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Frontier model developers aim to train models continually to possess emergent, diverse capabilities. To extend capabilities, the current pre-training and post-training paradigm requires manually starting training runs with static datasets or reward functions every time. Addressing this limitation, our work pursues the insight that open-endedness (via the coevolution of models and tasks) can discover models with increasingly novel skills in a single run. We introduce a new model development framework that extends coevolution to large language model (LLM) discovery, open-ended \textit{Assessment Coevolving with Diverse Capabilities} (AC/DC). AC/DC evolves both LLMs via model merging and natural language tasks via synthetic data generation. AC/DC discovers growing archives of LLMs that surpass the capabilities of larger LLMs while taking up less GPU memory. In particular, our LLM populations achieve a broader Coverage of expertise than other curated models or baselines on downstream benchmarks, without \textit{any} explicit benchmark optimization. Furthermore, AC/DC improves Coverage over time, continually innovates on tasks and models, and improves performance in multi-agent best-of-N selection. Our findings highlight the potential of coevolution as a means of discovering broader sets of capabilities from base LLMs. Overall, AC/DC brings us one step closer to a profoundly new paradigm of LLM development, where continual improvements to the diversity of model capabilities can be accelerated by leveraging existing models as stepping stones to increasingly powerful models.