Diffusion models have recently achieved success in solving Bayesian inverse problems using learned data priors. However, current methods struggle with complex nonlinear inverse problems, such as phase retrieval, due to their inability to correct errors from earlier sampling steps. To address this, the authors propose a new method called Decoupled Annealing Posterior Sampling (DAPS), which introduces a novel noise annealing process. DAPS decouples consecutive steps in the diffusion sampling trajectory, allowing them to vary significantly while ensuring their time marginals anneal to the true posterior as noise levels decrease. This approach enables the exploration of a larger solution space, improving the success rate for accurate reconstructions. Empirical results demonstrate that DAPS significantly improves sample quality and stability across multiple image restoration tasks, particularly in nonlinear inverse problems. For example, DAPS achieves a PSNR of 30.72dB on the FFHQ 256 dataset for phase retrieval, a significant improvement over existing methods. The code for DAPS is available on GitHub.Diffusion models have recently achieved success in solving Bayesian inverse problems using learned data priors. However, current methods struggle with complex nonlinear inverse problems, such as phase retrieval, due to their inability to correct errors from earlier sampling steps. To address this, the authors propose a new method called Decoupled Annealing Posterior Sampling (DAPS), which introduces a novel noise annealing process. DAPS decouples consecutive steps in the diffusion sampling trajectory, allowing them to vary significantly while ensuring their time marginals anneal to the true posterior as noise levels decrease. This approach enables the exploration of a larger solution space, improving the success rate for accurate reconstructions. Empirical results demonstrate that DAPS significantly improves sample quality and stability across multiple image restoration tasks, particularly in nonlinear inverse problems. For example, DAPS achieves a PSNR of 30.72dB on the FFHQ 256 dataset for phase retrieval, a significant improvement over existing methods. The code for DAPS is available on GitHub.