Implementing forward secrecy in OpenPGP with public key authentication
I'm going to describe two options that you have. There may be more that I don't know about.

The first is to use long-term signing keys to sign public diffie-hellman keys. Upload a bunch of those to the cloud. Then when someone wants to share a file with you, they: 


download your "next" signed public diffie-hellman key
verify the signature using OpenPGP, abort if it fails
generate their own new public diffie-hellman key
use your "next" key to generate a shared secret key (using their private diffie-hellman key), encrypt the file with that (you can actually use OpenPGP for this too, it would be the symmetric key for encryption)
sign their new public diffie-hellman key with their long term secret (using OpenPGP)
upload their signed public ephemeral diffie-hellman key, an index describing which of your temporary public keys they used, and the encrypted message
delete their new public diffie-hellman key, etc.


When you come along later to download the file, you:


download everything they uploaded in #5
check the digital signature using OpenPGP, if it fails abort
use your temporary private key for the given index to compute the shared secret key
decrypt the file
delete your temporary private key, their signed temporary public key, etc.


This is basically what Open Whisper Systems does for encrypted text messages.

Your other option is to throw away OpenPGP and do what is described in A Forward-Secure Public-Key Encryption Scheme and discussed in this answer*.

*Okay, that answer does mention my first proposal too as a "trivial (and hence awful) solution". I've added more detail and the link to Open Whisper Systems. Since Open Whisper Systems is doing it, it can't be too awful, right?