"von allein" is a more or less fixed phrase meaning "without others' influence".
Why naturally and not alone?
It sounds better in English, I guess. The calm wasn't caused by exterior causes, it just happened on its own - hence "naturally." "Alone" makes it sound a bit peculiar.
Peace comes from within or Peace comes from solitude would be better translations
Calmness comes on its own
"Quiet comes from alone" does not sound to me like a real English sentence! I don't think I'd understand what someone meant.