Specify the paths explicitly:
git diff HEAD:full/path/to/foo full/path/to/bar
Check out the --find-renames option in the git-diffdocs.
Credit: twaggs.
git diff <path> <path> will compare two working-tree files as long as at least one of them is not in a git repo or the command is run from outside of a git repo. If you want to ensure git knows you are only comparing files in the working-tree (that is, on files in your directory rather than files added or commited to git), use git diff --no-index <path> <path>