Can one have an authentic, but repudiable, message without a previously shared secret?
There's an obvious solution using DH: Alice has a private key $a$ and a public key $g^a$; Bob has a private key $b$ and a public key $g^b$.

When Bob sends a message, he computes the shared secret value $(g^a)^b$, converts that into a MAC key (possibly using a nonce to prevent key reuse), computes the MAC of the message, and sends the message and the MAC (and any nonce) to Alice.

When Alice receives the message, she computes the shared secret value $(g^b)^a$, converts that into a MAC key, and verifies the MAC.

Now, Eve cannot modify the message, because she doesn't know the MAC key, because she can't solve the DH problem based on the public keys $g^a$ and $g^b$.

Alice can validate that the message was sent by Bob.  However, she can't prove it to anyone else, even if she were willing to expose her private key, because she is just as able to generate that message as Bob was.