Closing the Approximation Gap in Simulation-free Latent SDEs
Abstract
Recovering dynamical systems from noisy observations is a recurring challenge across scientific domains, including neuroscience and physics. Latent stochastic differential equations (SDEs) address this by modeling the system as an unobserved state that evolves according to a learnable SDE and generates the observations. Variational inference (VI) provides a tractable objective for fitting latent SDEs. Traditional VI algorithms evaluate this objective by numerical simulation over a time discretization, trading fidelity for computational cost. A recent class of algorithms, simulation-free VI, sidesteps this tradeoff by parameterizing the posterior through its instantaneous marginals rather than its drift. In this work, we show that the efficiency of existing simulation-free VI algorithms comes at a price: their parameterizations restrict the approximate posterior to a subset of the SDEs available to simulation-based methods, degrading posterior inference and parameter learning. We propose Helmholtz-SDE, a simulation-free VI algorithm that closes this gap by optimizing over path laws compatible with a prescribed collection of marginals. Helmholtz-SDE recovers dynamics more faithfully than prior simulation-free methods, with the largest gains under high posterior uncertainty. It further matches the performance of simulation-based VI at a fraction of the runtime. Code is available at https://github.com/lindermanlab/helmholtz-sde .
Related
- Simulation-Free Learning of GP-SDEs from Irregular Observations
- Further Approaches of Dynamical Low-Rank Approximation for SDEs
- Existence of Dynamical Low-Rank Approximation for SDEs with Locally Lipschitz Coefficients
- Disentangling Continuous-Time Latent Dynamics: Identifiability of Latent SDEs via Diffusion Shifts
- Sharp Approximation Rates for Neural Networks with Affine Latent Parameterizations
BibTeX
@misc{smith2026closing,
title = {{Closing the Approximation Gap in Simulation-free Latent SDEs}},
author = {Henry D. Smith and Brian L. Trippe and Scott W. Linderman},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.16138},
eprint = {2606.16138},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.16138},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Closing the Approximation Gap in Simulation-free Latent SDEs
AU - Henry D. Smith
AU - Brian L. Trippe
AU - Scott W. Linderman
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2606.16138
UR - https://arxiv.org/abs/2606.16138
AB - Recovering dynamical systems from noisy observations is a recurring challenge across scientific domains, including neuroscience and physics. Latent stochastic differential equations (SDEs) address this by modeling the system as an unobserved state that evolves according to a learnable SDE and generates the observations. Variational inference (VI) provides a tractable objective for fitting latent SDEs. Traditional VI algorithms evaluate this objective by numerical simulation over a time discretization, trading fidelity for computational cost. A recent class of algorithms, simulation-free VI, sidesteps this tradeoff by parameterizing the posterior through its instantaneous marginals rather than its drift. In this work, we show that the efficiency of existing simulation-free VI algorithms comes at a price: their parameterizations restrict the approximate posterior to a subset of the SDEs available to simulation-based methods, degrading posterior inference and parameter learning. We propose Helmholtz-SDE, a simulation-free VI algorithm that closes this gap by optimizing over path laws compatible with a prescribed collection of marginals. Helmholtz-SDE recovers dynamics more faithfully than prior simulation-free methods, with the largest gains under high posterior uncertainty. It further matches the performance of simulation-based VI at a fraction of the runtime. Code is available at https://github.com/lindermanlab/helmholtz-sde .
ER -