Two referees are very positive about this paper and recommend acceptance, whereas two referees lean towards rejection. All referees agree that primal-dual graph networks have not been previously investigated for mesh processing, but disagree on whether the contribution should be considered significant and/or incremental. The rebuttal attempts to address this concern by highlighting that primal-dual approaches have only been applied on generic graph benchmarks and further emphasizing that the application of such approaches to meshes is not straightforward and only constitutes one part of the proposed approach. R1 and R4 raised concerns about the experimental validation. The rebuttal only partially addressed their concerns, but after discussion, R4 is convinced that the experimental validation is compelling enough. However, R4 still finds the contribution largely incremental. I agree with the overall assessment that this is a well executed contribution with compelling and comprehensive experimental validation, and I support R2 and R3's opinion that borrowing an existing approach to strengthen another approach may still be a valid contribution. Therefore, I recommend acceptance.