I've been in the same situation years ago. You walk through the open-space to go to your desk, and either a door is open or people are arguing (but think there's nobody else around). So, it's a "private professional" dispute. Conflicts like that happen all the time. It doesn't mean these people have an attitude or that the company is bad, it just means, from what I've witnessed, that, sometimes, 1 temper + 1 temper = 1 tempest :)
What can I say or do to appease the tension?
Nothing. Don't bother adding fuel to the fire. It will only make things worse.
Walk your way, don't interrupt them. Ignore them (at the time). Don't even say "Hi". You'll salute them later, when they've both cooled down. Act as if nothing happened, because it's none of your business, you're not involved.
Be professional, go to work, let them sort this out by themselves. Go back to them only when needed, for any question related to your work.
How do I get rid of this awkwardness when it happens?
Mind your own business, don't stop by. And, more important, never mention this to them. They know it happened, no need to remind them. They'll probably be grateful for being silent and discreet. My colleagues were. And when one was coming back to me with some kind of explanation ("yeah, about what you heard... bla bla bla..."), I always ended with a neutral:
- about what? heard nothing! and I guess I don't need to, you know :) (then change topic)
- well, it's a private dispute, nothing I should worry about, it's between you and them. No big deal.
What else? and go on...
Modify some parameters and think about it this way: you know two people, and see/hear them arguing in the street. Would you go straight to them and act as a referee, interfer without any knowledge about the situation/argument, or would you just walk your way?