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We propose a new task, video referring matting, which obtains the alpha matte of a specified instance by inputting a referring caption. We treat the dense prediction task of matting as video generation, leveraging the text-to-video alignment prior of video diffusion models to generate alpha mattes that are temporally coherent and closely related to the corresponding semantic instances. Moreover, we propose a new Latent-Constructive loss to further distinguish different instances, enabling more controllable interactive matting. Additionally, we introduce a large-scale video referring matting dataset with 10,000 videos. To the best of our knowledge, this is the first dataset that concurrently contains captions, videos, and instance-level alpha mattes. Extensive experiments demonstrate the effectiveness of our method. The dataset and code are available at https://github.com/Hansxsourse/VRMDiff.