What is the best way to create a database diagram for SQL Azure without having to install SQL Server?

UPDATE: The database diagrams were added back into SSMS 18.1(link)

UPDATE: the database diagram feature

Deprecated and removed features in 18.0 (GA) ... Database Diagrams https://docs.microsoft.com/en-us/sql/ssms/release-notes-ssms

The feature was also removed from Visual Studio 2019 SSDT.

Original Answer

The latest version of SSMS (as of v16) supports creating database diagrams for Azure SQL databases. You can download it here:

https://msdn.microsoft.com/en-us/library/mt238290.aspx

SQL Azure databases do not support diagrams in the same way 'normal' on premise SQL Servers do, so you are looking at workarounds or third-party tools. For example, you could install SQL Server Data Tools (SSDT), pull your model down, deploy to a local 'normal' dev server, create the diagram there. This would not involve much data so would be lightweight. Alternately use Viso, Powerpoint, dbForge, Erwin, RedGate, Apex ... paper and pencil etc : )

A little additional research shows Red Gate have recently added more support for SQL Azure and have a free trial, and SQL Power Doc which looks useful and could plug into NodeXL for example.

In summary, the tooling hasn't quite caught up but you have a few options.