提出分阶段筛选视频证据的方法，显著降低流式视频理解延迟。

Streaming video understanding requires Vision Language Models (VLLMs) to process growing video streams and answer user questions under tight latency constraints. Existing methods improve efficiency through token pruning and memory-bank schemes, but mainly reduce visual tokens after visual encoding. Consequently, downstream token pruning alone cannot substantially reduce end-to-end latency because the expensive frame encoding cost has already been incurred. We propose CoFiE, a Coarse-to-Fine Evidence Selection framework that decouples evidence selection into a coarse, query-agnostic filtering stage before the vision encoder and a fine, query-specific refinement stage during LLM prefill. CoFiE introduces Novelty-Guided Frame Filtering to retain visually distinctive candidate frames and Query-Specific Evidence Refinement to select the frames most relevant to the user query. This design removes substantial redundancy before frame encoding while preserving query-specific refinement once semantic information becomes available. Experiments show that CoFiE establishes a new state-of-the-art accuracy-efficiency trade-off across multiple video understanding benchmarks, reaching 78.86% accuracy on StreamingBench and 68.72% on OvO-Bench, with improvements of up to 3.15% over prior methods. Even with up to 80% evidence-frame filtering, CoFiE outperforms strong open-source multimodal models while improving end-to-end inference latency by up to 2.54 times.