The demand for condition-based and predictive maintenance is rising across industries, especially for remote, high-value, and high-risk assets. In this article, the diagnostic digital twin concept is introduced, discussed, and implemented for a floating offshore turbine. A diagnostic digital twin is a virtual representation of an asset that combines real-time data and models to monitor damage, detect anomalies, and diagnose failures, thereby enabling condition-based and predictive maintenance. By applying diagnostic digital twins to offshore assets, unexpected failures can be alleviated, but the implementation can prove challenging. Here, a diagnostic digital twin is implemented for an operational floating offshore wind turbine. The asset is monitored through measurements. Unsupervised learning methods are employed to build a normal operation model, detect anomalies, and provide a fault diagnosis. Warnings and diagnoses are sent through text messages, and a more detailed diagnosis can be accessed in a virtual reality interface. The diagnostic digital twin successfully detected an anomaly with high confidence hours before a failure occurred. The paper concludes by discussing diagnostic digital twins in the broader context of offshore engineering. The presented approach can be generalized to other offshore assets to improve maintenance and increase the lifetime, efficiency, and sustainability of offshore assets.