Autonomous driving policies are typically trained via open-loop behavior cloning of human demonstrations. However, such policies suffer from covariate shift when deployed in closed loop, leading to compounding errors. We introduce Rollouts as Demonstrations (RoaD), a simple and efficient method to mitigate covariate shift by leveraging the policy's own closed-loop rollouts as additional training data. During rollout generation, RoaD incorporates expert guidance to bias trajectories toward high-quality behavior, producing informative yet realistic demonstrations for fine-tuning. This approach enables robust closed-loop adaptation with orders of magnitude less data than reinforcement learning, and avoids restrictive assumptions of prior closed-loop supervised fine-tuning (CL-SFT) methods, allowing broader applications domains including end-to-end driving. We demonstrate the effectiveness of RoaD on WOSAC, a large-scale traffic simulation benchmark, where it performs similar or better than the prior CL-SFT method; and in AlpaSim, a high-fidelity neural reconstruction-based simulator for end-to-end driving, where it improves driving score by 41\% and reduces collisions by 54\%.