Recent advancements in diffusion models have been effective in learning data priors for solving inverse problems. They leverage diffusion sampling steps for inducing a data prior while using a measurement guidance gradient at each step to impose data consistency. For general inverse problems, approximations are needed when an unconditionally trained diffusion model is used since the measurement likelihood is intractable, leading to inaccurate posterior sampling. In other words, due to their approximations, these methods fail to preserve the generation process on the data manifold defined by the diffusion prior, leading to artifacts in applications such as image restoration. To enhance the performance and robustness of diffusion models in solving inverse problems, we propose Diffusion State-Guided Projected Gradient (DiffStateGrad), which projects the measurement gradient onto a subspace that is a low-rank approximation of an intermediate state of the diffusion process. DiffStateGrad, as a module, can be added to a wide range of diffusion-based inverse solvers to improve the preservation of the diffusion process on the prior manifold and filter out artifact-inducing components. We highlight that DiffStateGrad improves the robustness of diffusion models in terms of the choice of measurement guidance step size and noise while improving the worst-case performance. Finally, we demonstrate that DiffStateGrad improves upon the state-of-the-art on linear and nonlinear image restoration inverse problems.

本研究针对当前扩散模型在解决逆问题时存在的近似导致的不准确后验采样进行改进。提出的扩散状态引导投影梯度方法（DiffStateGrad）通过将测量梯度投影到扩散过程的一个低秩近似子空间中，提高了扩散模型在数据流形上的保持能力，并显著改善了线性和非线性图像恢复问题的性能。该方法在测量引导步长和噪声的选择上表现出更高的鲁棒性。 

扩散状态引导投影梯度用于逆问题