mlsanityData to 14 Oct 2026

Learning Paths for Dynamic Measure Transport: A Control Perspective

arXiv 2511.03797 ↗First posted 5 Nov 2025stat.ML cs.LG stat.COcited by 1

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Abstract (arXiv)

We bring a control perspective to the problem of identifying paths of measures for sampling via dynamic measure transport (DMT). We highlight the fact that commonly used paths may be poor choices for DMT and connect existing methods for learning alternate paths to mean-field games. Based on these connections we pose a flexible family of optimization problems for identifying tilted paths of measures for DMT and advocate for the use of objective terms which encourage smoothness of the corresponding velocities. We present a numerical algorithm for solving these problems based on recent Gaussian process methods for solution of partial differential equations and demonstrate the ability of our method to recover more efficient and smooth transport models compared to those which use an untilted reference path.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 28 of its 37 references that are in the map. First posted on arXiv 5 Nov 2025.

Builds on

28 of 37 references.

References · 28

  1. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  2. 2022Flow Matching for Generative Modelingcited by 5,702
  3. 2018Neural Ordinary Differential Equationscited by 3,779
  4. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flowcited by 3,700
  5. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,323
  6. 2022Building Normalizing Flows with Stochastic Interpolantscited by 995
  7. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 939
  8. 2018FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Modelscited by 594
  9. 2022A Survey on Generative Diffusion Modelcited by 240
  10. 2024Adjoint Matching: Fine-tuning Flow and Diffusion Generative Models with Memoryless Stochastic Optimal Controlcited by 233
  11. 2021Path Integral Sampler: a stochastic control approach for samplingcited by 181
  12. 2023Denoising Diffusion Samplerscited by 149
16 more
  1. 2022An optimal control perspective on diffusion-based generative modelingcited by 147
  2. 2021Solving and Learning Nonlinear PDEs with Gaussian Processescited by 129
  3. 2025Adjoint Sampling: Highly Scalable Diffusion Samplers via Adjoint Matchingcited by 85
  4. 2015Operator-valued Kernels for Learning from Functional Response Datacited by 60
  5. 2023Learning Interpolations between Boltzmann Densitiescited by 43
  6. 2023A mean-field games laboratory for generative modelingcited by 28
  7. 2024Sampling in Unit Time with Kernel Fisher-Rao Flowcited by 27
  8. 2025Convergence of Deterministic and Stochastic Diffusion-Model Samplers: A Simple Analysis in Wasserstein Distancecited by 21
  9. 2024Dynamical Measure Transport and Neural PDE Solvers for Samplingcited by 20
  10. 2023Gradient Flows for Sampling: Mean-Field Models, Gaussian Approximations and Affine Invariancecited by 16
  11. 2023An Explicit Expansion of the Kullback-Leibler Divergence along its Fisher-Rao Gradient Flowcited by 16
  12. 2024Neural Sampling from Boltzmann Densities: Fisher-Rao Curves in the Wasserstein Geometrycited by 13
  13. 2025Optimal Scheduling of Dynamic Transportcited by 13
  14. 2024Measure transport with kernel mean embeddingscited by 11
  15. 2025Data-Efficient Kernel Methods for Learning Differential Equations and Their Solution Operators: Algorithms and Error Analysiscited by 7
  16. 2025PDPO: Parametric Density Path Optimizationcited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Barron Optimal Transport I: Generative Modelingcited by 0