Domain shift (the difference between source and target domains) poses a significant challenge in clinical applications, e.g., Diabetic Retinopathy (DR) grading. Despite considering certain clinical requirements, like source data privacy, conventional transfer methods are predominantly model-centered and often struggle to prevent model-targeted attacks. In this paper, we address a challenging Online Model-aGnostic Domain Adaptation (OMG-DA) setting, driven by the demands of clinical environments. This setting is characterized by the absence of the model and the flow of target data. To tackle the new challenge, we propose a novel approach, Generative Unadversarial ExampleS (GUES), which enables adaptation from a data-centric perspective. Specifically, we first theoretically reformulate conventional perturbation optimization in a generative way—learning a perturbation generation function with a latent input variable. During model instantiation, we leverage a Variational AutoEncoder to express this function. The encoder with the reparameterization trick predicts the latent input, whilst the decoder is responsible for the generation. Furthermore, the saliency map is selected as pseudo-perturbation labels. Because it not only captures potential lesions but also theoretically provides an upper bound on the function input, enabling the identification of the latent variable. Extensive experiments on DR benchmarks with both frozen pre-trained models and trainable models demonstrate the superiority of GUES, showing robustness even with small batch size. The source code and data are available at https://github.com/tntek/GUES.