Native decoders limit how pretrained models combine local predictions under new structural constraints. We introduce Structured Re-Decoding (SRD), a training-free framework that constructs local candidates from model scores, samples, or external specifications, jointly optimizes their selection, and verifies reconstructed outputs. We show that candidate recombination expands feasible support and can improve attainable reward under a fixed KL divergence budget. Across molecular generation, protein design, RNA structure prediction, and antibody modeling, SRD enables improved structured inference, including verified molecules absent from the original sample pool. External chemical templates further extend SRD to noncanonical amino acids, peptide cyclization, and grammar-guided molecular construction. Preliminary experiments on a physical coherent Ising machine demonstrate the feasibility of hardware-based optimization, suggesting broader opportunities for quantum and quantum-inspired approaches to structured inference and combinatorial optimization across scientific domains.

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