Planning safe and efficient trajectories through signal-free intersections presents significant challenges for autonomous vehicles (AVs), particularly in dynamic, multi-task environments with unpredictable interactions and an increased possibility of conflicts. This study aims to address these challenges by developing a robust, adaptive framework to ensure safety in such complex scenarios. Existing approaches often struggle to provide reliable safety mechanisms in dynamic and learn multi-task behaviors from demonstrations in signal-free intersections. This study proposes a safety-critical planning method that integrates Dynamic High-Order Control Barrier Functions (DHOCBF) with a diffusion-based model, called Dynamic Safety-Critical Diffuser (DSC-Diffuser), offering a robust solution for adaptive, safe, and multi-task driving in signal-free intersections. Our approach incorporates a goal-oriented, task-guided diffusion model, enabling the model to learn multiple driving tasks simultaneously from real-world data. To further ensure driving safety in dynamic environments, the proposed DHOCBF framework dynamically adjusts to account for the movements of surrounding vehicles, offering enhanced adaptability compared to traditional control barrier functions. Validity evaluations of DHOCBF, conducted through numerical simulations, demonstrate its robustness in adapting to variations in obstacle velocities, sizes, uncertainties, and locations, effectively maintaining driving safety across a wide range of complex and uncertain scenarios. Performance evaluations across various scenes confirm that DSC-Diffuser provides realistic, stable, and generalizable policies, equipping it with the flexibility to adapt to diverse driving tasks.