Simple Approximation and Derivative Free Inference-Time Scaling for Diffusion Models via Sequential Monte Carlo on Path Measures
Authors: Chenyang Wang, Weizhong Wang, Yinuo Ren, Jose Blanchet, Yiping Lu
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.
We study inference-time alignment for diffusion-based generative models, aiming to steer a base model toward high-reward outputs without updating its weights. Recent Sequential Monte Carlo (SMC)-based steering methods approximate reward-tilted target distributions in a principled way, but their proposals remain largely tied to the base sampler. Since reward information is mainly used after propagation through particle reweighting and resampling, these methods can require large particle budgets and suffer from weight degeneracy and high-variance estimates. One way to reduce variance and improve particle efficiency is to iteratively learn twisting functions that provide look-ahead guidance, as in twisted SMC. However, existing learnable twisting methods are developed mainly for classical sequential inference and can be unstable when applied to diffusion-based alignment with high-dimensional state spaces and terminal, noisy, or black-box rewards. We propose Trust-Region Iterative Twisted Sequential Monte Carlo (TRI-TSMC), a trust-region framework for learning twisting functions in SMC-based inference-time alignment. Each iteration computes an exact KL-constrained update in path space, which admits a closed-form solution by tempered importance reweighting, and projects this target back to the parameterized twisted family by weighted maximum likelihood. Theoretically, we formalize the value-function interpretation of the optimal twisting function and show that it yields a zero-variance sampler. We prove that the trust-region update follows an escort path toward the target distribution, that the weighted maximum-likelihood update is a forward-KL projection, and that the path reduces residual importance-weight variance. Empirically, TRI-TSMC improves primary alignment objectives on discrete diffusion text generation and text-to-image generation under matched inference-time budgets.
Inference-time scaling has emerged as a major approach for improving reasoning capabilities, and has been increasingly applied to diffusion models. However, existing inference-time scaling methods for diffusion models typically rely on external verifiers or reward models to rank and select samples, limiting their scalability to settings where such evaluators are available and reliable. Moreover, while recent diffusion models perform sequential inference with region-wise, mixed-noise conditioning, inference-time scaling tailored to this setting remains relatively underexplored. We propose Iterative Partial Refinement (IPR), an inference-time scaling method for sequential diffusion that requires no external verifier. Starting from an already-generated sample, IPR re-noises a subset of regions and regenerates them conditioned on the remaining regions, enabling the model to revise earlier decisions under a richer context than was available during the initial generation. This iterative partial refinement produces more globally consistent samples without external verification. On reasoning tasks requiring global constraint satisfaction, IPR consistently improves performance: on MNIST Sudoku, the valid solution rate increases from 55.8% to 75.0%. These results show that iterative partial refinement alone can serve as an effective inference-time scaling strategy for diffusion models in sequential, mixed-noise settings. Code is available at: https://github.com/ahn-ml/IPR
Diffusion models have recently emerged as powerful learners for simulation-based inference (SBI), enabling fast and accurate estimation of latent parameters from simulated and real data. Their score-based formulation offers a flexible way to learn conditional or joint distributions over parameters and observations, thereby providing a versatile solution to various modeling problems. In this tutorial review, we synthesize recent developments on diffusion models for SBI, covering design choices for training, inference, and evaluation. We highlight opportunities created by various concepts such as guidance, score composition, flow matching, consistency models, and joint modeling. Furthermore, we discuss how efficiency and statistical accuracy are affected by noise schedules, parameterizations, and samplers. Finally, we illustrate these concepts with case studies across parameter dimensionalities, simulation budgets, and model types, and outline open questions for future research.