mlsanityData to 7 Oct 2026

Measure-valued spline curves: an optimal transport viewpoint

arXiv 1801.03186 ↗First posted 9 Jan 2018math.OC cs.SY eess.SYcited by 17

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Abstract (arXiv)

The aim of this article is to introduce and address the problem to smoothly interpolate (empirical) probability measures. To this end, we lift the concept of a spline curve from the setting of points in a Euclidean space that that of probability measures, using the framework of optimal transport.

Key facts. Cited by 17 papers in the map (data through 7 Oct 2026). First posted on arXiv 9 Jan 2018.

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Citing papers per year: 2021: 1; 2022: 4; 2023: 5; 2024: 2; 2025: 5.

17 papers.

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  1. 2023A Computational Framework for Solving Wasserstein Lagrangian Flowscited by 43
  2. 2023Deep Momentum Multi-Marginal Schr"odinger Bridgecited by 40
  3. 2021Towards a mathematical theory of trajectory inferencecited by 31
  4. 2023Scalable Optimal Transport Methods in Machine Learning: A Contemporary Surveycited by 27
  5. 2022Riemannian Metric Learning via Optimal Transportcited by 21
  6. 2023Tree-Based Diffusion Schr"odinger Bridge with Applications to Wasserstein Barycenterscited by 16
  7. 2025Multi-Marginal Stochastic Flow Matching for High-Dimensional Snapshot Data at Irregular Time Pointscited by 11
  8. 2025Trajectory Inference with Smooth Schr"odinger Bridgescited by 10
  9. 2024Efficient Trajectory Inference in Wasserstein Space Using Consecutive Averagingcited by 9
  10. 2022Neural ODE Control for Trajectory Approximation of Continuity Equationcited by 8
  11. 2025OAT-FM: Optimal Acceleration Transport for Improved Flow Matchingcited by 7
  12. 2023Bures-Wasserstein Means of Graphscited by 6
5 more
  1. 2025Learning of Population Dynamics: Inverse Optimization Meets JKO Schemecited by 6
  2. 2024Go With the Flow: Fast Diffusion for Gaussian Mixture Modelscited by 5
  3. 2022Wassersplines for Neural Vector Field--Controlled Animationcited by 2
  4. 2022The GenCol algorithm for high-dimensional optimal transport: general formulation and application to barycenters and Wasserstein splinescited by 1
  5. 2025From Kinetic Theory to AI: a Rediscovery of High-Dimensional Divergences and Their Propertiescited by 0