Changing the scope of 'diff' to something more granular?

I have a couple files that changed and can diff any pair of them with

$ vim old-a.txt new-a.txt

which works as expected. However, if I try to diff old-a/new-a and
also try to :diffsplit old-b/new-b, it compares *all* of those files.
Which is also expected. So currently I need to launch each diff in
its own session of vim.

shell1$ vim old-a.txt new-a.txt
...
shell2$ vim old-b.txt new-b.txt

While this is functional (and less bad within a tmux session), is it
possible to narrow the scope of a :vimdiff to a vim-tab so that I can
have a single vim session with multiple file-diff pairs within?

Mostly it's nice to have things like `gd`, `gD`, jump to places that
show the diffs in the destination as well.

Thanks for any ideas,

-tim



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