This paper proposes an Active Inference-based framework for autonomous trajectory design in UAV swarms. The method integrates probabilistic reasoning and self-learning to enable distributed mission allocation, route ordering, and motion planning. Expert trajectories generated using a Genetic Algorithm with Repulsion Forces (GA-RF) are employed to train a hierarchical World Model capturing swarm behavior across mission, route, and motion levels. During online operation, UAVs infer actions by minimizing divergence between current beliefs and model-predicted states, enabling adaptive responses to dynamic environments. Simulation results show faster convergence, higher stability, and safer navigation than Q-Learning, demonstrating the scalability and cognitive grounding of the proposed framework for intelligent UAV swarm control.