Is it okay to ignore my former colleagues when I run into them on the street after resigning?

When I was working at my previous job, there was a supervisor I didn't get along with and who really disliked me. I've recently changed jobs, but coincidentally, my new office is just two buildings away.
So, I think I might run into them occasionally during lunch breaks. While working at the same company, there are unspoken company rules regarding the obligation to accept greetings or follow instructions due to the clear subordinate-supervisor relationship,
but I've heard that people you meet at work are ultimately just business acquaintances met through professional duties.
From the moment I resigned, that person is no longer my supervisor; we are on equal footing. Even if we do happen to speak, the way I address them should change—for example, from "Assistant Manager [Name]" to "[Name]-ssi"—and my speech should shift from informal to formal, just as if I were meeting a stranger.
In that sense, even if they try to acknowledge me first, I don't believe I have any obligation to respond. If they try to talk to me later, I'm planning to just pretend I don't know them and ignore them, since we didn't get along anyway. Is that alright?
I know I would have an obligation to respond if I were still employed there.