Although existing video editing methods are generally feasible, they often require many costly iterations and still struggle to deliver high-quality yet satisfying editing results. We attribute this limitation to the prevalent data-to-data paradigm, which is less compatible with modern generative models than noise-to-data generation. To address this gap, we revisit video editing from a noise-to-data perspective and propose Streaming-Generation-based Video Editing (StreamGVE), which preserves few-step sampling while seamlessly injecting source-video conditions. Built on pre-trained streaming generation models, StreamGVE introduces dual-branch fast sampling with a self-attention bridge and cross-attention grounding/boosting to satisfy both sampling and conditioning requirements. We further propose source-oriented guidance to improve target-generation quality, and a visual prompting strategy to enhance editing flexibility and practicality. The method is effective, robust, and generalizable across different models. Extensive experiments on diverse video editing tasks show that StreamGVE consistently outperforms existing approaches, even in few-step settings with minimal time cost.