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，在图像超分辨率（SR）任务中取得了显著成果。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性能都会波动，尤其是在重采样步骤较少的采样器中。这种固有随机性导致模型效率低下且不稳定，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：通过充分分析和利用该随机性，构建了一种有效的即插即用采样方法，该方法有望惠及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（扩散ODE），从预训练的基于扩散的超分辨率模型中稳定采样高质量超分辨率图像，并分析边界条件选择与对应超分辨率结果之间的特征关系。我们的分析揭示了如何通过在全空间中进行高效探索来获得近似最优边界条件的路径。与使用相同预训练扩散超分辨率模型时当前方法在随机条件下采样的结果相比，本文所提方法在更少采样步骤下获得的超分辨率结果质量更优，这意味着我们的采样方法无需额外训练即可"提升"当前基于扩散的超分辨率模型。