(I'm not sure what you mean by non-interactive -- is it the one with the hashes? "interactive" in a ZKP is a process with a back-and-forth. I guess you mean the ZKP that doesn't need physical presence? Regardless, I explain that a bit in that blog post.)
For instance a zkSNARK as used in ZCash. It's just a piece of data that's put there on the blockchain. It's "non-interacrive" (a term I heard, not one I made up) in that no challenges are made on it by those verifying transactions. It just encapsulates the necessary evidence all on its own. Even though I roughly understand the interactive sort of zkp, this still blows my mind.
