The Divine Upgrade Path is a form of weapon ascension and becomes available to Andre of Astora after he receives the Divine Ember found in Darkroot Garden. Giving him the Large Divine Ember found in the Tomb of the Giants allows him to ascend Divine weapons to +6 and beyond. Creation of Divine weapons requires a standard weapon +5, Green Titanite Shards (for upgrading up to +5), White Titanite Chunks (for upgrading from +6 to +9), and a White Titanite Slab (for upgrading from +9 to +10).
The Divine Upgrade Path adds the Divine Auxiliary Effect, increases scaling with Faith and adds Magic Damage to weapons, but reduces Dexterity and Strength scaling. This makes Divine weapons suitable for players that have high Faith, but low Strength and Dexterity.
Divine weapons cannot be buffed. At high levels of Strength/Dexterity and Faith, a standard weapon enchanted with a miracle such as Sunlight Blade or Darkmoon Blade will out-damage Divine weapons in the short run. However, divine weapons hold the advantage of not having to be enchanted to reach their maximum potential.
This upgrade path is useless for shields. A Divine shield + 10 has exactly the same defense as a Normal shield +0. This could be a sign that the upgrade path wasn't completely finished, because one would expect magic defense to be added. However, the shield will get magic damage that scales with faith and a divine effect.