  The recent emergence of diffusion models has significantly advanced the
precision of learnable priors, presenting innovative avenues for addressing
inverse problems. Since inverse problems inherently entail maximum a posteriori
estimation, previous works have endeavored to integrate diffusion priors into
the optimization frameworks. However, prevailing optimization-based inverse
algorithms 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. By employing gradient truncation, the projection
gradient descent method is efficiently utilized to solve the corresponding
optimization problem. 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/.
