arXiv:2605.26580v2 Announce Type: replace Abstract: In shared-codebook unsourced random access (URA), a receiver must recover an unordered set of messages from simultaneous transmissions. Its outer decoder assembles ambiguous slot-wise evidence into distinct codewords while enforcing parity constraints. We propose CIDER, a learned outer decoder that combines masked-diffusion refinement with cross-row demixing and parity-aware propagation on the code's Tanner graph. At higher per-bin loads, quality-guided remasking selectively re-decodes low-confidence rows. On the evaluated GF(64) LDPC codes at $K=2$, CIDER has lower measured symbol and codeword error rates than SIC-BP and FFT-BP at all four code lengths. In same-GPU decoder-only measurements, the deployed mixed-precision implementation is $8.2\times$ to $167\times$ faster than our optimized FFT-BP implementation across those lengths. We also evaluate higher loads, estimated user counts, and detector mismatch. Code is available at https://github.com/jiyunyoung/CIDER/tree/neurips-2026.