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

2025/02/04 by Grigory Bartosh, Dmitry Vetrov, Bartosh, Grigory +3 · 2 voices · 8 citations
Computer Science · Mathematics · #Applied mathematics #Bayesian Modeling and Causal Inference #Computer science #Gaussian Processes and Bayesian Inference #Machine Learning and Data Classification #Matching (statistics) #Mathematical optimization #Mathematics #Physics #Scalability #Statistics #Stochastic differential equation #Training (meteorology)

paper · pdf · open access · doi:10.48550/arxiv.2502.02472

published in UvA-DARE (University of Amsterdam) (University of Amsterdam)

openalex publication_date 2025/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Doob's Lagrangian: A Sample-Efficient Variational Approach to Transition Path Sampling
• Neural Ordinary Differential Equations

Cited by

• Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise
• Diffusion differentiable resampling
• Recursive Entropic Variational Inference for Nonlinear State-Space Models
• Curly Flow Matching for Learning Non-gradient Field Dynamics
• Neural Stochastic Flows: Solver-Free Modelling and Inference for SDE Solutions
• Efficient Inference for Coupled Hidden Markov Models in Continuous Time and Discrete Space
• SING: SDE Inference via Natural Gradients
• Modelisation of chaotic systems with a latent Stochastic Differential Equation

Discussions

• Really excited about this! We note a connection between diffusion/flow models and neural/latent SDEs. We show how to use this for simulation-free learning of fully flexible SDEs. We refer to this as S [bsky, 50 points, 0 comments]
• 🔁 SDE Matching: Scalable and Simulation-Free Training of Latent Stochastic Differential Equations By @gbarto.bsky.social , Dmitry Vetrov, @canaesseth.bsky.social 📜 arxiv.org/abs/2502.02472 🧵5 / 8 [bsky, 4 points, 1 comments]

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• Scalable Inference in SDEs by Direct Matching of the Fokker-Planck-Kolmogorov Equation