Is it possible to ensure security with zero pre-shared information? Is it possible to secure a communications channel against both passive (sniffing) and active (injecting / MitM) attackers without either legitimate party knowing any pre-shared information?

I know that this isn't possible using "traditional" asymmetric crypto, since an active attacker could create its own public keys and relay the information on both sides. A trusted third party implies pre-shared information, since at least one party must provide their public key to the third party.

Are there any schemes that make this viable, or is it completely impossible?

Update: By "zero information", I mean other than the "address" of the other person, e.g. their computer's IP address, or even their mailing address.
No. Consider using encryption to protect against a passive adversary. In this case, encryption needs to hold from the sender to the receiver. The sender can verify that the message leaves them encrypted but they have no guarantee that it is not decrypted before the receiver unless if they can authenticate the receiver. Authentication requires knowledge of some secret which would constitute preshared information in your definition. 

The closest I believe you could come to a secure channel in this setting would be what is called Secure Message Transmission Protocols. The basic idea is that the sender would split up the message into shares (say 10 shares) such that some threshold (7 shares) are required to reconstruct the message. The sender would send the 10 shares over different channels. This is not secure against an adversary that is one all channels (which your question implies, which is why the answer is still likely "no") but if the adversary is on 6 or less, you get passive security. Active security is possible but the adversary is bounded to less than a third of the channels (byzantine agreement). Anyways, you could also argue that knowing the algorithm to reconstruct the message from the shares is pre-shared information (although not a secret).