Diffusion models, as a kind of powerful generative model, have given impressive results on image super-resolution (SR) tasks. However, due to the randomness introduced in the reverse process of diffusion models, the performances of diffusion-based SR models are fluctuating at every time of sampling, especially for samplers with few resampled steps. This inherent randomness of diffusion models results in ineffectiveness and instability, making it challenging for users to guarantee the quality of SR results. However, our work takes this randomness as an opportunity: fully analyzing and leveraging it leads to the construction of an effective plug-and-play sampling method that owns the potential to benefit a series of diffusion-based SR methods. More in detail, we propose to steadily sample high-quality SR images from pre-trained diffusion-based SR models by solving diffusion ordinary differential equations (diffusion ODEs) with optimal boundary conditions (BCs) and analyze the characteristics between the choices of BCs and their corresponding SR results. Our analysis shows the route to obtain an approximately optimal BC via an efficient exploration in the whole space. The quality of SR results sampled by the proposed method with fewer steps outperforms the quality of results sampled by current methods with randomness from the same pre-trained diffusion-based SR model, which means that our sampling method "boosts" current diffusion-based SR models without any additional training.

翻译：扩散模型作为一种强大的生成模型，已在图像超分辨率（SR）任务中展现出令人瞩目的成果。然而，由于扩散模型逆向过程中引入的随机性，基于扩散的超分辨率模型在每次采样时的表现存在波动，尤其在使用步长较少的采样器时更为显著。这种固有随机性导致模型效能低下且不稳定，使用户难以保证超分辨率结果的质量。但我们的工作将这种随机性视为机遇：通过深入分析与充分利用该特性，我们构建了一种即插即用的高效采样方法，有望提升一系列基于扩散的超分辨率方法。具体而言，我们提出通过求解具有最优边界条件（BCs）的扩散常微分方程（diffusion ODEs），从预训练的扩散超分辨率模型中稳定采样高质量超分辨率图像，并系统分析了边界条件选择与对应超分辨率结果之间的特性关系。研究表明，通过全局空间的高效探索可获得近似最优边界条件。相较于采用同源预训练扩散超分辨率模型的现有随机采样方法，本方法在更少采样步数下生成的结果在质量上更具优势，这意味着我们的采样方法无需额外训练即可"增强"现有基于扩散的超分辨率模型。