Q:

Do clerics, paladins, and warlocks gain level ups from their own power, or from their patrons or gods?

A friend and I (we both DM for each other occasionally) are having a discussion about where the increases in power of divine (cleric and paladin) and psuedo-divine (warlock) classes comes from at level ups. 
I'm under the impression that these classes are chosen by the gods (or their patron), and granted immense power early, but must learn to harness it as they grow. Levels happen to be discrete times when the mechanics of character growth match up with the "learned" abilities of the caster. From the cleric section of the PHB:

A cleric might learn formulaic prayers and ancient rites, but the ability to cast cleric spells relies on devotion and an intuitive sense of a deity's wishes (PHB 56)

This to me, reads as if a cleric's power grows as his devotion grows, and that devotion is denoted in-game as discrete levels.
To him, these classes are granted additional power by their gods at each level up. Their god (or patron) takes favor to them, and bestows greater powers upon them as needed. He quotes: 

The gods don't grant this power to everyone who seeks it, but only to those chosen to fulfill a higher calling. (PHB 56)

This seems to show that the powers and their use is governed by the gods, and not the cleric's own power in any respect. 
Both of these passages seem a bit ambiguous, and could be interpreted in ways that support either arguement. Is there any additional evidence in any official source that reveals where the powers granted to these classes comes from at each level up?

A:

It can be both
There is no reason these explanations must be mutually exclusive. Since there are places in the PHB supporting both of them, both can be true. Some powers are granted, and some are harnessed by the hero him/herself.
From the Warlock description, PHB p. 107 (emphasis mine):

... your otherworldly patron bestows a gift upon you for your loyal service. You gain one of the following features... 

the same page:

In your study of occult lore, you have unearthed eldritch
  invocations, fragments of forbidden knowledge that
  imbue you with an abiding magical ability

From the Cleric description, PHB p. 59:

As a cleric, you choose one aspect of your deity’s portfolio to emphasize,
  and you are granted powers related to that domain.

p. 58:

you gain the ability to channel divine energy directly from your deity, using that energy to fuel magical effects

A:

Both and neither
It's the same form of question you get when you look at other classes. Does the Barbarian get stronger because he's literally stronger? If so, why does Experience matter?
It's clear that, in DND 5e, all characters are actually gaining power through mastery of techniques. These techniques afford them greater mastery of powers, but it is these techniques that make them unique, not an ineffable "power". 
As one proof, even the magic items which permanently increase Strength are exercise books (or they set the stat to a specific value instead). It's clear that what makes the character exceptional is, even for purely martial classes, knowledge and training.
Hence, its both the character gaining power themselves, by learning something new, and characters becoming closer to their God or Patron-because that's what they learned. 
DND is and always has been a nerds game, so to speak, and knowledge is power.

