Spectral-Path Flow Matching for Antibody Generation

Therapeutic antibody design requires generating complementarity-determining region (CDR) loops whose sequences and three-dimensional conformations support antigen recognition. CDR-H3 remains particularly challenging because of its high sequence and structural diversity. Recent diffusion and flow-matching models can generate CDR sequence and structure, but their positional generative paths typically evolve all spatial components under a shared notion of progress, even though native CDR deformation is dominated by low-frequency components corresponding to overall loop shape. We introduce SP-FMAG, a spectral-path flow-matching framework that decomposes framework-anchored CDR deformation into ordered spatial modes and assigns each mode its own generative clock. This produces a coarse-to-fine positional path in which broad loop geometry is established before finer structural variation. On the standard SAbDab benchmark with 19 held-out antibody-antigen complexes, SP-FMAG reduces CDR-H3 backbone RMSD from 3.313 Å to 2.958 Å and increases Rosetta binding-energy improvement rate from 23.8% to 35.7% relative to linear positional flow matching. The structural advantage persists under reduced sampling budgets. Reversing the modal ordering to fine-to-coarse worsens H3 RMSD to 3.499 Å, indicating that the benefit depends on the coarse-to-fine direction. These results demonstrate that coarse-to-fine spatial ordering in the probability path can improve antibody loop generation without changing the underlying neural architecture.