Simple Approximation and Derivative Free Inference-Time Scaling for Diffusion Models via Sequential Monte Carlo on Path Measures

TL;DR

The paper introduces URGE, a simple, unbiased, derivative-free algorithm for inference-time scaling in diffusion models using path-wise importance reweighting with Girsanov change of measure.

Contribution

URGE is a novel, gradient-free inference method that simplifies path-wise importance reweighting in diffusion models, avoiding score, Hessian, and PDE evaluations.

Findings

URGE outperforms existing guidance methods on benchmarks.

URGE achieves better sample quality with simpler implementation.

URGE is fully gradient-free and unbiased.

Abstract

iffusion-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.