为带偏差提议的SMC推断提供非渐近误差界，首次统一控制扩散采样中多种误差来源。
Non-Asymptotic Error Bounds for SMC with Biased Proposals: Application to Conditional Diffusion Sampling
- 通过扩展Doeblin条件与漂移论证，建立条件分布的误差控制框架
- 首次给出扩散模型条件采样中初始化、离散化、得分逼近与粒子数量误差的联合界
- 适用于需后验调节的预训练生成模型，如基于分数的扩散模型
序列蒙特卡洛（SMC）方法是后处理调节预训练生成模型的自然选择，但在许多应用中，粒子系统的突变核是对理想费曼-卡茨流的有偏近似。本文建立了此类SMC采样器的非渐近误差分析。在前向平滑遗忘条件下，我们将总误差分解为核偏差（衡量用近似转移核替代理想核的影响）和有限粒子蒙特卡洛误差。该方法依赖于将局部Doeblin型条件和马尔可夫核的李亚普诺夫漂移论证推广至条件分布，从而实现对偏差的严格控制。随后，我们将此通用框架应用于基于分数的扩散模型的条件采样，并推导出首个非渐近误差界，同时控制反向扩散动力学中的初始误差、时间离散化、得分函数近似以及有限粒子蒙特卡洛误差。
原文摘要 · Abstract (English)
Sequential Monte Carlo (SMC) methods are a natural tool for post-hoc conditioning of pretrained generative models, but in many applications the mutation kernels used by the particle system are biased approximations of an ideal Feynman--Kac flow. This paper develops a non-asymptotic error analysis for such SMC samplers. Under forward-smoothing forgetting conditions, we decompose the total error into a kernel bias, measuring the effect of replacing the ideal transition kernels by approximate ones, and a finite-particle Monte Carlo error. Our approach relies on extending local Doeblin-type conditions and Lyapunov drift arguments for Markov kernels to conditional distributions, thereby enabling a principled control of the bias. We then instantiate this general framework for conditional sampling with score-based diffusion models, and derive the first non-asymptotic error bound that jointly controls initialization error, time discretization, and score approximation in the reverse diffusion dynamics as well as finite-particle Monte Carlo error.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。