这篇论文用扩散偏移解决了连续时间潜变量因果模型的可识别性难题，不需要稀疏性假设，还拿真实桥梁数据做了验证，做时间序列因果推断的值得看看。
研究团队在连续时间潜在随机微分方程（SDE）模型中提出了基于环境诱导的扩散协方差偏移的可识别性方法。在共享漂移但环境特定扩散协方差条件下，两个具有成对坐标方差比不同的对角扩散机制可将潜在坐标识别至置换和缩放。该结果首先在线性Ornstein-Uhlenbeck系统中证明，然后推广至一般加性噪声潜SDE。在温和光滑性下，瞬时漂移-雅可比因果图也可识别至相同置换。实验在合成系统和Hardanger大桥监测数据上验证了理论。
Disentangling Continuous-Time Latent Dynamics: Identifiability of Latent SDEs via Diffusion Shifts
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.