{
  "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 .",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.16138",
  "author_total": 3,
  "authors": [
    {
      "name": "Henry D. Smith"
    },
    {
      "name": "Brian L. Trippe"
    },
    {
      "name": "Scott W. Linderman"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b9jbg06nb8rvy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.16138",
  "fulltext_url": null,
  "id": "b9jbg06nb8rvy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.16138",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Gaussian Processes and Bayesian Inference"
    ]
  ],
  "openalex": "W7164931031",
  "pdf_url": "https://arxiv.org/pdf/2606.16138",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b9jbg06nb8rvy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:58Z",
      "native_id": "2606.16138",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.16138"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Closing the Approximation Gap in Simulation-free Latent SDEs",
  "title_text": "Closing the Approximation Gap in Simulation-free Latent SDEs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:58Z",
  "url": "https://research.draconitic.com/paper/b9jbg06nb8rvy",
  "venue": "arXiv",
  "versions": []
}