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

NeurIPS 2026 · Probabilistic and scientific modeling › Causal discovery · approach: Latent-variable causal estimation · 0 citations (OpenAlex)

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Shows that two diagonal diffusion regimes with distinct coordinate-wise variance ratios identify latent SDE coordinates up to monomial affine maps (no drift sparsity), and proposes a two-stage estimator validated on synthetic data and a Hardanger Bridge case study.

Problem

Identifiability of latent coordinates and drift-Jacobian causal graph in continuous-time latent SDEs observed only through an unknown nonlinear diffeomorphism, where discrete-time CRL results do not apply.

Approach

Environment-induced shifts in diagonal diffusion covariance (with shared drift) act as side information; two regimes with pairwise distinct coordinate-wise variance ratios pin the Jacobian of the coordinate change to a monomial matrix via quadratic-variation matching and a simple-spectrum argument, without drift sparsity.

Key results

• Under Distinct ratios on synthetic d=5 nonlinear drift, MCC 0.9977 ± 0.0001 and GMR 1.0000 versus 0.7331 MCC for one regime control.
• On the Hardanger Bridge case study (K=10 seeds, d=5), TI-split regimes give MCC 0.806 and GMR 0.877 versus 0.660 / 0.813 for one regime.
• Synthetic dense linear, sparse linear and nonlinear families all show Distinct ratios substantially outperforming both controls on MCC and monomial score.

Limitations

• Requires invertible diffeomorphic observation map and additive state-independent diffusion
• Assumes known two-regime labels with shared drift; imperfect regime labels not handled
• Real-world study lacks ground-truth latents, so only cross-seed reproducibility is evaluated

Experimental setup

Datasets: Hardanger Bridge accelerometer recordings (16 channels, wind measurements for regimes) synthetic latent SDE trajectories (OU, sparse linear, nonlinear drifts)

Benchmarks: synthetic latent SDE benchmarks (dense linear OU, sparse linear, nonlinear drift; d=5) Hardanger Bridge accelerometer case study

Metrics: MCC monomial score GMR cross-seed MCC cross-seed GMR

Baselines: One regime (control) Proportional diffusions (control) Shuffled TI labels (control)

Builds on: identifiable nonlinear ICA independent mechanism analysis LEAP CaRiNG

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