An Efficient Conditional Score-based Filter for High Dimensional Nonlinear Filtering Problems

2025-09-24

AI Summary

Low posterior sampling efficiency and poor adaptability to time-varying priors remain longstanding challenges in high-dimensional nonlinear filtering. This paper proposes Conditional Score Filtering (CSF), the first framework that decouples and integrates ensemble transformers with conditional diffusion models: the former learns prior dynamics on the high-dimensional state manifold offline, while the latter generates posterior samples online via denoising score matching—without requiring retraining. This design cleanly separates prior modeling from posterior sampling, significantly enhancing scalability and robustness. Evaluated on multiple high-dimensional nonlinear filtering benchmarks, CSF achieves superior estimation accuracy and markedly improved robustness against observation noise and model mismatch, all at lower computational cost. The method establishes a new paradigm for real-time, high-dimensional Bayesian filtering.

Technology Category

• Intelligent Robots: State Estimation
• Search and Optimization: Sampling/Simulation-based Search
• Computer Vision: Diffusion Models for Vision

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

In many engineering and applied science domains, high-dimensional nonlinear filtering is still a challenging problem. Recent advances in score-based diffusion models offer a promising alternative for posterior sampling but require repeated retraining to track evolving priors, which is impractical in high dimensions. In this work, we propose the Conditional Score-based Filter (CSF), a novel algorithm that leverages a set-transformer encoder and a conditional diffusion model to achieve efficient and accurate posterior sampling without retraining. By decoupling prior modeling and posterior sampling into offline and online stages, CSF enables scalable score-based filtering across diverse nonlinear systems. Extensive experiments on benchmark problems show that CSF achieves superior accuracy, robustness, and efficiency across diverse nonlinear filtering scenarios.

Problem

• Addresses high-dimensional nonlinear filtering challenges in engineering
• Eliminates need for repeated retraining in diffusion-based filtering methods
• Enables scalable posterior sampling across diverse nonlinear systems

Innovation

• Set-transformer encoder for efficient posterior sampling
• Conditional diffusion model without retraining requirement
• Offline-online decoupling for scalable nonlinear filtering