Autonomous visual navigation is an essential element in robot autonomy. Reinforcement learning (RL) offers a promising policy training paradigm. However existing RL methods suffer from high sample complexity, poor sim-to-real transfer, and limited runtime adaptability to navigation scenarios not seen during training. These problems are particularly challenging for drones, with complex nonlinear and unstable dynamics, and strong dynamic coupling between control and perception. In this paper, we propose a novel framework that integrates 3D Gaussian Splatting (3DGS) with differentiable deep reinforcement learning (DDRL) to train vision-based drone navigation policies. By leveraging high-fidelity 3D scene representations and differentiable simulation, our method improves sample efficiency and sim-to-real transfer. Additionally, we incorporate a Context-aided Estimator Network (CENet) to adapt to environmental variations at runtime. Moreover, by curriculum training in a mixture of different surrounding environments, we achieve in-task generalization, the ability to solve new instances of a task not seen during training. Drone hardware experiments demonstrate our method's high training efficiency compared to state-of-the-art RL methods, zero shot sim-to-real transfer for real robot deployment without fine tuning, and ability to adapt to new instances within the same task class (e.g. to fly through a gate at different locations with different distractors in the environment). Our simulator and training framework are open-sourced at: https://github.com/Qianzhong-Chen/grad_nav.