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

TL;DR

URGE is a novel, derivative-free particle filtering method for diffusion models that improves sample quality without requiring gradients or PDE evaluations, simplifying inference.

Contribution

It introduces a path-wise importance reweighting algorithm using Girsanov change of measure, providing an unbiased, gradient-free inference technique for diffusion models.

Findings

URGE outperforms existing guidance methods on benchmarks.

It achieves better generation quality with simpler implementation.

No score, Hessian, or PDE evaluation is needed.

Abstract

Diffusion-based generative models increasingly rely on inference-time guidance, adding a drift term or reweighting mixture of experts, to improve sample quality on task-specific objectives. However, most existing techniques require repeated score or gradient evaluations, introducing bias, high computational overhead, or both. We introduce \texttt{URGE}, Unbiased Resampling via Girsanov Estimation, a derivative-free inference-time scaling algorithm that performs path-wise importance reweighting via a Girsanov change of measure. Instead of computing gradient-based particle weights in previous work, \texttt{URGE} attaches a simple multiplicative weight to each simulated trajectory and periodically resamples. No score, no Hessian, and no PDE evaluation is required. We establish an equivalence between path-wise and particle-wise SMC: the Girsanov path weight admits a backward conditional expectation that recovers the previous particle-level weights, guaranteeing that both schemes produce the same unbiased terminal law. Empirically, \texttt{URGE} outperforms existing inference-time guidance baselines on synthetic tests and diffusion-model benchmarks, achieving better generation quality, while being significantly simpler to implement and fully gradient-free.