SURGE: Training-Free, Approximation-Free Particle Filter for Diffusion Models via Girsanov Estimation

Forum topic · 小凯 · 2026-05-20

Summary

SURGE (Unbiased Resampling via Girsanov Estimation) is a derivative-free, training-free inference-time scaling algorithm for diffusion-based generative models, presented in arXiv paper 2505.14304 by Lifu Wei, Yinuo Ren, and Naichen Shi. Inference-time guidance methods typically add drift terms or reweight experts to improve sample quality on task-specific objectives, but most require repeated score or gradient evaluations, introducing bias or high computational overhead. SURGE instead performs path-wise importance reweighting via a Girsanov change of measure: each simulated trajectory is attached a simple multiplicative weight, with periodic resampling, requiring no score, Hessian, or PDE evaluations. The authors establish an equivalence between path-level and particle-level sequential Monte Carlo, showing that Girsanov path weights allow backward conditional expectations to recover prior particle-level weights, so both schemes yield identical unbiased terminal distributions. Empirically, SURGE outperforms existing inference-time guidance baselines on synthetic tests and diffusion model benchmarks, achieving better generative quality with a significantly simpler, fully gradient-free approach.

Paper Overview

Field: Machine Learning
Authors: Lifu Wei, Yinuo Ren, Naichen Shi
Published: 2026-05-19
arXiv: 2505.14304

Abstract (Translated)

Diffusion-based generative models increasingly rely on inference-time guidance, adding a drift term or reweighting a 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.

This paper introduces SURGE (Unbiased Resampling via Girsanov Estimation), a derivative-free inference-time scaling algorithm that performs path-wise importance reweighting via a Girsanov change of measure. Unlike prior work that computes gradient-based particle weights, SURGE attaches a simple multiplicative weight to each simulated trajectory and periodically resamples. No score, no Hessian, and no PDE evaluation is required.

The authors establish an equivalence between path-level and particle-level sequential Monte Carlo (SMC): Girsanov path weights allow backward conditional expectations to recover previous particle-level weights, guaranteeing that both schemes produce the same unbiased terminal distribution.

Empirically, SURGE outperforms existing inference-time guidance baselines on synthetic tests and diffusion model benchmarks, achieving better generative quality while being significantly simpler and fully gradient-free.

Key Highlights

Training-free and approximation-free: no model retraining or score approximations needed
Derivative-free guidance: weights are multiplicative per trajectory, avoiding gradients entirely
Theoretical guarantee: path-level Girsanov weighting is shown equivalent to particle-level SMC, with unbiasedness preserved
Empirical gains: better sample quality than existing inference-time guidance baselines on both synthetic and diffusion benchmarks

Original Abstract (Excerpt)

> We introduce 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, URGE attaches a simple multiplicative weight to each simulated trajectory and periodically resamples. No score, no Hessian, and no PDE evaluation is required...

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*Auto-collected on 2026-05-20*