Upscale-A-Video is a diffusion-based model designed to increase video resolution by taking low-resolution videos and text prompts as input. The model ensures temporal consistency through two key mechanisms: locally, it integrates temporal layers into the U-Net and VAE-Decoder to maintain consistency in short sequences; globally, it introduces a stream-guided recurrent potential propagation module that enhances overall video stability by propagating and fusing potential information throughout the sequence. Due to the diffusion paradigm, our model balances fidelity and quality by allowing text prompts to guide texture creation and tunable noise levels, thus achieving a trade-off between restoration and generation. Extensive experiments have proved that Upscale-A-Video outperforms existing methods across synthetic and real-world benchmarks as well as AI-generated videos, demonstrating impressive visual fidelity and temporal consistency.