Source-Free Domain Adaptation (SFDA) aims to adapt a pre-trained source model to an unlabeled target domain with no access to the source data. Inspired by the success of large Vision-Language (ViL) models in many applications, the latest research has validated ViL's benefit for SFDA by using their predictions as pseudo supervision. However, we observe that ViL's supervision could be noisy and inaccurate at an unknown rate, potentially introducing additional negative effects during adaption. To address this thus-far ignored challenge, we introduce a novel Proxy Denoising (ProDe) approach. The key idea is to leverage the ViL model as a proxy to facilitate the adaptation process towards the latent domain-invariant space. Concretely, we design a proxy denoising mechanism to correct ViL's predictions. This is grounded on a proxy confidence theory that models the dynamic effect of proxy's divergence against the domain-invariant space during adaptation. To capitalize the corrected proxy, we further derive a mutual knowledge distilling regularization. Extensive experiments show that ProDe significantly outperforms the current state-of-the-art alternatives under both conventional closed-set setting and the more challenging open-set, partial-set, generalized SFDA, multi-target, multi-source, and test-time settings. Our code and data are available at https://github.com/tntek/source-free-domain-adaptation.