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.

通过采用深度平衡固定点系统，我们重新思考了基于扩散的图像修复模型，并且通过模型化扩散模型中的整个采样链作为多元固定点系统，以获得解析解，从而能够并行地进行单图像采样，无需训练。在 DEQ 中计算快速梯度，并发现初始化优化可以提高性能并控制生成方向。在基准测试和实际环境中进行的大量实验证明了我们提出的方法的有效性。代码和模型将公开提供。

深度平衡扩散修复与并行采样

Deep Equilibrium Diffusion Restoration with Parallel Sampling

Denoising Diffusion Probabilistic Models have shown an impressive generation
quality, although their long sampling chain leads to high computational costs.
In this paper, we observe that a long sampling chain also leads to an error
accumulation phenomenon, which is similar to the exposure bias problem in
autoregressive text generation. Specifically, we note that there is a
discrepancy between training and testing, since the former is conditioned on
the ground truth samples, while the latter is conditioned on the previously
generated results. To alleviate this problem, we propose a very simple but
effective training regularization, consisting in perturbing the ground truth
samples to simulate the inference time prediction errors. We empirically show
that the proposed input perturbation leads to a significant improvement of the
sample quality while reducing both the training and the inference times. For
instance, on CelebA 64$\times$64, we achieve a new state-of-the-art FID score
of 1.27, while saving 37.5% of the training time. The code is publicly
available at this https URL

通过加入输入扰动以模拟推理时间预测误差，本文提出了一种简单而有效的训练正则化方法，以减轻 Denoising Diffusion Probabilistic Models 模型中的错误积累现象，并在维持较高的采样质量的同时，显著减少训练和推理时间。