Disentangling Continuous-Time Latent Dynamics: Identifiability of Latent SDEs via Diffusion Shifts

• URL: http://arxiv.org/abs/2606.28228v1
• Date: Fri, 26 Jun 2026 16:18:28 GMT
• Title: Disentangling Continuous-Time Latent Dynamics: Identifiability of Latent SDEs via Diffusion Shifts
• Abstract summary: identifiability in continuous-time latent differential equation models remains largely open.<n>We study additive-noise latent SDEs observed through an unknown nonlinear diffeomorphism.<n>We propose a two-stage estimator for latent disentanglement and optional graph recovery.
• Score: 60.95873409673775
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 and scaling, 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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