Recently, diffusion models have been used to solve various inverse problems in an unsupervised manner with appropriate modifications to the sampling process. However, the current solvers, which recursively apply a reverse diffusion step followed by a projection-based measurement consistency step, often produce suboptimal results. By studying the generative sampling path, here we show that current solvers throw the sample path off the data manifold, and hence the error accumulates. To address this, we propose an additional correction term inspired by the manifold constraint, which can be used synergistically with the previous solvers to make the iterations close to the manifold. The proposed manifold constraint is straightforward to implement within a few lines of code, yet boosts the performance by a surprisingly large margin. With extensive experiments, we show that our method is superior to the previous methods both theoretically and empirically, producing promising results in many applications such as image inpainting, colorization, and sparse-view computed tomography. Code available https://github.com/HJ-harry/MCG_diffusion

翻译：最近，扩散模型通过适当修改采样过程，以无监督方式被用于解决各类逆问题。然而，当前求解器递归地应用反向扩散步骤并辅以基于投影的测量一致性步骤，往往产生次优结果。通过研究生成采样路径，我们在此表明当前求解器使采样路径偏离数据流形，从而导致误差累积。为此，我们提出一种受流形约束启发的额外校正项，该校正项可与先前的求解器协同使用，使迭代过程接近流形。所提出的流形约束仅需几行代码即可实现，却能以惊人幅度提升性能。通过大量实验，我们表明本方法在理论和经验上均优于先前方法，并在图像修复、着色和稀疏视角计算机断层扫描等众多应用中产生有前景的结果。代码地址：https://github.com/HJ-harry/MCG_diffusion