Does the monk's Diamond Soul feature apply to death saving throws?

Question

The description of the monk's class feature Diamond Soul says the following:

Beginning at 14th level, your mastery of ki grants you proficiency in all saving throws.

Additionally, whenever you make a saving throw and fail, you can spend 1 ki point to reroll it and take the second result.

Does the Diamond Soul feature allow you to apply your proficiency bonus to your death saving throws?

Normally you're only able to gain proficiency in saving throws that have an ability score associated with them, and thus are unable to apply them to death saving throws, but this ability explicitly says that you gain it with "all saving throws".

Answer 1

Yes, Diamond Soul applies to death saving throws

Your concern is probably this sentence from the rules on saving throws (PH, p. 179):

As with skill proficiencies, proficiency in a saving throw lets a character add his or her proficiency bonus to saving throws made using a particular ability score.

You are reading this as implying that the proficiency bonus can only be added to a saving throw made using some particular ability score. And, it is true that since the death saving throw isn't tied to any ability score, no character can be proficient in it due to a "normal" ability-linked saving throw proficiency. But:

1. The rules on death saving throws don't say that no class can be proficient in them, only that they aren't "tied to any ability score"; and
2. Diamond Soul clearly says "all saving throws".

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While Jeremy Crawford's tweets are not official rulings unless incorporated into the Sage Advice Compendium (and this is not included as of SAC v2.6 (2020)), this Crawford tweet from January 2016 indicates that he agrees that "all saving throws" means what it says:

The monk's Diamond Soul feature grants proficiency in all saves. A death saving throw is a save, so yes.

Answer 2

A death saving throw is a saving throw.

As you have observed, the Diamond Soul feature grants proficiency in “all saving throws”. Since death saving throws are saving throws, they count. For this to not work, there would have to be a rule that explicitly states you cannot be proficient in death saving throws, and there is no such rule.

The rules for death saving throws state:

Whenever you start your turn with 0 hit points, you must make a special saving throw, called a death saving throw, to determine whether you creep closer to death or hang onto life. Unlike other saving throws, this one isn't tied to any ability score. You are in the hands of fate now, aided only by spells and features that improve your chances of succeeding on a saving throw.

So death saving throws are explicitly a type of saving throw, and features that improve saving throw success are explicitly applicable to death saves, which in the absence of a rule forbidding it, includes proficiency.