The effort to love goes a long way.
They started off as comrades. Next they were friends. Soon after, lovers.
After their first night together, a night of passion and bliss, they both decided they liked it best that way. Neither of them knew exactly how they had gotten from one point to the other, but they supposed it didn't matter anyway.
Forgetting the past is hard, but it's much easier when your heart is full of love. Cid had just enough to make Vincent's past slip away.
As for Cid, Vincent's love made his heart soar; made him fly.