Fine-grained concurrent programs are difficult to get right, yet play an important role in modern-day computers. We want to prove strong specifications of such programs, with minimal user effort, in a trustworthy way. In this paper, we present Diaframe—an automated and foundational verification tool for fine-grained concurrent programs. Diaframe is built on top of the Iris framework for higher-order concurrent separation logic in Coq, which already has a foundational soundness proof and the ability to give strong specifications, but lacks automation. Diaframe equips Iris with strong automation using a novel, extendable, goal-directed proof search strategy, using ideas from linear logic programming and bi-abduction. A benchmark of 24 examples from the literature shows that the proof burden of Diaframe is competitive with existing non-foundational tools, while its expressivity and soundness guarantees are stronger.