Simulation is an indispensable tool in the development and testing of autonomous vehicles (AVs), offering an efficient and safe alternative to road testing by allowing the exploration of a wide range of scenarios. Despite its advantages, a significant challenge within simulation-based testing is the generation of safety-critical scenarios, which are essential to ensure that AVs can handle rare but potentially fatal situations. This paper addresses this challenge by introducing a novel generative framework, CaDRE, which is specifically designed for generating diverse and controllable safety-critical scenarios using real-world trajectories. Our approach optimizes for both the quality and diversity of scenarios by employing a unique formulation and algorithm that integrates real-world data, domain knowledge, and black-box optimization techniques. We validate the effectiveness of our framework through extensive testing in three representative types of traffic scenarios. The results demonstrate superior performance in generating diverse and high-quality scenarios with greater sample efficiency than existing reinforcement learning and sampling-based methods.