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

TL;DR

This paper introduces SDE Matching, a novel simulation-free training method for Latent SDEs that reduces computational costs while maintaining performance, inspired by Score- and Flow Matching algorithms.

Contribution

The paper presents a new training approach for Latent SDEs that eliminates the need for simulation, enabling scalable and efficient learning for time series modeling.

Findings

Achieves comparable performance to traditional methods

Significantly reduces computational complexity

Eliminates reliance on numerical simulations

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.