Existing end-to-end autonomous driving (E2E-AD) methods predominantly rely on single expert demonstration through imitation learning, often leading to conservative and homogeneous driving behaviors that struggle to generalize to complex real-world scenarios. In this work, we propose DIVER, a novel E2E-AD framework that combines diffusion-based multi-mode trajectory generation with reinforcement learning to produce diverse, safe, and goal-directed trajectories. First, the model conditions on map elements and surrounding agents to generate multiple reference trajectories from each ground-truth reference trajectory that overcome the inherent limitations of single-mode imitation. Second, we treat the diffusion process as a stochastic policy and employ Group Relative Policy Optimization (GPRO) objectives to guide the diffusion process. By optimizing trajectory-level rewards for both diversity and safety, GRPO directly mitigates mode collapse and enhances collision avoidance, encouraging exploration beyond expert demonstrations and ensuring physically plausible plans. Furthermore, to address the limitations of L2-based open-loop metrics in capturing trajectory diversity, we propose a novel trajectory diversity metric to evaluate the diversity of multi-mode predictions. Extensive experiments on the closed-loop NAVSIM and Bench2Drive benchmarks, as well as the open-loop nuScenes dataset, demonstrate that DIVER significantly improves trajectory diversity, effectively addressing the mode collapse problem inherent in imitation learning. The source code is available at https://github.com/adept-thu/diver.