Dexterous manipulation, particularly adept coordinating and grasping, constitutes a fundamental and indispensable capability for robots, facilitating the emulation of human-like behaviors. Integrating this capability into robots empowers them to supplement and even supplant humans in undertaking increasingly intricate tasks in both daily life and industrial settings. Unfortunately, contemporary methodologies encounter serious challenges in devising manipulation trajectories owing to the intricacies of tasks, the expansive robotic manipulation space, and dynamic obstacles. We propose a novel approach, APEX, to address all these difficulties by introducing a collision-free latent diffusion model for both robotic motion planning and manipulation. Firstly, we simplify the complexity of real-life ambidextrous dual-arm robotic manipulation tasks by abstracting them as aligning two vectors. Secondly, we devise latent diffusion models to produce a variety of robotic manipulation trajectories. Furthermore, we integrate obstacle information utilizing a classifier-guidance technique, thereby guaranteeing both the feasibility and safety of the generated manipulation trajectories. Lastly, we validate our proposed algorithm through extensive experiments conducted on the hardware platform of ambidextrous dual-arm robots. Our algorithm consistently generates successful and seamless trajectories across diverse tasks, surpassing conventional robotic motion planning algorithms. These results carry significant implications for the future design of diffusion robots, enhancing their capability to tackle more intricate robotic manipulation tasks with increased efficiency and safety. Complete video demonstrations of our experiments can be found in https://sites.google.com/view/apex-dual-arm/home.