mlsanityData to 7 Oct 2026

SDE Matching: Scalable and Simulation-Free Training of Latent Stochastic Differential Equations

arXiv 2502.02472 ↗First posted 4 Feb 2025stat.ML cs.LGcited by 19

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Abstract (arXiv)

The Latent Stochastic Differential Equation (SDE) is a powerful tool for time series and sequence modeling. However, training Latent SDEs typically relies on adjoint sensitivity methods, which depend on simulation and backpropagation through approximate SDE solutions, which limit scalability. In this work, we propose SDE Matching, a new simulation-free method for training Latent SDEs. Inspired by modern Score- and Flow Matching algorithms for learning generative dynamics, we extend these ideas to the domain of stochastic dynamics for time series and sequence modeling, eliminating the need for costly numerical simulations. Our results demonstrate that SDE Matching achieves performance comparable to adjoint sensitivity methods while drastically reducing computational complexity.

Key facts. Cited by 19 papers in the map (data through 7 Oct 2026). Builds on 40 of its 66 references that are in the map. First posted on arXiv 4 Feb 2025.

Builds on

40 of 66 references.

References · 40

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2020Denoising Diffusion Implicit Modelscited by 9,655
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  4. 2022Flow Matching for Generative Modelingcited by 5,426
  5. 2014Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translationcited by 4,016
  6. 2018Neural Ordinary Differential Equationscited by 3,733
  7. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flowcited by 3,550
  8. 2016Density estimation using Real NVPcited by 2,029
  9. 2018Glow: Generative Flow with Invertible 1x1 Convolutionscited by 1,539
  10. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,315
  11. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 897
  12. 2021Maximum Likelihood Training of Score-Based Diffusion Modelscited by 670
28 more
  1. 2020How to train your neural ODE: the world of Jacobian and kinetic regularizationcited by 228
  2. 2023Practical and Asymptotically Exact Conditional Sampling in Diffusion Modelscited by 218
  3. 2019Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limitcited by 168
  4. 2020Stochastic Normalizing Flowscited by 156
  5. 2021Neural Flows: Efficient Alternative to Neural ODEscited by 99
  6. 2020Learning Differential Equations that are Easy to Solvecited by 81
  7. 2021Efficient and Accurate Gradients for Neural SDEscited by 68
  8. 2019Elements of Sequential Monte Carlocited by 60
  9. 2018Learning unknown ODE models with Gaussian processescited by 54
  10. 2023Diffusion Models With Learned Adaptive Noisecited by 50
  11. 2024Neural Flow Diffusion Models: Learnable Forward Process for Improved Diffusion Modellingcited by 43
  12. 2020"Hey, that's not an ODE": Faster ODE Adjoints via Seminormscited by 35
  13. 2024Stable Neural Stochastic Differential Equations in Analyzing Irregular Time Series Datacited by 35
  14. 2020Causal models for dynamical systemscited by 34
  15. 2023Where to Diffuse, How to Diffuse, and How to Get Back: Automated Learning for Multivariate Diffusionscited by 27
  16. 2024Doob's Lagrangian: A Sample-Efficient Variational Approach to Transition Path Samplingcited by 25
  17. 2018Black-box Variational Inference for Stochastic Differential Equationscited by 24
  18. 2019Infinitely deep neural networks as diffusion processescited by 21
  19. 2024Trajectory Flow Matching with Applications to Clinical Time Series Modelingcited by 21
  20. 2023Neural Diffusion Modelscited by 20
  21. 2023DiffEnc: Variational Diffusion with a Learned Encodercited by 16
  22. 2023Amortized Reparametrization: Efficient and Scalable Variational Inference for Latent SDEscited by 15
  23. 2015Deep Temporal Sigmoid Belief Networks for Sequence Modelingcited by 13
  24. 2023Variational Gaussian Process Diffusion Processescited by 10
  25. 2023Variational Inference for SDEs Driven by Fractional Noisecited by 9
  26. 2024Amortized Control of Continuous State Space Feynman-Kac Model for Irregular Time Seriescited by 9
  27. 2018Adaptive Path-Integral Autoencoder: Representation Learning and Planning for Dynamical Systemscited by 7
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 9; 2026: 10.

19 papers.

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  1. 2025Curly Flow Matching for Learning Non-gradient Field Dynamicscited by 17
  2. 2025In-Context Learning of Stochastic Differential Equations with Foundation Inference Modelscited by 7
  3. 2025SING: SDE Inference via Natural Gradientscited by 4
  4. 2025A Jump-Diffusion Framework for Irregular Time Series Generationcited by 2
  5. 2025Neural Stochastic Flows: Solver-Free Modelling and Inference for SDE Solutionscited by 2
  6. 2025Diffusion differentiable resamplingcited by 2
  7. 2026Is Flow Matching Just Trajectory Replay for Sequential Data?cited by 2
  8. 2025Stochastic Optimal Control for Continuous-Time fMRI Representation Learningcited by 1
  9. 2026Neural Stochastic Processes for Satellite Precipitation Refinementcited by 1
  10. 2026First-Order Trajectory Matching: Fast Ensemble Predictions of Chaotic, Turbulent, Stochastic Systemscited by 1
  11. 2025Efficient Inference for Coupled Hidden Markov Models in Continuous Time and Discrete Spacecited by 0
  12. 2025Recursive Entropic Variational Inference for Nonlinear State-Space Modelscited by 0
7 more
  1. 2026Introduction to Stochastic Differential Equations for Generative Machine Learning: A Variational Perspectivecited by 0
  2. 2026Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noisecited by 0
  3. 2026Simulation-free and finite-time diffusion modelcited by 0
  4. 2026One-Step Generative Surrogate Models via Block-Triangular Joint Driftingcited by 0
  5. 2026Continuous-Time Trajectory Generation from Discrete Observations with Stochasticitycited by 0
  6. 2026Simulation-Free Learning of GP-SDEs from Irregular Observationscited by 0
  7. 2026Learning Continuous Neural Representation of Stochastic Hybrid Systemscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025TimeFlow: Towards Stochastic-Aware and Efficient Time Series Generation via Flow Matching Modeling
  2. 2026Training-free score-based diffusion for parameter-dependent stochastic dynamical systems
  3. 2025Generative Latent Neural PDE Solver using Flow Matching
  4. 2024Generative Modelling with High-Order Langevin Dynamics
  5. 2024A Training-Free Conditional Diffusion Model for Learning Stochastic Dynamical Systems
  6. 2025Operator Flow Matching for Timeseries Forecasting
  7. 2025Hierarchical Stochastic Differential Equation Models for Latent Manifold Learning in Neural Time Series
  8. 2023Closing the ODE-SDE gap in score-based diffusion models through the Fokker-Planck equation