mlsanityData to 7 Oct 2026

Multiscale Supervised Unbalanced Optimal Transport Flow Matching

arXiv 2605.16529 ↗First posted 15 May 2026cs.LG math.OCcited by 0

On the map: Diffusion models → Flow matching, time series and science

Abstract (arXiv)

Unbalanced optimal transport (UOT) provides a principled framework for modeling single-cell transitions and birth-death dynamics, but its high computational cost limits scalability to large-scale datasets. Although single-cell data often contain hierarchical annotations and known transition priors, existing UOT approximations rarely exploit this multiscale structure or prior knowledge. We introduce Multiscale Supervised Unbalanced Optimal Transport Flow Matching (MUST-FM), a simulation-free framework that scales UOT by leveraging hierarchical data structure. MUST-FM further supports an optional supervised formulation that incorporates transition priors, such as cell lineages, to guide the learning of displacement fields and mass variations. Experiments show that MUST-FM reduces computational overhead while achieving robust and biologically meaningful trajectory inference, enabling dynamic modeling of atlas-scale single-cell datasets.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 23 of its 55 references that are in the map. First posted on arXiv 15 May 2026.

Builds on

23 of 55 references.

Closest ancestors · 6

Same direction, newest first

  1. 2026WFR-MFM: One-Step Inference for Dynamic Unbalanced Optimal Transport28 Jan
  2. 2026WFR-FM: Simulation-Free Dynamic Unbalanced Optimal Transport11 Jan
  3. 2025Joint Velocity-Growth Flow Matching for Single-Cell Dynamics Modeling19 May
  4. 2023GENOT: Entropic (Gromov) Wasserstein Flow Matching with Applications to Single-Cell Genomics13 Oct
  5. 2023Improving and generalizing flow-based generative models with minibatch optimal transport1 Feb
  6. 2022Flow Matching for Generative Modeling6 Oct

Other references · 17

  1. 2018Neural Ordinary Differential Equationscited by 3,733
  2. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,277
  3. 2022Building Normalizing Flows with Stochastic Interpolantscited by 964
  4. 2020TrajectoryNet: A Dynamic Optimal Transport Network for Modeling Cellular Dynamicscited by 155
  5. 2015Optimal Entropy-Transport problems and a new Hellinger-Kantorovich distance between positive measurescited by 138
  6. 2022Action Matching: Learning Stochastic Dynamics from Samplescited by 94
  7. 2019On Robustness of Neural Ordinary Differential Equationscited by 83
  8. 2022Manifold Interpolating Optimal-Transport Flows for Trajectory Inferencecited by 63
  9. 2023Unbalancedness in Neural Monge Maps Improves Unpaired Domain Translationcited by 32
  10. 2024Learning stochastic dynamics from snapshots through regularized unbalanced optimal transportcited by 30
  11. 2018Optimal Transport: Fast Probabilistic Approximation with Exact Solverscited by 27
  12. 2022Low-rank Optimal Transport: Approximation, Statistics and Debiasingcited by 21
5 more
  1. 2017Multiscale Strategies for Computing Optimal Transportcited by 18
  2. 2025Variational Regularized Unbalanced Optimal Transport: Single Network, Least Actioncited by 10
  3. 2025Integrating Dynamical Systems Modeling with Spatiotemporal scRNA-seq Data Analysiscited by 9
  4. 2023Unbalanced Low-rank Optimal Transport Solverscited by 7
  5. 2022Supervised Optimal Transportcited by 4

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  1. 2026Simulation-free Unbalanced Dynamic Optimal Transport with General Growth Penalty
  2. 2026TempoBridge: Source-Conditioned Flow Matching with Optimal Transport Couplings for Single-Cell Population Transitions
  3. 2026Multimarginal flow matching with optimal transport potentials
  4. 2026MIOFlow 2.0: A unified framework for inferring cellular stochastic dynamics from single cell and spatial transcriptomics data
  5. 2026Optimal Transport Flow Matching by Design
  6. 2026From Snapshots to Trajectories: Learning Single-Cell Gene Expression Dynamics via Conditional Flow Matching
  7. 2026FLUX: Geometry-Aware Longitudinal Flow Matching with Mixture of Experts
  8. 2026TRACE: Transport Alignment Conformal Prediction via Diffusion and Flow Matching Models