SURGE: Approximation and Training Free Particle Filter for Diffusion Surrogate

Data assimilation (DA) tackles the sequential estimation of a dynamical system’s latent state from noisy, partial observations. In this paper, we study DA in a setting where the system dynamics are represented by a pretrained diffusion model used as a surrogate forecaster. We focus on how to integrate incoming observations into the diffusion surrogate’s predictions to support continuous state correction and progressively refining the estimated trajectory over time. After receiving noisy observations, the diffusion model is guided using the observation likelihood to steer the generation process toward observation-consistent states. However, such guidance does not guarantee sampling from the true posterior. Motivated by particle filtering methods, we represent the posterior distribution using an ensemble of particles. We perform Sequential Monte Carlo over diffusion trajectories, working with their path measure. We compute importance weights for generated particles and resample to focus on trajectories consistent with the observations. This procedure corrects the generation dynamics, drives the particle approximation toward the desired posterior and leads to an approximation-free particle filtering method that rigorously fuses observational data with diffusion model simulations.

Many physical systems such as weather or ocean currents change over time, but we can only observe them through sparse, noisy measurements. The challenge is to continuously estimate a system's true hidden state as new measurements arrive. We use a pretrained AI model that has learned how such systems typically evolve, and steer its predictions to stay consistent with incoming observations. But simple steering can drift from the statistically correct answer, so we run many parallel predictions, score each by how well it matches the data, and repeatedly keep the best ones. This rigorously fuses real measurements with AI simulation to track the true state over time.