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

翻译：基于扩散的图像复原方法旨在利用扩散模型从退化图像中恢复高质量图像，并取得了显著性能。由于扩散模型的固有特性，大多数此类方法需要长序列采样链逐步恢复高质量图像，从而导致昂贵的采样时间和高昂的计算成本。此外，这种长采样链阻碍了恢复结果与输入之间关联的理解，因为计算整个链的梯度十分困难。本研究拟从不同视角——即深度平衡不动点系统——重新审视基于扩散的图像复原模型。具体而言，通过将扩散图像复原模型中的整个采样链建模为联合多变量不动点系统，我们推导出一个解析解。借助该解析解，我们能够以并行方式实现单图像采样，并在无需训练的情况下恢复高质量图像。进一步地，我们计算了深度平衡系统中的快速梯度，发现初始化优化可提升性能并控制生成方向。在基准数据集上的大量实验证明了所提方法在典型图像复原任务和真实场景中的有效性。代码和模型将公开发布。