Recurrent Geometric Coupling Refinement for RNA Inverse Folding

RNA inverse folding seeks nucleotide sequences compatible with a target three-dimensional structure. Base-pairing and stacking interactions couple nucleotide choices in RNA, yet sampling positions independently within each generation step can fail to preserve their joint compatibility. We introduce **Recurrent Geometric Coupling Refinement (RGCR)**, which builds on **Masked Diffusion Language Modeling (MDLM)** to learn joint nucleotide distributions over geometry-derived pairs and triples. Estimates of their expected log-score gains over singleton predictions guide geometric message passing that recurrently refines both the joint distributions and these estimates. The final scores select disjoint groups for joint sampling among the positions generated at each step. We establish a normalized generative process and decompose its predictive gains into contributions from dependence retention and marginal prediction. RGCR improves structure fidelity and recovery performance on the RNA inverse-folding benchmark. Code and checkpoints are available at https://anonymous.4open.science/r/rgcr-5241/.