Path planning for a robotic system in high-dimensional cluttered environments needs to be efficient, safe, and adaptable for different environments and hardware. Conventional methods face high computation time and require extensive parameter tuning, while prior learning-based methods still fail to generalize effectively. The primary goal of this research is to develop a path planning framework capable of generalizing to unseen environments and new robotic manipulators without the need for retraining. We present GADGET (Generalizable and Adaptive Diffusion-Guided Environment-aware Trajectory generation), a diffusion-based planning model that generates joint-space trajectories conditioned on voxelized scene representations as well as start and goal configurations. A key innovation is GADGET's hybrid dual-conditioning mechanism that combines classifier-free guidance via learned scene encoding with classifier-guided Control Barrier Function (CBF) safety shaping, integrating environment awareness with real-time collision avoidance directly in the denoising process. This design supports zero-shot transfer to new environments and robotic embodiments without retraining. Experimental results show that GADGET achieves high success rates with low collision intensity in spherical-obstacle, bin-picking, and shelf environments, with CBF guidance further improving safety. Moreover, comparative evaluations indicate strong performance relative to both sampling-based and learning-based baselines. Furthermore, GADGET provides transferability across Franka Panda, Kinova Gen3 (6/7-DoF), and UR5 robots, and physical execution on a Kinova Gen3 demonstrates its ability to generate safe, collision-free trajectories in real-world settings.