mlsanityData to 7 Oct 2026

Conditional Lagrangian Wasserstein Flow for Time Series Imputation

arXiv 2410.07550 ↗First posted 10 Oct 2024cs.LG stat.MLcited by 3

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Abstract (arXiv)

Time series imputation is important for numerous real-world applications. To overcome the limitations of diffusion model-based imputation methods, e.g., slow convergence in inference, we propose a novel method for time series imputation in this work, called Conditional Lagrangian Wasserstein Flow (CLWF). Following the principle of least action in Lagrangian mechanics, we learn the velocity by minimizing the corresponding kinetic energy. Moreover, to enhance the model's performance, we estimate the gradient of a task-specific potential function using a time-dependent denoising autoencoder and integrate it into the base estimator to reduce the sampling variance. Finally, the proposed method demonstrates competitive performance compared to other state-of-the-art imputation approaches.

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 37 of its 63 references that are in the map. First posted on arXiv 10 Oct 2024.

Builds on

37 of 63 references.

References · 37

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  3. 2022Flow Matching for Generative Modelingcited by 5,426
  4. 2018Neural Ordinary Differential Equationscited by 3,733
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  7. 2022Are Transformers Effective for Time Series Forecasting?cited by 1,400
  8. 2022TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysiscited by 1,030
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  10. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 897
  11. 2023Improving and generalizing flow-based generative models with minibatch optimal transportcited by 835
  12. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modelingcited by 594
25 more
  1. 2021CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputationcited by 577
  2. 2022Rectified Flow: A Marginal Preserving Approach to Optimal Transportcited by 277
  3. 2023Multisample Flow Matching: Straightening Flows with Minibatch Couplingscited by 267
  4. 2021Likelihood Training of Schr"odinger Bridge using Forward-Backward SDEs Theorycited by 216
  5. 2021Path Integral Sampler: a stochastic control approach for samplingcited by 175
  6. 2019GP-VAE: Deep Probabilistic Time Series Imputationcited by 171
  7. 2022Less Is More: Fast Multivariate Time Series Forecasting with Light Sampling-oriented MLP Structurescited by 158
  8. 2022An optimal control perspective on diffusion-based generative modelingcited by 145
  9. 2020OT-Flow: Fast and Accurate Continuous Normalizing Flows via Optimal Transportcited by 143
  10. 2022Action Matching: Learning Stochastic Dynamics from Samplescited by 94
  11. 2023Predict, Refine, Synthesize: Self-Guiding Diffusion Models for Probabilistic Time Series Forecastingcited by 86
  12. 2023Simulation-free Schr"odinger bridges via score and flow matchingcited by 81
  13. 2020Solving high-dimensional Hamilton-Jacobi-Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path spacecited by 80
  14. 2023Diffusion Models for Time Series Applications: A Surveycited by 72
  15. 2019Wasserstein Proximal Algorithms for the Schr"odinger Bridge Problem: Density Control with Nonlinear Driftcited by 50
  16. 2022Entropic Neural Optimal Transport via Diffusion Processescited by 49
  17. 2023A Computational Framework for Solving Wasserstein Lagrangian Flowscited by 43
  18. 2023Generalized Schr"odinger Bridge Matchingcited by 40
  19. 2022Modeling Temporal Data as Continuous Functions with Stochastic Process Diffusioncited by 39
  20. 2023Stochastic Optimal Control Matchingcited by 39
  21. 2022Stochastic Optimal Control for Collective Variable Free Sampling of Molecular Transition Pathscited by 36
  22. 2019Potential Flow Generator with L2 Optimal Transport Regularity for Generative Modelscited by 31
  23. 2023Provably Convergent Schr"odinger Bridge with Applications to Probabilistic Time Series Imputationcited by 26
  24. 2024The Rise of Diffusion Models in Time-Series Forecastingcited by 25
  25. 2024Stochastic Optimal Control for Diffusion Bridges in Function Spacescited by 16

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 1; 2026: 2.

3 papers.

  1. 2026A Call to Lagrangian Action: Learning Population Mechanics from Temporal Snapshotscited by 1
  2. 2025STDiff: A State Transition Diffusion Framework for Time Series Imputation in Industrial Systemscited by 0
  3. 2026PAMF: Prior-Aware Multimodal Fusion for Incomplete Time Series Datacited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2026Analyzing and Improving Diffusion Models for Time-Series Data Imputation: A Proximal Recursion Perspective
  2. 2025LSCD: Lomb-Scargle Conditioned Diffusion for Time series Imputation
  3. 2025Diffusion Transformers for Imputation: Statistical Efficiency and Uncertainty Quantification
  4. 2026Discretizing Continuous Time Series for Imputation with Masked Diffusion Training
  5. 2024MTSCI: A Conditional Diffusion Model for Multivariate Time Series Consistent Imputation
  6. 2026RDDMPI: Residual Denoising Diffusion Model for Probabilistic Multivariate Time Series Imputation
  7. 2024Latent Space Score-based Diffusion Model for Probabilistic Multivariate Time Series Imputation
  8. 2024Rethinking the Diffusion Models for Numerical Tabular Data Imputation from the Perspective of Wasserstein Gradient Flow