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

2026-05-18

AI Summary

Existing inference-time guidance methods for diffusion models typically rely on repeated gradient or score evaluations, incurring high computational costs and introducing bias. This work proposes URGE, an algorithm that establishes, for the first time, the equivalence between path-level and particle-level sequential Monte Carlo (SMC) formulations. By leveraging Girsanov’s measure transformation, URGE performs path-space importance reweighting of diffusion trajectories and integrates periodic SMC resampling to achieve derivative-free, unbiased, and entirely gradient-free inference-time guidance. The method significantly outperforms existing approaches on both synthetic tasks and standard diffusion model benchmarks, simultaneously enhancing generation quality, simplifying implementation, and completely eliminating the need for gradient computation.

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.

Problem

• diffusion models
• inference-time guidance
• gradient-free
• computational overhead
• bias

Innovation

• derivative-free
• sequential Monte Carlo
• Girsanov change of measure
• inference-time scaling
• diffusion models