I've been into storytelling since I was a little kid and a friend of mine introduced me to D&D a couple months ago and I was instantly hooked. I have been into fantasy and RPGs since I could remember and this just hit all the right notes for me. Not only is the community a great one, but one that promotes use of imagination and creativity for both DMs and players alike. 

So I am writing my first campaign and I am going very into a Dark Souls/Amnesia: The Dark Descent type of ambience. Obviously, with very heavy emotional themes that vary on nihilism, depression, bleakness, and world that was once proud is now fading into nothing. Now, my question is that obviously with creating a very heavy emotional atmosphere, exhaustion is a big concern. I do not want to lose my players because they are so over the depressing landscape that they just lose interest in the story.

What sort of techniques/ideas do you guys have to mix up the emotions/atmosphere to give players a break while not killing the immersion?

As a background on my campaign: they start out shipwrecked on a very foggy and damp rocky shore which leads to an exile camp (took a little inspiration from PoE) where they are all excommunicated from the main continent and are "led to die". Due to the curse of the lands and exposure to depressing conditions, these exile NPCs slowly turn into "Pale Men", a sort of ghoulish entity that make them go mad and turn away from light, making them disappear into the caves and remain there until they die. The players have many options to continue, whether it is making a climb up the path of the cliffs, find shortcuts, or many others (not wanting to write everything out).

After the players make the climb, they go up and find a way into the main continent, and their journey continues. They find ruins, slavers, cultists, and beasts of many types of shapes. There are slave-giants that are chained to a massive wall whose only purpose is to feed on anyone trying to get into the walls. Due to the hostility of the world, the only cities are hidden, such as being inside of a hill or in remnants of salt mines. In the eastern part of the world, an abyss is swallowing up the earth itself, and all that remains are floating islands that are held up via magic. The world is meant to be "empty", as in it feels deserted. There are still many NPCs and characters, but each is sarcastic and doesn't feel like fighting anymore. All honor is lost.

I'm not sure how you are going to relieve the bleakness given what you described.

There are some techniques... humor for example. But it doesn't sound like there are going to be a lot of joker/funny NPCs in this world, as you have described it. If the heroes are true noble heroes like Captain America or Wonder Woman -- both of those had some pretty bleak movie plots to work with and yet came out of their trials with their heads held high and the world made into a better place. But you're going to have to allow people to be truly saved (not just temporarily) and actual victory over the darkness possible by the PCs. Otherwise, if they're just fighting a delaying action till they inevitably die... not sure how you make that less depressing.

As BioWizard said that is very bleak. The path is just a long dark tunnel with no signs of light at the end. 

Having an NPC or two in this camp who are optimistic, caring or some other good trait will help. That NPC can still talk of their concern about the many others who have almost given up. Perhaps there is talk of a rebellion group who want to right the world, a small sense of hope, even if it just turns out to be a rumour later down the line. The last standing city of free and equal people on another island somewhere or something.

Provide some kind of light in the bleak darkness of the world. Something for both NPC and PC to cling on to and persevere towards.

This is a little off topic, but remember D&D is not the same as telling a story. The players have their own choices about what to do, and they might not do what you expect. Maybe the players just decide to build a raft and get the hell off the island.

To your question, give the players a win. An unadulterated win. Let them beat back the darkness in a spot. Then they can keep going back to it. And even one win makes them think they can have another. Maybe one day you give them a second, let them build points of light in the darkness. 

I think a good idea would be to have a likeable NPC that travels with the group. Many (or all) of their loved ones are dead, and humor is their way of coping. Note that this isn't a DMPC, but an NPC that the players want to protect because they like him/her. It gives them an objective and reason to fight other than just to not die themselves, and it could be the source of some interesting roleplaying. Of course, if you want to lean into the despair of the setting, you can have the NPC killed off after the players have grown to treat them as a friend. This will give them drive and a motivation to avenge the NPC's death. Of course, make sure that the players do have a chance to save them and/or bring them back.

on the loosing side of a war, helping refugees flee before they are exterminated a glimmer of hope perhaps that fellow in the beaten armor is actually the kings brother time to resist. 

Pets/familiars/beast companions/etc with personalities that make for levity.  Also potential hook for dramatic tension if the characters' emotional survival draws on them.

You could use a "floating inspiration/guidance/pay it forward" mechanic. By that I mean, have some encounter early on where a character that displays some upbeat, positive or optimistic sentiment to an NPC gets a d4 or d6 inspiration dice that they can give to NPC's; its a boon they bestow on someone else to represent them bolstering an npc with good vibes, inspiring pep talk etc. Each character could build up a number of these equal to their proficincey bonus, if they use (insert number) of  inspirations on different npc's in a settlement then they lift the spirits of the settlers and things become a bit better, people become happier as the npc's they affected go on to spread their own inspirations etc. Hopefully that would make the players interactions with the npc's have a bit more to them than just rolling dice to influence them. An example would be they visit the local blacksmith, he's old and his joints ache but he still does everything thats expected of him. A player talks to him, maybe rolls some dice to haggle over prices, but before leaving just gives the blacksmith a hand shake and thanks him for his hard work and service and then uses one of his inspiration dice. If they return to the blacksmith a few days later then they find he has taken on an apprentice and he's happier as he is passing on his knowledge, the apprentice is happy because he was an orphan living on the streets when the blacksmith asked if he wanted to come work for him and showed him that things can be better (or in other words the blacksmith passed on the inspiration dice he was given).