Recently, automatic speaker verification (ASV) based on deep learning is easily contaminated by adversarial attacks, which is a new type of attack that injects imperceptible perturbations to audio signals so as to make ASV produce wrong decisions. This poses a significant threat to the security and reliability of ASV systems. To address this issue, we propose a Diffusion-Based Adversarial Purification (DAP) method that enhances the robustness of ASV systems against such adversarial attacks. Our method leverages a conditional denoising diffusion probabilistic model to effectively purify the adversarial examples and mitigate the impact of perturbations. DAP first introduces controlled noise into adversarial examples, and then performs a reverse denoising process to reconstruct clean audio. Experimental results demonstrate the efficacy of the proposed DAP in enhancing the security of ASV and meanwhile minimizing the distortion of the purified audio signals.