Device Model Generalization (DMG) is a practical yet under-investigated research topic for on-device machine learning applications. It aims to improve the generalization ability of pre-trained models when deployed on resource-constrained devices, such as improving the performance of pre-trained cloud models on smart mobiles. While quite a lot of works have investigated the data distribution shift across clouds and devices, most of them focus on model fine-tuning on personalized data for individual devices to facilitate DMG. Despite their promising, these approaches require on-device re-training, which is practically infeasible due to the overfitting problem and high time delay when performing gradient calculation on real-time data. In this paper, we argue that the computational cost brought by fine-tuning can be rather unnecessary. We consequently present a novel perspective to improving DMG without increasing computational cost, i.e., device-specific parameter generation which directly maps data distribution to parameters. Specifically, we propose an efficient Device-cloUd collaborative parametErs generaTion framework DUET. DUET is deployed on a powerful cloud server that only requires the low cost of forwarding propagation and low time delay of data transmission between the device and the cloud. By doing so, DUET can rehearse the device-specific model weight realizations conditioned on the personalized real-time data for an individual device. Importantly, our DUET elegantly connects the cloud and device as a 'duet' collaboration, frees the DMG from fine-tuning, and enables a faster and more accurate DMG paradigm. We conduct an extensive experimental study of DUET on three public datasets, and the experimental results confirm our framework's effectiveness and generalisability for different DMG tasks.