Large text-to-video models trained on internet-scale data have demonstrated exceptional capabilities in generating high-fidelity videos from arbitrary textual descriptions. However, similar to proprietary language models, large text-to-video models are often black boxes whose weight parameters are not publicly available, posing a significant challenge to adapting these models to specific domains such as robotics, animation, and personalized stylization. Inspired by how a large language model can be prompted to perform new tasks without access to the model weights, we investigate how to adapt a black-box pretrained text-to-video model to a variety of downstream domains without weight access to the pretrained model. In answering this question, we propose \emph{\methodname}, which leverages the score function of a large pretrained video diffusion model as a probabilistic prior to guide the generation of a task-specific small video model. Our experiments show that, by incorporating broad knowledge and fidelity of the pretrained model probabilistically, a small model with as few as 1.25% parameters of the pretrained model can generate high-quality yet domain-specific videos for a variety of downstream domains such as animation, egocentric modeling, and modeling of simulated and real-world robotics data. As large text-to-video models starting to become available as a service similar to large language models, we advocate for private institutions to expose scores of video diffusion models as outputs in addition to generated videos to allow flexible adaptation of large pretrained text-to-video models by the general public.