While Unmanned Aerial Vehicles (UAVs) have gained significant traction across various fields, path planning in 3D environments remains a critical challenge, particularly under size, weight, and power (SWAP) constraints. Traditional modular planning systems often introduce latency and suboptimal performance due to limited information sharing and local minima issues. End-to-end learning approaches streamline the pipeline by mapping sensory observations directly to actions but require large-scale datasets, face significant sim-to-real gaps, or lack dynamical feasibility. In this paper, we propose a self-supervised UAV trajectory planning pipeline that integrates a learning-based depth perception with differentiable trajectory optimization. A 3D cost map guides UAV behavior without expert demonstrations or human labels. Additionally, we incorporate a neural network-based time allocation strategy to improve the efficiency and optimality. The system thus combines robust learning-based perception with reliable physics-based optimization for improved generalizability and interpretability. Both simulation and real-world experiments validate our approach across various environments, demonstrating its effectiveness and robustness. Our method achieves a 31.33% improvement in position tracking error and 49.37% reduction in control effort compared to the state-of-the-art.