A Novel Framework for Inverse Problems: Fixed-Point Iteration Using Consistency Models

Inverse problems play a crucial role in science and engineering, especially in the field of computer vision, where tasks such as deblurring, super-resolution, and colorization can be formally modeled as inverse problems. Consistency models excel in generation speed while maintaining high quality, making them a promising family of generative models. However, existing sampling methods struggle to achieve high-quality results when applying consistency models to image inverse problems. To address this limitation, we propose the Consistency Inverse Reconstruction Sampling (CIRS) framework, which incorporates two modes: CIRS-Hybrid and CIRS-Pure. In CIRS-Hybrid, the posterior formula of inverse problems is utilized by estimating the prior term using a diffusion denoiser and the likelihood term with a consistency model, enabling reconstruction under dual-model guidance. To overcome the complexities of dual-model tuning and inefficiencies caused by employing a diffusion denoiser, we introduce CIRS-Pure, which relies solely on a consistency model. By eliminating the iterative noise addition and denoising steps, the iterative procedure is transformed into a fixed-point iteration, achieving efficient and high-quality restoration. Extensive experiments demonstrate that CIRS-Pure outperforms state-of-the-art methods in zero-shot image restoration tasks such as image deblurring and colorization while achieving competitive performance in super-resolution.