You want run Windows 8.1 as an Azure VM without using an MSDN subscription. This currently is not an option to run as an Azure VM as of yet. What can I do as a workaround? You can run the Windows 8.1 desktop shell on top of Windows Server 2012 R2 (foundational code base has shared parts):
How can I do this?
1. Build a Windows Server 2012 R2 VM in Azure either using HUB or from the Azure Gallery. See my other post here on how to use the BYOL HUB model.
2. Start the VM and RDP into it.
3. Select Control Panel > Programs > Add/Remove features > features > user interface and infrastructure > desktop experience
4. Reboot and login. It will now log into the Windows 8.1 classic desktop even though it is running Windows Server 2012 R2 underneath in the Azure VM. You can add in Windows 8.1 desktop themes, change the colors, etc.