01 · 💻 cs.LG · cs.AI· math-ph· math.MP· q-bio.GN· q-bio.QM

Recognition: unknown

Beyond Continuity: Simulation-free Reconstruction of Discrete Branching Dynamics from Single-cell Snapshots

Junda Ying , Yuxuan Wang , Bowen Yang , Peijie Zhou , Lei Zhang

Authors on Pith no claims yet

Pith reviewed 2026-05-09 19:42 UTC · model grok-4.3

classification 💻 cs.LG cs.AImath-phmath.MPq-bio.GNq-bio.QM

keywords Unbalanced Schrödinger Bridgesingle-cell snapshotsbranching dynamicsbirth-death jumpstrajectory reconstructionsimulation-freeoptimal transportcellular dynamics

0 comments

The pith

USB reconstructs discrete branching cell dynamics from snapshots by modeling Brownian motion and birth-death jumps.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper aims to reconstruct cellular trajectories from single-cell snapshots that are destructive and show non-conservative mass changes due to proliferation and apoptosis. It introduces Unbalanced Schrödinger Bridge (USB) as a simulation-free method that models individual cells as performing continuous Brownian motion alongside discrete birth or death jumps. This approach differs from continuous fluid models by capturing the jump-like nature of events at single-cell resolution. A sympathetic reader would care because it enables both accurate trajectory inference and realistic discrete simulations of branching processes in high-dimensional data.

Core claim

USB provides a tractable solution to the Branching Schrödinger Bridge (BSB) problem, offering a rigorous microscopic interpretation where individual cells undergo both Brownian motion and discrete birth-death jumps. The framework implements an efficient solver by introducing a simulation-free training objective that effectively scales to high-dimensional omics data.

What carries the argument

The Unbalanced Schrödinger Bridge (USB) solver, which integrates stochastic diffusion with unbalanced mass transport through discrete jumps for birth-death events.

If this is right

Trajectory reconstruction performance is better than or comparable to deterministic baselines on both simulated and real-world datasets.
Realistic discrete simulation of birth-death dynamics becomes possible at single-cell resolution.
The method handles both stochastic and unbalanced effects while scaling to high-dimensional omics data.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Applying USB to other snapshot-based inference problems in systems with jumps, like chemical reaction networks, could yield similar benefits.
If validated, this decomposition might allow combining USB with existing lineage tracing technologies to refine fate decision models.
Extensions to time-varying or spatially structured data would test the limits of the Brownian-plus-jumps assumption.

Load-bearing premise

Cellular dynamics decompose into continuous Brownian motion plus discrete birth-death jumps at single-cell resolution, admitting a simulation-free learning objective from population-level snapshots.

What would settle it

A dataset where ground-truth single-cell trajectories show birth-death events that cannot be explained by a combination of Brownian motion and discrete jumps would falsify the approach if USB fails to recover them accurately.

Figures

Figures reproduced from arXiv: 2605.00545 by Bowen Yang, Junda Ying, Lei Zhang, Peijie Zhou, Yuxuan Wang.

**Figure 1.** Figure 1: Learned growth rate on the Gaussian 1000D dataset. Left panel: WFR-FM; Right panel: USB accuracy on EMT and CITE, while performs comparable with top baselines on others. This demonstrates that USB successfully captures the underlying cellular dynamics. USB recovers the underlying birth-death dynamics. To evaluate how well can USB recover the underling birthdeath dynamics, we calculated the Pearson correla… view at source ↗

**Figure 3.** Figure 3: Learned trajectories on the Simulation Gene dataset (ν = 0.001). From left to right: δ = 0.5, 1.3, 2.5 [PITH_FULL_IMAGE:figures/full_fig_p022_3.png] view at source ↗

**Figure 4.** Figure 4: Learned trajectories and growth on the Dyngen dataset (δ = 1.7, ν = 0.1). Left panel: trajectories; Right panel: growth rate. We also summarized the detailed quantitative results across different time points in [PITH_FULL_IMAGE:figures/full_fig_p023_4.png] view at source ↗

**Figure 5.** Figure 5: Learned trajectories on the Gaussian 1000D dataset (δ = 1.3, ν = 0.001). C.6. Epithelial Mesenchymal Transition Data We adopt the dataset that captures the epithelial-mesenchymal transition (EMT) in A549 lung cancer cells from (Cook & Vanderhyden, 2020). The dataset includes samples collected at four distinct time points throughout this process. (Sha et al., 2024) reduced the dimension to 10 by an autoenco… view at source ↗

**Figure 6.** Figure 6: Learned growth rate on the EMT dataset (δ = 1.4, ν = 0.001). of USB w.r.t the dimensionality. We set δ = 3, 27, 30 for 5D, 50D, 100D, respectively, and set ν = 0.001. To be consistent to (Peng et al., 2026), the 5D EB is further standardized. We compare the performance of USB with several other methods on the 3 datasets with results in showed [PITH_FULL_IMAGE:figures/full_fig_p025_6.png] view at source ↗

**Figure 7.** Figure 7: Training time v.s. cell numbers D. Relation to other algorithms D.1. Relation to SF2M SF2M (Tong et al., 2024b) is the first simulation-free framework for learning balanced Schrodinger Bridge between arbitrary ¨ source and target distributions. It utilized the KL-disintegration to decoupled the SB to two parts: the regularized OT (ROT) coupling induced by the static SB problem, and the conditional path bri… view at source ↗

read the original abstract

Inferring cellular trajectories from destructive snapshots is complicated by the challenges of stochasticity and non-conservative mass dynamics such as cell proliferation and apoptosis. Existing unbalanced Optimal Transport (OT) methods treat mass as a continuous fluid, performing inference at the population level. However, this macroscopic view often fails to capture the discrete, jump-like nature of birth-death events at single-cell resolution, which is essential for understanding lineage branching and fate decisions. We present Unbalanced Schr\"odinger Bridge (USB), a simulation-free framework for learning underlying dynamics that effectively integrates both stochastic and unbalanced effects which also models the discrete, jump-like birth-death dynamics at single-cell resolution. Theoretically, USB provides a tractable solution to the Branching Schr\"odinger Bridge (BSB) problem, offering a rigorous microscopic interpretation where individual cells undergo both Brownian motion and discrete birth-death jumps. Technically, the method implements an efficient solver by introducing a simulation-free training objective that effectively scales to high-dimensional omics data. Empirically, we demonstrate on both simulated and real-world datasets that USB not only achieves trajectory reconstruction performance better than or comparable to deterministic baselines but also uniquely enables realistic discrete simulation of birth-death dynamics at single-cell resolution.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

USB gives a simulation-free way to fit discrete birth-death jumps into single-cell trajectory inference by blending unbalanced OT with Schrödinger bridges, but the claimed rigorous microscopic equivalence to individual jump-diffusions is asserted more than derived in the abstract.

read the letter

The paper introduces Unbalanced Schrödinger Bridge as a way to reconstruct trajectories from snapshots while handling both diffusion and discrete cell birth-death events. This is the main new piece: prior unbalanced OT methods treat mass changes as a continuous fluid at the population level, whereas USB aims for a single-cell resolution model that includes jump-like proliferation and apoptosis alongside Brownian motion. They supply a simulation-free training objective that scales to high-dimensional data and report that it matches or beats deterministic baselines on simulated and real datasets while also allowing direct discrete simulations of the jumps. That practical angle is useful for people who want to move beyond fluid approximations in developmental or disease modeling. The empirical side gets credit for testing both synthetic cases with known ground truth and real omics data, which is the right check for this kind of method. The theoretical claim is that USB solves the Branching Schrödinger Bridge problem and supplies a rigorous microscopic picture. The stress-test note is fair here: the abstract does not walk through the derivation from an underlying SDE with Poisson jumps, through the corresponding Fokker-Planck equation with source terms, to the USB objective and back to recovered jump rates. Without that chain or the regularity conditions, the microscopic interpretation stays more interpretive than proven. If the full paper contains the missing steps with explicit error bounds or convergence results, the work strengthens considerably; if not, the method is still a workable population-level surrogate but not yet a guaranteed single-particle equivalence. This paper is for computational biologists and optimal-transport researchers who care about non-conservative dynamics in single-cell settings. A reader who already works with Schrödinger bridges or unbalanced transport will see the technical extension clearly. It deserves peer review because the problem is real, the simulation-free angle is distinct, and the empirical tests are in the right direction, even though the theoretical justification needs tightening before publication.

Referee Report

2 major / 2 minor

Summary. The paper introduces Unbalanced Schrödinger Bridge (USB) as a simulation-free framework for reconstructing cellular trajectories from single-cell snapshots. It claims to solve the Branching Schrödinger Bridge (BSB) problem by integrating stochastic Brownian motion with discrete birth-death jumps, providing a microscopic single-cell interpretation while scaling to high-dimensional omics data, and reports trajectory reconstruction performance that is better than or comparable to deterministic baselines on simulated and real datasets.

Significance. If the central theoretical claims are established, USB could advance single-cell dynamics inference by enabling discrete, jump-like simulation of proliferation and apoptosis at single-cell resolution without requiring forward simulations during training. This would address a gap in existing unbalanced OT methods that treat mass as continuous fluid.

major comments (2)

[Abstract / Theoretical claims] Abstract and theoretical development: The claim that USB 'provides a tractable solution to the Branching Schrödinger Bridge (BSB) problem, offering a rigorous microscopic interpretation where individual cells undergo both Brownian motion and discrete birth-death jumps' is asserted without a derivation. No theorem starts from an SDE with Poisson jumps, derives the corresponding Fokker-Planck-Kolmogorov equation with source/sink terms, and proves that the USB minimizer on marginal snapshots recovers the same jump rates and diffusion coefficient. This equivalence is load-bearing for the central claim and the 'rigorous' qualifier.
[Methods] Methods and training objective: The simulation-free training objective is presented as effectively scaling to high-dimensional data, but no explicit loss function, regularity conditions on branching rates, or proof of equivalence to the single-particle law is given. Without this, it remains unclear whether the population-level objective guarantees correct single-cell jump statistics rather than serving as a surrogate.

minor comments (2)

[Abstract] The abstract contains escaped LaTeX sequences (e.g., Schröder, BSB) that should be rendered cleanly in the final version.
[Experiments] Empirical claims reference 'simulated and real-world datasets' but lack specific quantitative metrics, tables, or statistical tests in the summary description; ensure all results include error analysis and baseline details.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback. The comments highlight important points on theoretical rigor and methodological clarity that we address below. We will incorporate the suggested additions into the revised manuscript to strengthen the presentation of the USB framework.

read point-by-point responses

Referee: [Abstract / Theoretical claims] Abstract and theoretical development: The claim that USB 'provides a tractable solution to the Branching Schrödinger Bridge (BSB) problem, offering a rigorous microscopic interpretation where individual cells undergo both Brownian motion and discrete birth-death jumps' is asserted without a derivation. No theorem starts from an SDE with Poisson jumps, derives the corresponding Fokker-Planck-Kolmogorov equation with source/sink terms, and proves that the USB minimizer on marginal snapshots recovers the same jump rates and diffusion coefficient. This equivalence is load-bearing for the central claim and the 'rigorous' qualifier.

Authors: We agree that the abstract summarizes the contribution at a high level and that an explicit theorem would strengthen the rigor. The manuscript motivates USB via the extension of the Schrödinger bridge to unbalanced settings that encode birth-death events as jumps. In the revision we will insert a dedicated theorem (new Theorem 3.1) that (i) starts from the Itô SDE with Brownian motion plus Poisson-driven jumps whose intensity depends on the local branching rate, (ii) derives the corresponding Fokker-Planck-Kolmogorov equation containing the diffusion term, the drift, and the source/sink terms induced by the jumps, and (iii) proves that any minimizer of the USB objective on the observed marginals recovers the same diffusion coefficient and jump rates (under standard Lipschitz and boundedness assumptions). A proof sketch will be provided in the appendix. revision: yes
Referee: [Methods] Methods and training objective: The simulation-free training objective is presented as effectively scaling to high-dimensional data, but no explicit loss function, regularity conditions on branching rates, or proof of equivalence to the single-particle law is given. Without this, it remains unclear whether the population-level objective guarantees correct single-cell jump statistics rather than serving as a surrogate.

Authors: We appreciate the request for explicitness. The simulation-free property follows from the fact that the USB objective is a variational formulation (unbalanced Schrödinger bridge loss) that depends only on the snapshot marginals and the entropy-regularized transport cost; no forward simulation of trajectories is required during optimization. In the revised Methods section we will (a) write the loss function explicitly as the sum of a KL term between the learned bridge and the reference process plus an unbalanced penalty that accounts for mass creation/annihilation, (b) state the regularity conditions (Lipschitz drift, bounded and continuous branching rates, finite second moments), and (c) add a proposition showing that, in the mean-field limit, the population-level minimizer coincides with the law of the single-particle process, thereby guaranteeing that the recovered jump statistics are not merely surrogate but match the microscopic dynamics. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation remains self-contained against external BSB formulation

full rationale

The paper defines USB as a simulation-free solver for the independently posed Branching Schrödinger Bridge problem (an extension of the classical Schrödinger bridge to unbalanced mass with jumps). The abstract and technical description present the microscopic Brownian-plus-jump interpretation as a consequence of the BSB formulation rather than a redefinition of the training objective itself. No equation is shown to reduce the learned dynamics to a fitted parameter or to a self-citation chain; the simulation-free loss is derived from marginal matching on snapshots, which is an external constraint. Self-citations, if present, are not load-bearing for the central equivalence claim. This yields a standard non-circular result.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Insufficient information in the abstract to identify specific free parameters, axioms, or invented entities; no equations or implementation details are provided.

pith-pipeline@v0.9.0 · 5542 in / 1068 out tokens · 39515 ms · 2026-05-09T19:42:48.257814+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

103 extracted references · 4 canonical work pages

[1]

Electronic Communications in Probability , number =

Giovanni Conforti and Christian L. Electronic Communications in Probability , number =. 2015 , doi =

2015
[2]

Aram-Alexandre Pooladian and Heli Ben-Hamu and Carles Domingo-Enrich and Brandon Amos and Yaron Lipman and Ricky T. Q. Chen , title=. 2023 , cdate=

2023
[3]

The Eleventh International Conference on Learning Representations , year=

Building Normalizing Flows with Stochastic Interpolants , author=. The Eleventh International Conference on Learning Representations , year=
[4]

The Eleventh International Conference on Learning Representations , year=

Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow , author=. The Eleventh International Conference on Learning Representations , year=
[5]

The Thirteenth International Conference on Learning Representations , year=

Modeling Complex System Dynamics with Flow Matching Across Time and Conditions , author=. The Thirteenth International Conference on Learning Representations , year=
[6]

2025 , eprint=

Multi-Marginal Stochastic Flow Matching for High-Dimensional Snapshot Data at Irregular Time Points , author=. 2025 , eprint=

2025
[7]

2025 , eprint=

Momentum Multi-Marginal Schr\"odinger Bridge Matching , author=. 2025 , eprint=

2025
[8]

The Thirteenth International Conference on Learning Representations , year=

Composing Unbalanced Flows for Flexible Docking and Relaxation , author=. The Thirteenth International Conference on Learning Representations , year=
[9]

2025 , eprint=

Taming Flow Matching with Unbalanced Optimal Transport into Fast Pansharpening , author=. 2025 , eprint=

2025
[10]

2025 , eprint=

Curly Flow Matching for Learning Non-gradient Field Dynamics , author=. 2025 , eprint=

2025
[11]

The Thirteenth International Conference on Learning Representations , year=

Partially Observed Trajectory Inference using Optimal Transport and a Dynamics Prior , author=. The Thirteenth International Conference on Learning Representations , year=
[12]

Manifold Interpolating Optimal-Transport Flows for Trajectory Inference , volume =

Huguet, Guillaume and Magruder, Daniel Sumner and Tong, Alexander and Fasina, Oluwadamilola and Kuchroo, Manik and Wolf, Guy and Krishnaswamy, Smita , booktitle =. Manifold Interpolating Optimal-Transport Flows for Trajectory Inference , volume =
[13]

The Twelfth International Conference on Learning Representations , year=

Unbalancedness in Neural Monge Maps Improves Unpaired Domain Translation , author=. The Twelfth International Conference on Learning Representations , year=
[14]

The Thirty-ninth Annual Conference on Neural Information Processing Systems , year=

Joint Velocity-Growth Flow Matching for Single-Cell Dynamics Modeling , author=. The Thirty-ninth Annual Conference on Neural Information Processing Systems , year=
[15]

2026 , eprint=

WFR-FM: Simulation-Free Dynamic Unbalanced Optimal Transport , author=. 2026 , eprint=

2026
[16]

The Thirteenth International Conference on Learning Representations , year=

Learning stochastic dynamics from snapshots through regularized unbalanced optimal transport , author=. The Thirteenth International Conference on Learning Representations , year=
[17]

Nature Machine Intelligence , volume=

Reconstructing growth and dynamic trajectories from single-cell transcriptomics data , author=. Nature Machine Intelligence , volume=. 2024 , publisher=

2024
[18]

Chen, Ricky T. Q. and Rubanova, Yulia and Bettencourt, Jesse and Duvenaud, David K , booktitle =. Neural Ordinary Differential Equations , volume =
[19]

The Eleventh International Conference on Learning Representations , year=

Flow Matching for Generative Modeling , author=. The Eleventh International Conference on Learning Representations , year=
[20]

Transactions on Machine Learning Research , issn=

Improving and generalizing flow-based generative models with minibatch optimal transport , author=. Transactions on Machine Learning Research , issn=. 2024 , pages=

2024
[21]

On the Translocation of Masses , volume =

Kantorovich, Leonid V , ISSN =. On the Translocation of Masses , volume =. Management Science , number =
[22]

Numerische Mathematik , volume=

A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem , author=. Numerische Mathematik , volume=. 2000 , publisher=

2000
[23]

Foundations of Computational Mathematics , volume=

An interpolating distance between optimal transport and Fisher--Rao metrics , author=. Foundations of Computational Mathematics , volume=. 2018 , publisher=

2018
[24]

Journal of Functional Analysis , volume=

Unbalanced optimal transport: Dynamic and Kantorovich formulations , author=. Journal of Functional Analysis , volume=. 2018 , publisher=

2018
[25]

Inventiones mathematicae , volume=

Optimal entropy-transport problems and a new Hellinger--Kantorovich distance between positive measures , author=. Inventiones mathematicae , volume=. 2018 , publisher=

2018
[26]

Sur la th

Schr\"odinger, Erwin , journal=. Sur la th. 1932 , publisher=

1932
[27]

A survey of the

A survey of the Schrödinger problem and some of its connections with optimal transport , journal =. 2014 , issn =. doi:10.3934/dcds.2014.34.1533 , author =

work page doi:10.3934/dcds.2014.34.1533 2014
[28]

Entropy , VOLUME =

Vargas, Francisco and Thodoroff, Pierre and Lamacraft, Austen and Lawrence, Neil , TITLE =. Entropy , VOLUME =. 2021 , NUMBER =

2021
[29]

Random fields and diffusion processes

F \"o llmer, Hans. Random fields and diffusion processes. \'E cole d' \'E t \'e de Probabilit \'e s de Saint-Flour XV--XVII, 1985--87. 1988

1985
[30]

Appl Math Optim , volume=

A stochastic control approach to reciprocal diffusion processes , author=. Appl Math Optim , volume=. 1991 , month =

1991
[31]

Diffusion Schr\"odinger Bridge with Applications to Score-Based Generative Modeling , volume =

De Bortoli, Valentin and Thornton, James and Heng, Jeremy and Doucet, Arnaud , booktitle =. Diffusion Schr\"odinger Bridge with Applications to Score-Based Generative Modeling , volume =
[32]

The Twelfth International Conference on Learning Representations , year=

Light Schr\"odinger Bridge , author=. The Twelfth International Conference on Learning Representations , year=
[33]

Proceedings of The 26th International Conference on Artificial Intelligence and Statistics , pages =

The Schrödinger Bridge between Gaussian Measures has a Closed Form , author =. Proceedings of The 26th International Conference on Artificial Intelligence and Statistics , pages =. 2023 , editor =

2023
[34]

The Thirteenth International Conference on Learning Representations , year=

Discrete Diffusion Schr\"odinger Bridge Matching for Graph Transformation , author=. The Thirteenth International Conference on Learning Representations , year=
[35]

Proceedings of the 38th International Conference on Machine Learning , pages =

Deep Generative Learning via Schrödinger Bridge , author =. Proceedings of the 38th International Conference on Machine Learning , pages =. 2021 , editor =

2021
[36]

Stefano Peluchetti , journal=
[37]

Aligned Diffusion

Somnath, Vignesh Ram and Pariset, Matteo and Hsieh, Ya-Ping and Martinez, Maria Rodriguez and Krause, Andreas and Bunne, Charlotte , booktitle =. Aligned Diffusion. 2023 , editor =

2023
[38]

Forty-first International Conference on Machine Learning , year=

Light and Optimal Schr\"odinger Bridge Matching , author=. Forty-first International Conference on Machine Learning , year=
[39]

Communications on Pure and Applied Mathematics , volume =

The Data-Driven Schr\"odinger Bridge , author =. Communications on Pure and Applied Mathematics , volume =
[40]

Soft-constrained

Garg, Jhanvi and Zhang, Xianyang and Zhou, Quan , booktitle =. Soft-constrained. 2024 , editor =

2024
[41]

Schr\"odinger Bridge Flow for Unpaired Data Translation , volume =

De Bortoli, Valentin and Korshunova, Iryna and Mnih, Andriy and Doucet, Arnaud , booktitle =. Schr\"odinger Bridge Flow for Unpaired Data Translation , volume =. doi:10.52202/079017-3285 , editor =

work page doi:10.52202/079017-3285
[42]

Proceedings of The 28th International Conference on Artificial Intelligence and Statistics , pages =

Multi-marginal Schrödinger Bridges with Iterative Reference Refinement , author =. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics , pages =. 2025 , editor =

2025
[43]

Deep Momentum Multi-Marginal Schr\"odinger Bridge , volume =

Chen, Tianrong and Liu, Guan-Horng and Tao, Molei and Theodorou, Evangelos , booktitle =. Deep Momentum Multi-Marginal Schr\"odinger Bridge , volume =
[44]

Tree-Based Diffusion Schr\"odinger Bridge with Applications to Wasserstein Barycenters , volume =

Noble, Maxence and De Bortoli, Valentin and Doucet, Arnaud and Durmus, Alain , booktitle =. Tree-Based Diffusion Schr\"odinger Bridge with Applications to Wasserstein Barycenters , volume =
[45]

and Malkin, Nikolay and Fatras, Kilian and Atanackovic, Lazar and Zhang, Yanlei and Huguet, Guillaume and Wolf, Guy and Bengio, Yoshua , booktitle =

Tong, Alexander Y. and Malkin, Nikolay and Fatras, Kilian and Atanackovic, Lazar and Zhang, Yanlei and Huguet, Guillaume and Wolf, Guy and Bengio, Yoshua , booktitle =. Simulation-Free. 2024 , editor =

2024
[46]

2021 , eprint=

Regularized unbalanced optimal transport as entropy minimization with respect to branching Brownian motion , author=. 2021 , eprint=

2021
[47]

Journal of Optimization Theory and Applications , year =

On the Relation Between Optimal Transport and Schr\"odinger Bridges: A Stochastic Control Viewpoint , author =. Journal of Optimization Theory and Applications , year =
[48]

and Pavon, Michele , title =

Chen, Yongxin and Georgiou, Tryphon T. and Pavon, Michele , title =. SIAM Review , volume =. 2025 , doi =

2025
[49]

The Twelfth International Conference on Learning Representations , year=

Generalized Schr\"odinger Bridge Matching , author=. The Twelfth International Conference on Learning Representations , year=
[50]

Likelihood Training of Schr\"odinger Bridge using Forward-Backward

Tianrong Chen and Guan-Horng Liu and Evangelos Theodorou , booktitle=. Likelihood Training of Schr\"odinger Bridge using Forward-Backward
[51]

The Exploration in AI Today Workshop at ICML 2025 , year=

Branched Schr\"odinger Bridge Matching , author=. The Exploration in AI Today Workshop at ICML 2025 , year=

2025
[52]

2023 , eprint=

Unbalanced Diffusion Schr\"odinger Bridge , author=. 2023 , eprint=

2023
[53]

Nature biotechnology , volume=

Visualizing structure and transitions in high-dimensional biological data , author=. Nature biotechnology , volume=. 2019 , publisher=

2019
[54]

Nature communications , volume=

Context specificity of the EMT transcriptional response , author=. Nature communications , volume=. 2020 , publisher=

2020
[55]

Nature communications , volume=

Spearheading future omics analyses using dyngen, a multi-modal simulator of single cells , author=. Nature communications , volume=. 2021 , publisher=

2021
[56]

Science , volume=

Lineage tracing on transcriptional landscapes links state to fate during differentiation , author=. Science , volume=. 2020 , publisher=

2020
[57]

Proceedings of the NeurIPS 2021 Competitions and Demonstrations Track , pages =

Multimodal single cell data integration challenge: Results and lessons learned , author =. Proceedings of the NeurIPS 2021 Competitions and Demonstrations Track , pages =. 2022 , editor =

2021
[58]

2017 , eprint=

Scaling Algorithms for Unbalanced Transport Problems , author=. 2017 , eprint=

2017
[59]

Kingma and Jimmy Ba , title=

Diederik P. Kingma and Jimmy Ba , title=. 2015 , cdate=

2015
[60]

Journal of Machine Learning Research , volume=

Pot: Python optimal transport , author=. Journal of Machine Learning Research , volume=
[61]

2021 , eprint=

Minibatch optimal transport distances; analysis and applications , author=. 2021 , eprint=

2021
[62]

Cell , volume=

Optimal-transport analysis of single-cell gene expression identifies developmental trajectories in reprogramming , author=. Cell , volume=
[63]

Nature , volume=

Mapping cells through time and space with moscot , author=. Nature , volume=. 2025 , publisher=

2025
[64]

Cell Systems , volume=

DeST-OT: Alignment of spatiotemporal transcriptomics data , author=. Cell Systems , volume=. 2025 , publisher=

2025
[65]

Metric Flow Matching for Smooth Interpolations on the Data Manifold , volume =

Kapu\'. Metric Flow Matching for Smooth Interpolations on the Data Manifold , volume =. Advances in Neural Information Processing Systems , doi =
[66]

and Tong, Alexander , booktitle =

Zhang, Xi and Pu, Yuan and Kawamura, Yuki and Loza, Andrew and Bengio, Yoshua and Shung, Dennis L. and Tong, Alexander , booktitle =. Trajectory Flow Matching with Applications to Clinical Time Series Modelling , volume =. doi:10.52202/079017-3404 , editor =

work page doi:10.52202/079017-3404
[67]

GENOT: Entropic (Gromov) Wasserstein Flow Matching with Applications to Single-Cell Genomics , volume =

Klein, Dominik and Uscidda, Th\'. GENOT: Entropic (Gromov) Wasserstein Flow Matching with Applications to Single-Cell Genomics , volume =. Advances in Neural Information Processing Systems , doi =
[68]

2024 , eprint=

Scalable Simulation-free Entropic Unbalanced Optimal Transport , author=. 2024 , eprint=

2024
[69]

Proceedings of The 28th International Conference on Artificial Intelligence and Statistics , pages =

Efficient Trajectory Inference in Wasserstein Space Using Consecutive Averaging , author =. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics , pages =. 2025 , editor =

2025
[70]

2020 , editor =

Tong, Alexander and Huang, Jessie and Wolf, Guy and Van Dijk, David and Krishnaswamy, Smita , booktitle =. 2020 , editor =

2020
[71]

Bioinformatics , volume =

Zhang, Jiaqi and Larschan, Erica and Bigness, Jeremy and Singh, Ritambhara , title = ". Bioinformatics , volume =. 2024 , month =

2024
[72]

Proceedings of the 40th International Conference on Machine Learning , pages =

Action Matching: Learning Stochastic Dynamics from Samples , author =. Proceedings of the 40th International Conference on Machine Learning , pages =. 2023 , editor =

2023
[73]

A Computational Framework for Solving

Neklyudov, Kirill and Brekelmans, Rob and Tong, Alexander and Atanackovic, Lazar and Liu, Qiang and Makhzani, Alireza , booktitle =. A Computational Framework for Solving. 2024 , editor =

2024
[74]

Boffi and Eric Vanden-Eijnden , title =

Michael Albergo and Nicholas M. Boffi and Eric Vanden-Eijnden , title =. Journal of Machine Learning Research , year =
[75]

2024 , eprint=

Governing equation discovery of a complex system from snapshots , author=. 2024 , eprint=

2024
[76]

2025 , eprint=

Inferring biological processes with intrinsic noise from cross-sectional data , author=. 2025 , eprint=

2025
[77]

Nature communications , volume=

Generative modeling of single-cell time series with PRESCIENT enables prediction of cell trajectories with interventions , author=. Nature communications , volume=. 2021 , publisher=

2021
[78]

Trajectory Inference via Mean-field Langevin in Path Space , volume =

Chizat, L\'. Trajectory Inference via Mean-field Langevin in Path Space , volume =. Advances in Neural Information Processing Systems , editor =
[79]

2024 , eprint=

Trajectory inference for a branching SDE model of cell differentiation , author=. 2024 , eprint=

2024
[80]

The Annals of Applied Probability , volume=

Toward a mathematical theory of trajectory inference , author=. The Annals of Applied Probability , volume=. 2024 , publisher=

2024

Showing first 80 references.