mlsanityData to 14 Oct 2026

Neural Stochastic Flows: Solver-Free Modelling and Inference for SDE Solutions

arXiv 2510.25769 ↗First posted 29 Oct 2025cs.LG stat.MLcited by 5

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Abstract (arXiv)

Stochastic differential equations (SDEs) are well suited to modelling noisy and irregularly sampled time series found in finance, physics, and machine learning. Traditional approaches require costly numerical solvers to sample between arbitrary time points. We introduce Neural Stochastic Flows (NSFs) and their latent variants, which directly learn (latent) SDE transition laws using conditional normalising flows with architectural constraints that preserve properties inherited from stochastic flows. This enables one-shot sampling between arbitrary states and yields up to two orders of magnitude speed-ups at large time gaps. Experiments on synthetic SDE simulations and on real-world tracking and video data show that NSFs maintain distributional accuracy comparable to numerical approaches while dramatically reducing computation for arbitrary time-point sampling.

Key facts. Cited by 5 papers in the map (data through 14 Oct 2026). Builds on 39 of its 58 references that are in the map. First posted on arXiv 29 Oct 2025.

Builds on

39 of 58 references.

References · 39

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  3. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,255
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  11. 2018Glow: Generative Flow with Invertible 1x1 Convolutionscited by 1,545
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27 more
  1. 2023Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusioncited by 459
  2. 2015A Recurrent Latent Variable Model for Sequential Datacited by 362
  3. 2020Scalable Gradients for Stochastic Differential Equationscited by 271
  4. 2022On Neural Differential Equationscited by 268
  5. 2018Stochastic Video Generation with a Learned Priorcited by 245
  6. 2019Latent ODEs for Irregularly-Sampled Time Seriescited by 183
  7. 2016Structured Inference Networks for Nonlinear State Space Modelscited by 182
  8. 2019Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limitcited by 176
  9. 2019Learning Likelihoods with Conditional Normalizing Flowscited by 172
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  14. 2020Stochastic Latent Residual Video Predictioncited by 108
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  18. 2015Hierarchical Variational Modelscited by 89
  19. 2020Coupling-based Invertible Neural Networks Are Universal Diffeomorphism Approximatorscited by 85
  20. 2018Learning unknown ODE models with Gaussian processescited by 54
  21. 2024Stable Neural Stochastic Differential Equations in Analyzing Irregular Time Series Datacited by 36
  22. 2023Neural Continuous-Discrete State Space Models for Irregularly-Sampled Time Seriescited by 29
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 5.

5 papers.

  1. 2026Strong Stochastic Flow Mapscited by 6
  2. 2026Learning Continuous Neural Representation of Stochastic Hybrid Systemscited by 0
  3. 2026Gaussian Flow Dynamics: Simulation-Free Neural SDE Learning Beyond One-Time Marginalscited by 0
  4. 2026Langevin Flow Maps: Efficient Molecular Dynamics and Transition Path Samplingcited by 0
  5. 2026Scan-Parallel Variational Inference for event-driven Latent Jump Modelscited by 0