All healthy distributions will have either a Changes file, or a ChangeLog file. Sometimes authors also leave older versions on CPAN, and you can scan through them. Example: Module::Starter.

Many currently-maintained modules have public repositories such as a Github repo, or a Subversion repo. Example: The Module::Starter Github repo.

Backpan maintains practically all versions of all past CPAN releases.

There's The Gitpan Project, which has a pretty good Git history for almost all CPAN modules that were in existence about three years ago. That project was assembled a few years back, and hasn't been updated. But if you want to look at really old diffs, it's there.

If you have a specific need that isn't covered here, email the module's author and ask him if he's got what you need.