This paper introduces a dynamic kernel prior (DKP) model to address the blind super-resolution (BSR) problem without requiring supervised pre-training. The DKP model consists of two main components: a random kernel sampling (RKS) module and a prior kernel estimation (PKE) module. The RKS module uses Markov Chain Monte Carlo (MCMC) sampling to generate random kernels, which serve as kernel priors. These priors are then used by the PKE module to estimate the blur kernel, which is crucial for high-resolution (HR) image restoration. The DKP model is designed to be plug-and-play, meaning it can be easily integrated with existing image restoration models such as deep image prior (DIP) and diffusion models. Extensive experiments on both synthetic and real-world datasets demonstrate that the DKP model significantly improves kernel estimation accuracy and leads to superior BSR results. The proposed methods, DIP-DKP and Diff-DKP, achieve state-of-the-art performance in both Gaussian and motion kernel scenarios, validating the effectiveness and flexibility of the DKP model.This paper introduces a dynamic kernel prior (DKP) model to address the blind super-resolution (BSR) problem without requiring supervised pre-training. The DKP model consists of two main components: a random kernel sampling (RKS) module and a prior kernel estimation (PKE) module. The RKS module uses Markov Chain Monte Carlo (MCMC) sampling to generate random kernels, which serve as kernel priors. These priors are then used by the PKE module to estimate the blur kernel, which is crucial for high-resolution (HR) image restoration. The DKP model is designed to be plug-and-play, meaning it can be easily integrated with existing image restoration models such as deep image prior (DIP) and diffusion models. Extensive experiments on both synthetic and real-world datasets demonstrate that the DKP model significantly improves kernel estimation accuracy and leads to superior BSR results. The proposed methods, DIP-DKP and Diff-DKP, achieve state-of-the-art performance in both Gaussian and motion kernel scenarios, validating the effectiveness and flexibility of the DKP model.