Unleashing the Denoising Capability of Diffusion Prior for Solving Inverse Problems

The recent emergence of diffusion models has significantly advanced the precision of learnable priors, presenting innovative avenues for addressing inverse problems. Previous works have endeavored to integrate diffusion priors into the maximum a posteriori estimation (MAP) framework and design optimization methods to solve the inverse problem. However, prevailing optimization-based rithms primarily exploit the prior information within the diffusion models while neglecting their denoising capability. To bridge this gap, this work leverages the diffusion process to reframe noisy inverse problems as a two-variable constrained optimization task by introducing an auxiliary optimization variable that represents a 'noisy' sample at an equivalent denoising step. The projection gradient descent method is efficiently utilized to solve the corresponding optimization problem by truncating the gradient through the $\mu$-predictor. The proposed algorithm, termed ProjDiff, effectively harnesses the prior information and the denoising capability of a pre-trained diffusion model within the optimization framework. Extensive experiments on the image restoration tasks and source separation and partial generation tasks demonstrate that ProjDiff exhibits superior performance across various linear and nonlinear inverse problems, highlighting its potential for practical applications. Code is available at https://github.com/weigerzan/ProjDiff/.