Diffusion model-based image restoration (IR) aims to use diffusion models to recover high-quality (HQ) images from degraded images, achieving promising performance. Due to the inherent property of diffusion models, most existing methods need long serial sampling chains to restore HQ images step-by-step, resulting in expensive sampling time and high computation costs. Moreover, such long sampling chains hinder understanding the relationship between inputs and restoration results since it is hard to compute the gradients in the whole chains. In this work, we aim to rethink the diffusion model-based IR models through a different perspective, i.e., a deep equilibrium (DEQ) fixed point system, called DeqIR. Specifically, we derive an analytical solution by modeling the entire sampling chain in these IR models as a joint multivariate fixed point system. Based on the analytical solution, we can conduct parallel sampling and restore HQ images without training. Furthermore, we compute fast gradients via DEQ inversion and found that initialization optimization can boost image quality and control the generation direction. Extensive experiments on benchmarks demonstrate the effectiveness of our method on typical IR tasks and real-world settings.

翻译：基于扩散模型的图像恢复旨在利用扩散模型从退化图像中恢复高质量图像，取得了显著成效。然而受扩散模型固有特性限制，现有方法大多需要长序列采样链逐步恢复高质量图像，导致采样时间长且计算成本高昂。此外，此类长采样链难以计算整条链上的梯度，阻碍了对输入与恢复结果间关系的理解。本文从全新视角重新审视基于扩散模型的图像恢复模型，提出名为DeqIR的深度均衡固定点系统。具体而言，通过将图像恢复模型中整个采样链建模为联合多变量固定点系统，推导出解析解。基于该解析解，无需训练即可实现并行采样并恢复高质量图像。进一步利用深度均衡反演计算快速梯度，发现初始化优化可提升图像质量并控制生成方向。在基准数据集上的大量实验表明，该方法在典型图像恢复任务和真实场景中均具有有效性。