Recent advancements in solving Bayesian inverse problems have spotlighted denoising diffusion models (DDMs) as effective priors. Although these have great potential, DDM priors yield complex posterior distributions that are challenging to sample. Existing approaches to posterior sampling in this context address this problem either by retraining model-specific components, leading to stiff and cumbersome methods, or by introducing approximations with uncontrolled errors that affect the accuracy of the produced samples. We present an innovative framework, divide-and-conquer posterior sampling, which leverages the inherent structure of DDMs to construct a sequence of intermediate posteriors that guide the produced samples to the target posterior. Our method significantly reduces the approximation error associated with current techniques without the need for retraining. We demonstrate the versatility and effectiveness of our approach for a wide range of Bayesian inverse problems. The code is available at \url{https://github.com/Badr-MOUFAD/dcps}

翻译：近年来，在求解贝叶斯逆问题方面取得的进展凸显了去噪扩散模型作为有效先验的潜力。尽管这些模型前景广阔，但DDM先验会产生复杂的后验分布，使得采样极具挑战性。该领域现有的后验采样方法要么通过重新训练模型特定组件来解决此问题，导致方法僵化且繁琐；要么引入误差不可控的近似，从而影响生成样本的准确性。我们提出了一种创新的框架——分治后验采样，该框架利用DDMs的固有结构构建一系列中间后验分布，引导生成的样本逼近目标后验。我们的方法显著降低了现有技术相关的近似误差，且无需重新训练。我们证明了该方法在广泛的贝叶斯逆问题中的通用性和有效性。代码可在 \url{https://github.com/Badr-MOUFAD/dcps} 获取。