Causal representation learning cracks continuous-time latent SDE identifiability

A team of researchers including Yuanyuan Wang, Wenjie Wang, Haoxuan Li, Mingming Gong, and Kun Zhang has tackled a long-standing gap in causal representation learning: identifying latent dynamics in continuous-time stochastic differential equation (SDE) models. While discrete-time latent causal models have strong identifiability results, continuous-time models have remained largely open. Their paper, posted on arXiv, leverages environment-induced shifts in diffusion covariance to break the symmetry. Specifically, they study additive-noise latent SDEs observed through an unknown nonlinear diffeomorphism, where the drift is shared across environments but the diffusion (noise) covariance varies.

By assuming two diagonal diffusion regimes with pairwise distinct coordinate-wise variance ratios, they prove that the latent coordinates are identifiable up to permutation and scaling – no sparsity constraints on drift required. The result first holds for linear Ornstein–Uhlenbeck systems and then generalizes to arbitrary additive-noise SDEs. They also show the instantaneous drift-Jacobian causal graph is identifiable under mild smoothness. A two-stage estimator handles latent disentanglement and optional graph recovery. Experiments on synthetic systems confirm the predicted identifiability boundary, and an application to Hardanger Bridge monitoring data demonstrates the method on real sensor trajectories.