What hash structure is Facebook Diem using?

Some cryptocurrencies use fixed values in some positions in the resulting hash, like a fixed amount of initial zeros. What fixed positions and fixed values are Facebook Diem using?

As far as I understood, you are speaking about proof-of-work. But contrarily to what your question said :

Some Crypto currencies use fixed values in some positions in the resulting hash.

It corresponds to proof-of-work. The idea is the following, to guarantee that people which valid a transaction are "real", the have to solve a puzzle, which is basically a preimage of $\{0\}^\lambda\times\{0,1\}^{256-\lambda}$ for a specific hash function (parametrized by the transaction) (you can look this to have more precision : Complexity of Hash mining/signing)

But not all the cryptocurrency are using proof-of-work. And in particular, as far as I understood it's not the case for DIEM

Citation in the white-paper: "Second, this class of consensus protocols enables high transaction throughput, low latency, and a more energy-efficient approach to consensus than “proof of work” "

Link : https://www.diem.com/en-us/white-paper/#the-libra-blockchain

Citation in "The Libra Blockchain" paper:

"To do this, we plan to gradually transition to a proof-of-stake":

https://diem-developers-components.netlify.app/papers/the-diem-blockchain/2020-05-26.pdf