Video matting has traditionally been limited by the lack of high-quality ground-truth data. Most existing video matting datasets provide only human-annotated imperfect alpha and foreground annotations, which must be composited to background images or videos during the training stage. Thus, the generalization capability of previous methods in real-world scenarios is typically poor. In this work, we propose to solve the problem from two perspectives. First, we emphasize the importance of large-scale pre-training by pursuing diverse synthetic and pseudo-labeled segmentation datasets. We also develop a scalable synthetic data generation pipeline that can render diverse human bodies and fine-grained hairs, yielding around 200 video clips with a 3-second duration for fine-tuning. Second, we introduce a novel video matting approach that can effectively leverage the rich priors from pre-trained video diffusion models. This architecture offers two key advantages. First, strong priors play a critical role in bridging the domain gap between synthetic and real-world scenes. Second, unlike most existing methods that process video matting frame-by-frame and use an independent decoder to aggregate temporal information, our model is inherently designed for video, ensuring strong temporal consistency. We provide a comprehensive quantitative evaluation across three benchmark datasets, demonstrating our approach's superior performance, and present comprehensive qualitative results in diverse real-world scenes, illustrating the strong generalization capability of our method. The code is available at https://github.com/aim-uofa/GVM.