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Fast and Smooth Interpolation on Wasserstein Space

arXiv 2010.12101 ↗First posted 22 Oct 2020math.ST math.OC stat.THcited by 21

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Abstract (arXiv)

We propose a new method for smoothly interpolating probability measures using the geometry of optimal transport. To that end, we reduce this problem to the classical Euclidean setting, allowing us to directly leverage the extensive toolbox of spline interpolation. Unlike previous approaches to measure-valued splines, our interpolated curves (i) have a clear interpretation as governing particle flows, which is natural for applications, and (ii) come with the first approximation guarantees on Wasserstein space. Finally, we demonstrate the broad applicability of our interpolation methodology by fitting surfaces of measures using thin-plate splines.

Key facts. Cited by 21 papers in the map (data through 7 Oct 2026). First posted on arXiv 22 Oct 2020.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 2; 2022: 2; 2023: 3; 2024: 5; 2025: 5; 2026: 4.

21 papers.

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  1. 2023A Computational Framework for Solving Wasserstein Lagrangian Flowscited by 43
  2. 2021Towards a mathematical theory of trajectory inferencecited by 31
  3. 2022Riemannian Metric Learning via Optimal Transportcited by 21
  4. 2023Algorithms for mean-field variational inference via polyhedral optimization in the Wasserstein spacecited by 20
  5. 2024Wasserstein Wormhole: Scalable Optimal Transport Distance with Transformerscited by 14
  6. 2024Partially Observed Trajectory Inference using Optimal Transport and a Dynamics Priorcited by 13
  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. 2024Parametric model reduction of mean-field and stochastic systems via higher-order action matchingcited by 8
  11. 2025Learning of Population Dynamics: Inverse Optimization Meets JKO Schemecited by 6
  12. 2025DICE: Discrete inverse continuity equation for learning population dynamicscited by 6
9 more
  1. 2021On the Latent Holes of VAEs for Text Generationcited by 4
  2. 2024Squared Wasserstein-2 Distance for Efficient Reconstruction of Stochastic Differential Equationscited by 3
  3. 2022Wassersplines for Neural Vector Field--Controlled Animationcited by 2
  4. 2023Generative modeling of time-dependent densities via optimal transport and projection pursuitcited by 2
  5. 2026Two-Parameter Flows for Learning Population Dynamics of Physical Systemscited by 1
  6. 2025From Kinetic Theory to AI: a Rediscovery of High-Dimensional Divergences and Their Propertiescited by 0
  7. 2026A Temporal Spatial Minimax Rate for Smoothly-Varying Distributions in Wasserstein Spacecited by 0
  8. 2026Intrinsic Flow Matching on Quantum Pure-State Manifolds with Phase-Aligned Transportcited by 0
  9. 2026Trajectory inference via Acceleration Matchingcited by 0