SURGE: Approximation-free Training Free Particle Filter for Diffusion Surrogate

2026-05-19 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Robotics & Autonomous Systems, Data Science & Analytics · Depth: Expert, extended

Summary

SURGE (Sequential Unbiased Resampling via Girsanov Estimation) is a novel, training-free data assimilation framework designed to enhance diffusion surrogate models when dealing with noisy, partial observations. It integrates particle filtering during the inference phase to rigorously fuse observational data with diffusion model simulations, correcting predictions in high-dimensional, nonlinear dynamical systems without introducing systematic bias from approximate guidance. SURGE casts diffusion-based forecasting as inference over a path distribution, performing reweighting and resampling on diffusion trajectories using Girsanov's theorem to compute importance weights. This method progressively incorporates observation likelihoods to mitigate particle degeneracy and stabilize filtering. Evaluated on chaotic Lorenz systems, forced incompressible Navier-Stokes flow, and real-world weather forecasting (SEVIR dataset), SURGE consistently outperforms classical filtering baselines (BPF, EnKF) and score-based methods (SDA, FlowDAS) in metrics like RMSE and Critical Success Index, particularly in challenging scenarios such as extreme super-resolution and long-term autoregressive prediction with sparse data.

Key takeaway

For Machine Learning Engineers developing or deploying diffusion models for complex dynamical systems, SURGE offers a critical, training-free enhancement. You should integrate SURGE into your inference pipeline to achieve approximation-free data assimilation, especially when working with sparse, noisy observations in high-dimensional, nonlinear regimes. This approach can significantly improve prediction accuracy and physical consistency without requiring model retraining, but be mindful of its dependence on the base model's stability and hyperparameter sensitivity.

Key insights

SURGE offers an approximation-free particle filter for diffusion models, rigorously fusing observations with simulations via path-space resampling.

Principles

• Particle filtering corrects bias from approximate guidance.
• Girsanov's theorem quantifies path measure deviation.
• Progressive likelihood incorporation stabilizes resampling.

Method

SURGE performs Sequential Monte Carlo over diffusion trajectories, reweighting and resampling full paths using Girsanov change-of-measure to correct bias from likelihood guidance, and gradually incorporates likelihoods to stabilize weights.

In practice

• Apply SURGE as a plug-and-play inference-time enhancement.
• Use for high-dimensional, long-horizon physical processes.
• Effective for sparse, noisy observation scenarios.

Topics

• SURGE Filter
• Data Assimilation
• Diffusion Models
• Particle Filtering
• Girsanov's Theorem

Best for: AI Scientist, Research Scientist, Machine Learning Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.