Okay so there's a story behind them but basically over in Ritou, Inazuma there is a shop that sells Monstadt goods, including wine. Diluc owns the wine tavern over in Monstadt so he goes with his shipment one time to Inazuma
So as he goes there, he sees some trouble with the and goes all Dark Knight Hero which sends a report to the Tenryou Commission
The description of a guy with a claymore, beating up criminals makes Kujou Sara suspect its Itto so she tries to catch him in the act, only to see it's Diluc
She denies any feelings she has for him (even though its super obvious) and he kind of develops feelings for her too
Of course when he goes back to Monstadt, it does hurt Kujou Sara, but he promises to keep in touch. So they start writing letters to each other
The letters start off casual, but feelings start to show and they become more romantic and passionate
Diluc decides to return to Inazuma to confess his feelings for Sara
She accepts the confession and even though their relationship is long distance, they make it work
