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

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.

Generative diffusion models are increasingly improved at inference time, where users want samples that better satisfy a task objective than standard sampling from the base model. Many existing correction methods rely on reward derivatives, which can be expensive or unavailable for practical reward models. We propose $\texttt{URGE}$, a training-free inference-time scaling method that simulates multiple trajectories, reweights them at the path level, and periodically resamples to correct guided generation. Our analysis shows that $\texttt{URGE}$ corrects guided sampling in a principled way, and that its path-level reweighting is consistent with earlier particle-based correction methods after marginalization. We evaluate $\texttt{URGE}$ on a Gaussian-mixture toy model, inverse problems, and text-to-image generation benchmarks. Across these settings, $\texttt{URGE}$ consistently improves over baseline sampling, while achieving performance on the same order as methods that require reward derivatives when such derivatives are available. These results suggest that $\texttt{URGE}$ provides a simple and practical path to stronger inference-time control in diffusion models.