avoiding replay attack resistance w/o seq nos or challenge response

[Major Variola (ret)]

I'm interested in avoiding replay attacks on a protocol that uses UDP.
Assume a secret key is shared.

As far as I can tell, it is *fundamental*  that you use
either sequence numbers for a series of packets, or perform a
challenge-response handshake for each packet.  (The latter is
essentially a "sequence" of length 1
re-established for each packet)

Both methods require the maintenance of some state, essentially
creating a "session", although that state is just the active sequence
number
(and a window given UDPs un-ordering), not a whole moby IPSEC security
association.

Yes, I'm aware that if you use UDP you end up reinventing TCP...

My question is, are there less well known methods, or is this
statefulness
fundamentally *imposed* by replay attack resistance, by virtue of what
it means to
"re-play"?  (Which is my suspicion)