The efficacy of modern generative models is commonly contingent upon the precision of score estimation along the diffusion path, with a focus on diffusion models and their ability to generate high-quality data samples. This study delves into the potentialities of posterior sampling through reverse diffusion. An examination of the sampling literature reveals that score estimation can be transformed into a mean estimation problem via the decomposition of the transition kernel. By estimating the mean of the auxiliary distribution, the reverse diffusion process can give rise to a novel posterior sampling algorithm, which diverges from traditional gradient-based Markov Chain Monte Carlo (MCMC) methods. We provide the convergence analysis in total variation distance and demonstrate that the isoperimetric dependency of the proposed algorithm is comparatively lower than that observed in conventional MCMC techniques, which justifies the superior performance for high dimensional sampling with error tolerance. Our analytical framework offers fresh perspectives on the complexity of score estimation at various time points, as denoted by the properties of the auxiliary distribution.

翻译：现代生成模型的效能通常依赖于扩散路径上分数估计的精确性，重点在于扩散模型及其生成高质量数据样本的能力。本研究深入探讨了通过逆向扩散进行后验采样的潜力。对采样文献的考察表明，通过分解转移核，分数估计可转化为均值估计问题。通过估计辅助分布的均值，逆向扩散过程可衍生出一种新型后验采样算法，该算法有别于传统的基于梯度的马尔可夫链蒙特卡洛（MCMC）方法。我们提供了总变差距离下的收敛性分析，并证明所提算法的等周依赖性相较于传统MCMC技术更低，这验证了其在允许误差容限的高维采样中的优越性能。我们的分析框架为不同时间点分数估计的复杂度提供了新视角，这种复杂度由辅助分布的性质所表征。