Link-adaptive regeneration (LAR) is a novel relaying strategy other than decode-and-forward (DF) or amplify-and-forward (AF) in user cooperative communications. Requiring simple channel state information (CSI) of both the source-relay and the relay-destination links, LAR has been shown to achieve full diversity using coherent modulations. In this paper, we generalize the idea of LAR into differential and non-coherent cooperative transmissions, which do not require CSI at either relays or destination. We prove that full spatial diversity gain can still be achieved in such systems, without incurring the overhead of cyclic redundancy check (CRC) codes. Simulations demonstrate that the proposed scheme is universally applicable to multi-branch and multi-hop cooperation regardless of the constellation size and outperforms existing alternatives.