发表机构
Sorbonne Université and Université Paris Cité, CNRS, LPSM; Center for Statistics and Images, Mines Paris, PSL University; CREST, ENSAE Paris, Institut Polytechnique de Paris（索邦大学和巴黎大学，法国国家科学研究中心，巴黎高等师范学院; 统计与图像中心，巴黎 Mines，PSL 大学; CREST，ENSAE 巴黎，巴黎理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对带偏置核的SMC采样器，推导非渐近误差分解框架，为条件扩散采样场景得到首个联合控制多类误差的非渐近界。
AI 中文摘要
序贯蒙特卡洛（SMC）方法是对预训练生成模型进行事后条件化的天然工具，但在诸多应用中，粒子系统使用的变异核是理想Feynman-Kac流的偏置近似。本文针对这类SMC采样器开展非渐近误差分析。在前向平滑遗忘条件下，我们将总误差分解为用于衡量用近似核替换理想转移核影响的核偏置，以及有限粒子蒙特卡洛误差。我们的方法依赖于将针对马尔可夫核的局部Doeblin型条件与李雅普诺夫漂移论证扩展到条件分布，从而实现对偏置的原则性控制。随后我们将该通用框架实例化到基于得分的扩散模型的条件采样场景，推导得到首个非渐近误差界，该界可联合控制反向扩散动力学中的初始化误差、时间离散化误差、得分近似误差以及有限粒子蒙特卡洛误差。
英文摘要
Post-hoc conditioning of pretrained diffusion models can be addressed using Sequential Monte Carlo (SMC) methods. By evolving an interacting particle system, SMC-guided diffusion samplers combine unconditional reverse-diffusion dynamics with sequential reweighting to approximate conditional distributions. Nevertheless, even in the infinite-particle limit, the implemented sampler may differ from the ideal conditional target because of errors in the diffusion model, its numerical implementation, and the guidance mechanism. We characterize how these local errors propagate through forward-smoothing kernels, which jointly account for the reverse dynamics and the remaining conditioning information. This yields non-asymptotic error bounds that capture both finite-particle fluctuations and approximation errors arising from initialization, numerical integration, score approximation, and potential design. In doing so, we extend stability guarantees for diffusion models to the conditional setting. Finally, we apply our framework to several state-of-the-art SMC-guided diffusion algorithms, providing a unified theoretical perspective on their approximation mechanisms and sources of error.
