Kukulu: Diffusion-Based Reconstruction of Antibody CDR Loops using a Structure-Aware Joint Embedding Predictive Architecture

Antibody complementarity-determining regions (CDRs), especially CDR-H3, are a dominant source of binding specificity but remain difficult to design due to coupled sequence-structure constraints and local geometric variability. Here we present Kukulu, a structure-aware Joint Embedding Predictive Architecture (JEPA) combined with conditional diffusion for CDR loop reconstruction in antibody-antigen complexes. Our pipeline prepares structures by chain-aware cleanup, Fv trimming, Chothia-indexed CDR identification, and in silico CDR masking, then trains on paired prepared/masked structures represented in an atom37 format. The model uses a context encoder over masked structures, a transformer predictor for latent CDR representations, and a diffusion head that reconstructs loop coordinates, atom presence, and residue identities under geometry-aware losses. During generation, Kukulu denoises only masked CDR residues while preserving frame-work context, then optionally rebuilds sidechains with local frame templates and performs post-generation structural relaxation. This manuscript provides a methods-focused overview of the models implementation details and an evaluation protocol based on structure quality and docking-oriented scoring for integration into existing antibody design workflows.