{
  "abstract": "Causal representation learning for time series has developed strong identifiability results in discrete-time latent causal models, but identifiability in continuous-time latent stochastic differential equation (SDE) models remains largely open. We address this gap using environment-induced shifts in diffusion covariance. We study additive-noise latent SDEs observed through an unknown nonlinear diffeomorphism, with shared drift but environment-specific diffusion covariance. We show that two diagonal diffusion regimes with pairwise distinct coordinate-wise variance ratios identify the latent coordinates up to permutation, coordinate-wise scaling, and a possible constant shift, without any sparsity assumption on the drift. We first prove this result for linear Ornstein-Uhlenbeck systems and then extend it to general additive-noise latent SDEs. Under mild smoothness, the instantaneous drift-Jacobian causal graph is identifiable up to the same permutation. We propose a two-stage estimator for latent disentanglement and optional graph recovery; experiments on synthetic systems confirm the predicted identifiability boundary, and an application to Hardanger Bridge monitoring data illustrates the approach on real sensor trajectories.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.28228",
  "author_total": 5,
  "authors": [
    {
      "name": "Yuanyuan Wang"
    },
    {
      "name": "Wenjie Wang"
    },
    {
      "name": "Haoxuan Li"
    },
    {
      "name": "Mingming Gong"
    },
    {
      "name": "Kun Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6g6jeg48f3za5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.28228",
  "fulltext_url": null,
  "id": "6g6jeg48f3za5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.28228",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "2207|Control Systems and Identification"
    ]
  ],
  "openalex": "W7166570524",
  "pdf_url": "https://arxiv.org/pdf/2606.28228",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6g6jeg48f3za5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:14Z",
      "native_id": "2606.28228",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.28228"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Disentangling Continuous-Time Latent Dynamics: Identifiability of Latent SDEs via Diffusion Shifts",
  "title_text": "Disentangling Continuous-Time Latent Dynamics: Identifiability of Latent SDEs via Diffusion Shifts",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:14Z",
  "url": "https://research.draconitic.com/paper/6g6jeg48f3za5",
  "venue": "arXiv",
  "versions": []
}