Is there a way to use `git diff` to get a diff between two commits, but only show the diff for the files that exist in both commits?

I have a branch I created a couple of weeks ago, and our main code has diverged quite a bit from it by now. As a result, if I do a diff between my current HEAD and the tip of the old branch, I get dozens of changed files, but it's mostly just noise.

I really want to see a diff that shows only the files that exist in both branches. I know one way to do this would be to cherry-pick the other branch's commits on top of the current HEAD, but is there a way to do it just using `git diff`?