Disentangling Continuous-Time Latent Dynamics: Identifiability of Latent SDEs via Diffusion Shifts
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.
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BibTeX
@misc{wang2026disentangling,
title = {{Disentangling Continuous-Time Latent Dynamics: Identifiability of Latent SDEs via Diffusion Shifts}},
author = {Yuanyuan Wang and Wenjie Wang and Haoxuan Li and Mingming Gong and Kun Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.28228},
eprint = {2606.28228},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.28228},
}
RIS
TY - UNPB
TI - Disentangling Continuous-Time Latent Dynamics: Identifiability of Latent SDEs via Diffusion Shifts
AU - Yuanyuan Wang
AU - Wenjie Wang
AU - Haoxuan Li
AU - Mingming Gong
AU - Kun Zhang
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2606.28228
UR - https://arxiv.org/abs/2606.28228
AB - 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.
ER -