A new framework for Bayesian data assimilation is presented that leverages pretrained stochastic interpolants, flow matching, and diffusion models as posterior samplers without retraining. By conditioning the interpolant path on observations, a shared likelihood‑score correction is applied to the drift or velocity, unifying stochastic and deterministic sampling methods. The approach yields exact posterior samples when the intermediate likelihood score is known, and practical approximations use a Gaussian surrogate with bias‑corrected mean and inflated covariance, enabling tractable high‑dimensional applications such as linear‑Gaussian dynamics, stochastic Navier‑Stokes, and urban airflow simulations with up to $O(10^4)$ degrees of freedom.
arXiv:2607. 12975v1 Announce Type: cross Abstract: Data assimilation estimates the state of a dynamical system from model forecasts and incoming observations.
The paper introduces FREESIA, a training‑free, covariance‑aware posterior transport method for data assimilation that embeds forecast cross‑covariance into a flow‑based transport to recover unobserved states while preserving non‑Gaussian posterior structure. It combines an observation‑adaptive proposal with posterior correction, providing an asymptotically exact approximation of nonlinear posteriors and a Wasserstein error bound. Experiments on Double‑Well, Lorenz‑96, and Kolmogorov flow demonstrate that FREESIA captures complex posterior structures and achieves up to a 56% reduction in RMSE compared to the best baseline in sparse, nonlinear, non‑injective observation scenarios.
Data assimilation estimates the state of a dynamical system from model forecasts and incoming observations. Many observation mechanisms, however, are many-to-one, implicit, non-smooth, or accessible only through simulation, and need not provide the residual structures or likelihood guidance required by existing ensemble filters.
arXiv:2608. 05103v1 Announce Type: new Abstract: Data assimilation (DA) uses Bayesian inference to update the state of a numerical forecast model with observed data.
PR‑Smoother is an amortized smoothing method that preserves the explicit use of a prescribed simulator in both the evidence lower bound and the variational family. It learns only future‑conditioned corrections to the simulator’s rollout, yielding a non‑Gaussian smoothing distribution that can jointly infer state, parameters, and sensor bias from observations alone. The approach recovers the exact smoother in deterministic and linear‑Gaussian limits and has been shown to capture multimodal posteriors in Lorenz‑96 and scale to 16,384‑dimensional Kolmogorov flow.
The paper introduces prequential posteriors, a Bayesian approach that uses a predictive‑sequential loss function to update deep generative forecasting models (DGFMs) when new data arrive. By adopting a consistency notion suitable for model misspecification, the authors prove that both the loss minimizer and the posterior concentrate on parameters with optimal predictive performance. Scalable inference is achieved with parallelisable waste‑free sequential Monte Carlo samplers that employ preconditioned gradient kernels, and the method is validated on synthetic and real meteorological time‑series data.
arXiv:2608. 05103v2 Announce Type: replace Abstract: Data assimilation (DA) uses Bayesian inference to update the state of a numerical forecast model with observed data.
arXiv:2508. 13313v4 Announce Type: replace-cross Abstract: Data assimilation (DA) estimates a dynamical system's state from noisy observations.
arXiv:2609.35944v1 Announce Type: new Abstract: Data Assimilation (DA) aims to recover the full state of a dynamical system that is only partially observed. A solution is to use Score-based models to...
arXiv:2609.28015v1 Announce Type: cross Abstract: Data assimilation estimates a dynamical state from partial and noisy observations. Classical ensemble filters are efficient but restrict analysis upd...
arXiv:2610.03314v1 Announce Type: cross Abstract: Flow- and diffusion-based generative models have recently emerged as flexible and highly efficient forecasting models for dynamical systems. When com...
arXiv:2604.07169v3 Announce Type: replace-cross Abstract: Bayesian filtering and smoothing are central to data assimilation in nonlinear dynamical systems. Recent advances in deep generative models p...