The paper investigates how to recover the parameters of a multivariate Ornstein-Uhlenbeck process using only steady-state observational and interventional data. It proves that a single intervention per strongly connected component of the drift graph is sufficient to identify all parameters generically, up to a global scaling factor, provided the SCC condensation graph is connected with a single root and certain spectral conditions hold. A recursive learning algorithm and a regularized least-squares estimator are proposed, and experiments confirm the theoretical results.
By Saber Salehkaleybar
arXiv:2603. 08311v2 Announce Type: replace-cross Abstract: We study identifiability in continuous-time linear stationary stochastic differential equations with a known causal structure.
By Gijs van Seeventer, Saber Salehkaleybar
arXiv:2604.27443v3 Announce Type: replace
Abstract: Generating continuous-time, continuous-space stochastic processes (e.g., videos, weather forecasts) conditioned on partial observations (e.g., firs...
By Gabe Guo, Thanawat Sornwanee, Lutong Hao, Elon Litman, Stefano Ermon, Jose Blanchet
arXiv:2606. 30467v1 Announce Type: cross Abstract: We consider sparse multivariate stochastic systems that evolve in continuous time according to a causal mechanism and present methodology to recover the system's time-infinitesimal transition mechanism from mere cross-sectional data.
By Richard Schwank, Mathias Drton
arXiv:2608. 04827v1 Announce Type: cross Abstract: We introduce the Intrinsic Hybrid Latent Diffusion Model (ILDM), a generative framework that integrates probabilistic dimensionality reduction with geometry-aware diffusion on unknown manifolds.
By Yizhu Wang, Mu Niu, Xiaochen Yang
arXiv:2605. 19805v2 Announce Type: replace-cross Abstract: Irregular multivariate time series impose a trade-off for long-horizon forecasting: discrete methods can distort temporal structure via re-gridding, while continuous-time models often require sequential solvers prone to drift.
By Zinuo You, Jin Zheng, John Cartlidge
arXiv:2608. 02799v1 Announce Type: cross Abstract: Score-based diffusion models are typically formulated using continuous-time stochastic differential equations and measure-theoretic stochastic calculus.
By Sunder Ram Krishnan
We introduce the Intrinsic Hybrid Latent Diffusion Model (ILDM), a generative framework that integrates probabilistic dimensionality reduction with geometry-aware diffusion on unknown manifolds. While diffusion models (DMs) have achieved state-of-the-art results in high-dimensional data synthesis, they rely on large training datasets and ignore intrinsic geometric structure.
arXiv:2604. 02751v2 Announce Type: replace Abstract: Diffusion models often degrade in latent spaces, yet the formal causes remain poorly understood.
By Jing Gu, Morteza Mardani, Wonjun Lee, Dongmian Zou, Gilad Lerman
Parameter estimation in stochastic differential equations is a classical statistical problem of much importance in many scientific fields. Recent work of Tapia Costa et al.
The paper introduces a sequential change‑point detection method for time‑ordered data where neither the pre‑ nor post‑change distributions have closed forms. It trains a conditional diffusion model on pre‑change data, uses its probability flow ODE to map observations to a Gaussian latent space, and then applies the Maximum Mean Discrepancy as a test statistic. The authors derive closed‑form components under the Gaussian null, establish the statistic’s asymptotic distribution as a degenerate U‑statistic, and implement an online Shiryaev–Roberts procedure with exact threshold calibration to detect arbitrary distributional shifts without parametric assumptions.
By Artem Kraevskiy, Artem Prokhorov
arXiv:2606. 02664v1 Announce Type: cross Abstract: Latent state-space models are widely used to study partially observed dynamical systems, yet most formulations assume that process variability is independent of latent-state position.
By Imani Beckett