Divine Form

The Divine Form, also known as the Immortal Form or Godly Form, is the true, natural form of the Gods. Looking upon a god in this state will incinerate the onlooker. Titans also have a divine form, which differs from that of the Olympians in that they are able to destroy mortal beings simply by being in their presence. It is unknown if this is because the divine form of a Titan is more powerful than that of a god, or simply more volatile and chaotic.

Description
Gods, in their natural state, radiate the true, unbridled power of their divine essence. Their bodies are enveloped in an intense light, which seems to differ in color based on the god, along with waves of power and energy. For example Poseidon's godly form is a merman. Mortals cannot witness a god in this form, lest they burn up from the sight. To interact safely with mortal beings, the gods will take on their default human appearance which can be looked at harmlessly. While the gods can take any guise they choose, whether it be a human, an animal, or a flame, they have a default human appearance that they cannot augment without the Mist and most accurately fits their personality and essence. This is the closest a mortal would ever come to seeing a god's true, divine form.

Trivia
There is a reference to demigods having a divine form in The Battle of the Labyrinth when the empousai, Kelli called Percy "fish". This implies that if demigods do have a divine form, than Percy's is fish-like, inherited from Poseidon.

Demigods
Demigods (because they are born of a divine being) are able to see the smallest bit of a god's divine form by looking into their eyes, which shine with their essence and power. The gods can also use this phenomenon to show the demigod visions through their eyes, such as Hestia and Dionysus have done for Percy. Mortals might be able to observe this glimpse of godly power as well, should they be able to see through the Mist.