arXiv：cs.LG· Nikolaj T. M\"ucke, Benjamin Sanderse·· 3 小时前AI 评分31
用生成模型与观测插值实现贝叶斯数据同化的统一框架
A Unified Framework for Bayesian Data Assimilation with Generative Models and Observation Interpolants
AI 导读
研究者提出观测插值框架，可将预训练的随机插值、flow matching 和扩散模型直接转为后验采样器，无需重新训练。该方法通过对插值路径施加观测条件，得到漂移或速度上的共享似然分数修正，统一了随机与确定性后验采样。在线性高斯动力学、随机二维 Navier-Stokes 及城市气流等最高约 O(10^4) 自由度的任务上完成了评估。
正文
Abstract:Bayesian data assimilation combines model forecasts with noisy observations, but sampling high-dimensional, non-Gaussian posteriors remains challenging. We introduce an observation-interpolant framework that turns pretrained stochastic interpolant, flow matching, and diffusion models into posterior samplers without retraining. Conditioning the interpolant path on observations yields a shared likelihood-score correction to the drift or velocity, unifying stochastic and deterministic posterior sampling. The resulting SDEs and ODEs sample the exact posterior when the intermediate likelihood score is known. For practical computation, we approximate this score using a closed-form Gaussian surrogate with a bias-corrected mean and covariance inflated by the model's source covariance. Jacobian-free and ensemble-shared approximations make the method tractable in high dimensions. We evaluate the framework on linear-Gaussian dynamics, stochastic two-dimensional Navier-Stokes, and urban airflow with up to $O(10^4)$ degrees of freedom.
| Subjects: | Machine Learning (cs.LG); Computational Engineering, Finance, and Science (cs.CE) |
| Cite as: | arXiv:2610.03396 [cs.LG] |
| (or arXiv:2610.03396v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.03396 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Nikolaj Takata Mücke [view email]
[v1]
Fri, 2 Oct 2026 14:46:44 UTC (21,375 KB)
来源：arXiv：cs.LG · arxiv.org