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

Chenyang Wang, Weizhong Wang, Yinuo Ren, Jose Blanchet, Yiping Lu
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:130728-130764, 2026.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-wang26ih, title = {Simple Approximation and Derivative Free Inference-Time Scaling for Diffusion Models via Sequential {M}onte {C}arlo on Path Measures}, author = {Wang, Chenyang and Wang, Weizhong and Ren, Yinuo and Blanchet, Jose and Lu, Yiping}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {130728--130764}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/wang26ih/wang26ih.pdf}, url = {https://proceedings.mlr.press/v306/wang26ih.html}, 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.} }
Endnote
%0 Conference Paper %T Simple Approximation and Derivative Free Inference-Time Scaling for Diffusion Models via Sequential Monte Carlo on Path Measures %A Chenyang Wang %A Weizhong Wang %A Yinuo Ren %A Jose Blanchet %A Yiping Lu %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-wang26ih %I PMLR %P 130728--130764 %U https://proceedings.mlr.press/v306/wang26ih.html %V 306 %X 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.
APA
Wang, C., Wang, W., Ren, Y., Blanchet, J. & Lu, Y.. (2026). Simple Approximation and Derivative Free Inference-Time Scaling for Diffusion Models via Sequential Monte Carlo on Path Measures. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:130728-130764 Available from https://proceedings.mlr.press/v306/wang26ih.html.

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