For example DbVisualizer can be used to connect to a DB and create nice diagram out of existing tables and their relations. But in this specific case I do not have a live database but I have bunch of create table and alter statements.
Is there any tool to generate similar diagrams out of SQL DDL?
I believe that Embarcadero's ERStudio can import a SQL script into a diagram, but it's a pricey tool to use just for something like this. You could always just create an empty database and run the scripts then point to that.