Centralized Application-Context Aware Firewall with Generative AI (CACAF-AI) is a next-generation network security framework designed to overcome the limitations of traditional port-based firewall systems. The proposed architecture integrates Deep Packet Inspection (DPI), identity-aware monitoring, behavioural anomaly detection, and AI-assisted threat interpretation to improve network visibility and threat detection. The system provides real-time traffic monitoring, user and device context mapping, centralized policy enforcement, and intelligent alert interpretation using Generative AI. Machine learning models analyze traffic patterns to detect anomalies such as abnormal data transfers, unauthorized access attempts, and suspicious lateral movement. Experimental evaluation demonstrates that the framework achieves 94.2% application classification accuracy and an anomaly detection rate of 89.5% with minimal processing latency. The integration of Gen-AI enhances operational efficiency by converting security alerts into human-readable explanations and assisting administrators in policy generation. The CACAF-AI framework provides a scalable and intelligent approach for modern distributed networks, enabling proactive threat detection and simplified security management for enterprise and institutional environments.