Vision-language models (VLMs) have shown strong performance in video anomaly detection (VAD) while providing interpretable predictions. However, existing VLM-based VAD methods suffer from a fundamental mismatch between training and inference in both data distribution and model configuration. First, most approaches rely on static post-training adaptation, limiting generalization under distribution shifts such as unseen environments or anomaly types. Second, they train VLMs on sparse frames from long videos, but perform inference on densely sampled short segments, creating inconsistencies between training and testing. To address these limitations, we propose COPRA, a conditional parameter adaptation framework for VLM-based VAD. Instead of fixed prompts or shared parameter updates, COPRA generates input-specific parameter updates to dynamically adapt a frozen VLM for each video segment during both training and inference. Experiments show strong performance on standard VAD benchmarks, consistently outperforming static baselines in both in-domain and cross-domain settings. Moreover, COPRA generalizes beyond VAD to unseen tasks such as multiple-choice Video Question Answering and Dense Captioning. These results highlight COPRA as an effective weight-space generation framework for scalable, adaptive, and context-aware video understanding. The code will be released at https://github.com/THE-MALT-LAB/COPRA