We present a framework for training large language models (LLMs) as diagnostic agents with reinforcement learning, enabling them to manage multi-turn interactive diagnostic processes, adaptively select examinations, and commit to final diagnoses. Unlike instruction-tuned models trained on static data, our method acquires diagnostic strategies through dynamic exploration and outcome-based feedback, mapping evolving patient states to the next optimal examination and subsequent diagnosis. Our contributions include: (i) DiagGym, a diagnostics world model trained with electronic health records, serving as a virtual clinical environment to support closed-loop in-silico training and evaluation for interactive diagnosis; (ii) DiagAgent, trained via end-to-end multi-turn RL to learn dynamic diagnostic policies that optimize both interactive effectiveness and final accuracy; (iii) DiagBench, a multi-center diagnostic benchmark designed to evaluate multi-turn diagnostic interaction trajectories. The benchmark comprises 2.2K physician-validated cases sourced from 4 distinct distributions, alongside 3.3K physician-written rubrics for granular process-oriented evaluation. (iv) Extensive evaluations demonstrate DiagAgent's superior performance across both in-domain and out-of-domain (OOD) settings. DiagAgent significantly outperforms 11 SOTA LLMs and 2 prompt-engineered agents. In the end-to-end setting, it delivers a 11.20% increase in diagnostic accuracy and a 17.58% boost in examination recommendation F1 score, while consistently maintaining SOTA performance across all three external centers. Furthermore, in rubric-based evaluations, it surpasses the next-best model by 7.1% in weighted rubric score. These findings indicate that learning policies in interactive clinical environments confers long-term diagnostic management abilities unattainable through passive training.