I guess I should explain all of Celestia's partners and the stories behind them, because I've only vaguely explained the timeline.

Prince Rutherford and Celestia
Early on into Celestia's ruling, the Yaks were having issues with finding a suitable partner to help raise the next generation of royalty. Rutherford would have no creature but Celestia; as she was an elegant and powerful pony. Celestia agreed, being the quite generous pony she was. Yelrah was raised in Yaktakistan, where she currently resides.

Queen Novo and Celestia
Celestia had never had any special interest in any creature; or so she thought. Years after Yelrah was born, she met Queen Novo; the most beautiful hippogriff she had ever laid eyes on. Novo felt the same about her. It first started out with visit to each other's kingdoms, just regular royal duties. But over the years their bond grew stronger and they grew closer, and began dating. Seafoam was created with the magic from them both, and they intended to raise her together. But due to their kingdoms being so far, and the Hippogriffs retreating underwater, this made it impossible. They soon made the sad agreement to end their relations, as it was best for both kingdoms and their residents.

Thorax and Celestia
Celestia did not quickly find love again after her departure from Novo, she was devastated. But Thorax brought the light of life into her that she needed. Helping him build the new kingdom of the changelings, she discovered what an exquisite creature he was. One thing led to another, and they became a couple. Celestia is the current lover of Thorax, as they raise their daughter Aurora in both Canterlot and the Changeling Kingdom.