This is "I Believe" from the movie My Sassy Girl. The English translation has some small grammatical errors but the gist of it reminds me of Cloud and Aerith

I Believe..
by Shin Seung Hun

though you're not here by my side
this is not the end, is it?

I believe..
the road you chose to come back
is just a bit detoured, isn't it?

Living in my memories
I hurt myself
crying out my tears

Hope you don't cry as much as I do
Hope you can leave me without tears
I know that you'll come back (to me) someday
because I believe (you'll come back)
I'll wait for you, it has to be you

I believe..
you couldn't cry
coz you worried about my pain

I believe..
my tears will bring you back to me
I can't erase you from my eyes
which makes me cry

Hope you don't cry as much as I do
Hope you can leave me without tears
I know that you'll come back (to me) someday
because I believe (you'll come back)
I'll wait for you, it has to be you

Before I knew you
the world was not as beautiful as now
now under the same sky

I'm alone with tears
but I'll stay here
just because of you

even with my hopeless waiting
I'll be happy enough
just to think about love

I forget another day is coming and going
I'll wait for you, it has to be you
It has to be you

thats wonderful KY. its really beautiful ^_^ i loved it

The movie is awesome!! ;__; And the song is beautiful *wipes tears*