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Enhancing Diffusion Posterior Sampling for Inverse Problems by Integrating Crafted Measurements

Diffusion models have emerged as a powerful foundation model for visual generation. With an appropriate sampling process, it can effectively serve as a generative prior to solve general inverse problems. Current posterior sampling based methods take the measurement (i.e., degraded image sample) into the posterior sampling to infer the distribution of the target data (i.e., clean image sample). However, in this manner, we show that high-frequency information can be prematurely introduced during the early stages, which could induce larger posterior estimate errors during the restoration sampling. To address this issue, we first reveal that forming the log posterior gradient with the noisy measurement ( i.e., samples from a diffusion forward process) instead of the clean one can benefit the reverse process. Consequently, we propose a novel diffusion posterior sampling method DPS-CM, which incorporates a Crafted Measurement (i.e., samples generated by a reverse denoising process, compared to random sampling with noise in standard methods) to form the posterior estimate. This integration aims to mitigate the misalignment with the diffusion prior caused by cumulative posterior estimate errors. Experimental results demonstrate that our approach significantly improves the overall capacity to solve general and noisy inverse problems, such as Gaussian deblurring, super-resolution, inpainting, nonlinear deblurring, and tasks with Poisson noise, relative to existing approaches.

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