This paper introduces a novel method called Stochastic Localization via Iterative Posterior Sampling (SLIPS) for sampling from unnormalized target densities. SLIPS is based on a general stochastic localization framework that allows for flexible denoising schedules. The method leverages Markov chain Monte Carlo (MCMC) estimation to estimate the denoiser, which is crucial for sampling from the target distribution. The authors provide a detailed methodology, including theoretical and numerical considerations, and demonstrate the effectiveness of SLIPS on various benchmarks, including multi-modal distributions, Bayesian logistic regression, and high-dimensional field systems. The paper also discusses the "duality of log-concavity," a key concept in understanding the trade-offs between sampling from the observation process and the SL posterior. SLIPS is shown to perform well in high-dimensional settings, outperforming or matching other sampling methods in terms of accuracy and efficiency.This paper introduces a novel method called Stochastic Localization via Iterative Posterior Sampling (SLIPS) for sampling from unnormalized target densities. SLIPS is based on a general stochastic localization framework that allows for flexible denoising schedules. The method leverages Markov chain Monte Carlo (MCMC) estimation to estimate the denoiser, which is crucial for sampling from the target distribution. The authors provide a detailed methodology, including theoretical and numerical considerations, and demonstrate the effectiveness of SLIPS on various benchmarks, including multi-modal distributions, Bayesian logistic regression, and high-dimensional field systems. The paper also discusses the "duality of log-concavity," a key concept in understanding the trade-offs between sampling from the observation process and the SL posterior. SLIPS is shown to perform well in high-dimensional settings, outperforming or matching other sampling methods in terms of accuracy and efficiency.