The paper introduces the Belief Flow Filter (BFF), a generative filtering framework that encodes the evolving posterior distribution directly into flow matching model weights and updates them via test‑time gradient descent. By avoiding particle representations and Gaussian assumptions, BFF aligns structurally with Bayesian filtering and targets the recursive filtering operator. Empirical results on five physical systems—including chaotic dynamics, sparse observations, and a tokamak plasma estimation task—show that BFF outperforms existing methods in most benchmark metrics.
By Ruiqi Feng, Chongyi Wang, Tao Zhang, Tailin Wu
arXiv:2606. 02767v1 Announce Type: cross Abstract: Kalman filtering performance is highly sensitive to model mismatch and noise covariance tuning.
By Jiho Lee, Nisar R. Ahmed, Rebecca Russell
arXiv:2510. 25693v3 Announce Type: replace-cross Abstract: State-space models (SSMs) are a widely used tool in time series analysis.
By John-Joseph Brady, Benjamin Cox, Yunpeng Li, V\'ictor Elvira
arXiv:2607. 20521v1 Announce Type: new Abstract: The state of a dynamic system evolves over time, switching among several latent modes that govern its observable behavior.
By Lei Cao, Sihang Feng, Jixin Yan, Tao Sun, Naichen Shi
arXiv:2609.30498v1 Announce Type: cross
Abstract: Sequential inference estimates latent states from noisy and incomplete observations. Particle Filters (PFs), a class of Monte Carlo methods based on...
By Apoorv Srivastava, Eric Darve
arXiv:2607. 01012v1 Announce Type: new Abstract: Data assimilation models state dynamics conditioned on sequential observations, and has wide-ranging scientific applications.
By Chandni Nagda, Mayank Shrivastavam Gudrun Thorkelsdottir, Gan Zhang, Morteza Mardani, Arindam Banerjee
arXiv:2606. 01468v1 Announce Type: cross Abstract: Due to their explicit priors and ability to model uncertainty, Bayesian methods have played a major role in dynamical latent variable modeling of single-cell neural recordings.
By JR Huml, Jonathan Wenger, John P. Cunningham
arXiv:2508. 13313v4 Announce Type: replace-cross Abstract: Data assimilation (DA) estimates a dynamical system's state from noisy observations.
By Taos Transue, Bohan Chen, So Takao, Bao Wang
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.
By Yuta Tarumi
arXiv:2601. 07013v2 Announce Type: replace-cross Abstract: Traditional filtering algorithms for state estimation -- such as classical Kalman filtering, unscented Kalman filtering, and particle filters -- show performance degradation when applied to nonlinear systems whose uncertainty follows arbitrary non-Gaussian, and potentially multi-modal distributions.
By Luke S. Lagunowich, Guoxiang Grayson Tong, Daniele E. Schiavazzi
arXiv:2606. 16985v1 Announce Type: cross Abstract: State-space models (SSMs) are the standard formalism for Bayesian treatment of dynamical systems, with natural applications in statistics, signal processing, and machine learning.
By Daniel Waxman, Dmitry Batenkov, John Feser, Andy Zane, Eli Bingham, Youssef Marzouk, Matthew E. Levine
arXiv:2608. 19377v1 Announce Type: cross Abstract: Bayesian inference via Markov Chain Monte Carlo (MCMC) provides effective parameter estimation, but its real-time application in complex physical systems is hindered by heavy computational bottlenecks and extreme sensitivity to statistical noise.
By Liyun Zhang, Naoya Mamada, Kentaro Sakai, Takeo Hoshi, Toru Aonishi