This paper presents a deep reinforcement learning (DRL) based controller for collective navigation of unmanned aerial vehicle (UAV) swarms in communication-denied environments, enabling robust operation in complex, obstacle-rich environments. Inspired by biological swarms where informed individuals guide groups without explicit communication, we employ an implicit leader-follower framework. In this paradigm, only the leader possesses goal information, while follower UAVs learn robust policies using only onboard LiDAR sensing, without requiring any inter-agent communication or leader identification. Our system utilizes LiDAR point clustering and an extended Kalman filter for stable neighbor tracking, providing reliable perception independent of external positioning systems. The core of our approach is a DRL controller, trained in GPU-accelerated Nvidia Isaac Sim, that enables followers to learn complex emergent behaviors - balancing flocking and obstacle avoidance - using only local perception. This allows the swarm to implicitly follow the leader while robustly addressing perceptual challenges such as occlusion and limited field-of-view. The robustness and sim-to-real transfer of our approach are confirmed through extensive simulations and challenging real-world experiments with a swarm of five UAVs, which successfully demonstrated collective navigation across diverse indoor and outdoor environments without any communication or external localization.