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

2026-05-18

AI Summary

Existing inference-time guidance methods for diffusion models rely on repeated gradient or score evaluations, introducing bias and incurring high computational costs. This work proposes URGE, the first fully gradient-free and approximation-free guidance algorithm during inference. URGE leverages Girsanov’s measure transformation to perform path-level importance reweighting of diffusion trajectories and integrates periodic particle resampling from sequential Monte Carlo, eliminating the need for any gradient, Hessian, or PDE computations. The method establishes equivalence between path-level and particle-level guidance, ensuring an unbiased target distribution at termination. Experiments demonstrate that URGE achieves superior generation quality on both synthetic tasks and standard diffusion model benchmarks, while offering a simpler architecture and significantly improved computational efficiency.

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.

Problem

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

Innovation

• diffusion models
• inference-time guidance
• Girsanov change of measure
• gradient-free
• sequential Monte Carlo