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 pretrained 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 pretrained diffusion-based SR model, which means that our sampling method ``boosts'' current diffusion-based SR models without any additional training.

通过有效控制扩散模型回流过程中的随机性来提高预训练图像超分辨率模型的采样质量，在边界条件的选择上，我们通过对整个空间的高效探索来获取近似最优边界条件，并且通过我们的方法进行的采样结果质量要优于现有方法的随机结果。

使用最优边界条件解决扩散常微分方程以实现更好的图像超分辨率