Solving Diffusion ODEs with Optimal Boundary Conditions for Better Image Super-Resolution

Diffusion models, as a kind of powerful generative model, have givenimpressive results on image super-resolution (SR) tasks. However, due to therandomness introduced in the reverse process of diffusion models, theperformances of diffusion-based SR models are fluctuating at every time ofsampling, especially for samplers with few resampled steps. This inherentrandomness 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 andleveraging it leads to the construction of an effective plug-and-play samplingmethod that owns the potential to benefit a series of diffusion-based SRmethods. More in detail, we propose to steadily sample high-quality SR imagesfrom pre-trained diffusion-based SR models by solving diffusion ordinarydifferential equations (diffusion ODEs) with optimal boundary conditions (BCs)and analyze the characteristics between the choices of BCs and theircorresponding SR results. Our analysis shows the route to obtain anapproximately optimal BC via an efficient exploration in the whole space. Thequality of SR results sampled by the proposed method with fewer stepsoutperforms the quality of results sampled by current methods with randomnessfrom the same pre-trained diffusion-based SR model, which means that oursampling method "boosts" current diffusion-based SR models without anyadditional training.