Rethinking Forward Processes for Score-Based Data Assimilation in High Dimensions

2026-04-03

AI Summary

This work addresses the trade-off between accuracy and computational efficiency in high-dimensional data assimilation, where conventional filtering methods struggle and existing score-based filters suffer from error accumulation due to heuristic approximations of the likelihood score—stemming from a decoupling between the forward diffusion process and observations. To overcome this limitation, the paper proposes the Measurement-Aware Score-based Filter (MASF), which uniquely embeds observational information directly into the forward diffusion process. This yields a measurement-aware forward model that enables an analytically tractable likelihood score, which, when combined with a learned prior score, allows for accurate posterior estimation. Theoretical analysis and extensive high-dimensional experiments demonstrate that MASF significantly improves estimation accuracy and temporal stability, outperforming current state-of-the-art methods.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Probabilistic Inference

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Data assimilation is the process of estimating the time-evolving state of a dynamical system by integrating model predictions and noisy observations. It is commonly formulated as Bayesian filtering, but classical filters often struggle with accuracy or computational feasibility in high dimensions. Recently, score-based generative models have emerged as a scalable approach for high-dimensional data assimilation, enabling accurate modeling and sampling of complex distributions. However, existing score-based filters often specify the forward process independently of the data assimilation. As a result, the measurement-update step depends on heuristic approximations of the likelihood score, which can accumulate errors and degrade performance over time. Here, we propose a measurement-aware score-based filter (MASF) that defines a measurement-aware forward process directly from the measurement equation. This construction makes the likelihood score analytically tractable: for linear measurements, we derive the exact likelihood score and combine it with a learned prior score to obtain the posterior score. Numerical experiments covering a range of settings, including high-dimensional datasets, demonstrate improved accuracy and stability over existing score-based filters.

Problem

• score-based data assimilation
• high-dimensional filtering
• likelihood score approximation
• measurement update
• Bayesian filtering

Innovation

• score-based generative models
• data assimilation
• measurement-aware forward process
• likelihood score
• high-dimensional filtering