Dave Hayden blogs about Craig Larman's book Applying UML and Patterns: An Introduction to Object-Oriented Analysis and Design and Iterative Development.
An important note is that “the output of an iteration is not an experimental or throw-away prototype, and iterative development is not prototyping. Rather, the output is a production-grade subset of the final system.“
This is a fundamental tenet of Scrum. Although there is another scenario in Scrum, that of throwing away the product of an iteration.
In previous Scrum projects I've avoided using UML because its heavyweight nature and the friction it incurs and have preferred an eXtreme Whiteboarding approach, using lightweight entity diagrams quickly sketched on a whiteboard, although UML diagrams have been generated for documentation, from the code we've written, using tools such as Assembly2Visio - Visio 2003 UML Diagram Editor.