Guiding Where the Antibody Binds: Amortised Cross-Subsample Particle Steering for Antibody–Antigen Co-Folding

Co-folding models have advanced antibody-antigen structure prediction, but a dominant failure mode persists. They often dock the antibody onto the wrong epitope. Docking has two problems. A sampler must produce an acceptable complex at the correct interface, and a verifier must then rank it above the alternatives. We address the first, site coverage, since a verifier cannot select an epitope the sampler never proposed. Drawing more seeds or samples adds variety around the pose the model already favours, but does not relocate it. We introduce CAST (Cross-subsample Amortised Site Tilting), which steers diffusion trajectories toward a binding site using a reward built from a candidate epitope map, training-free and with no reference structure. The sampler approximates an ideal target whose tilt provably changes the site marginal but not the pose at a site. Amortising $K$ alignment-subsample latents into one steered pool cuts the cost of exploring them from $\mathcal{O}(KN)$ to $\mathcal{O}(N+K)$ for a pool of $N$ particles. At a matched $720$ structures and $4$ conditionings, CAST holds an acceptable pose on $36$ of the $50$ difficulty-balanced CFA50 targets against $26$ for Best-of-$N$, and raises mean max DockQ from $0.322$ to $0.373$, a gain of $15.8$. On $21$ targets that a $1,000$-seed run fails to reach CAPRI-medium quality, CAST reaches mean max DockQ $0.370$ at $720$ structures and brings $18$ of the $21$ to an acceptable pose against $9$ at the same budget. Best-of-$N$ flattens, spending $5.3\times$ the compute and trailing by $20.1$. Raising the latent count alongside the samples carries this to $0.457$, beyond every Best-of-$N$ budget. On CFA50 CAST also matches the best Best-of-$N$ allocation of $720$ structures, at $1.5\times$ less compute. Such steering is a reallocation, changing little where the base model already succeeds and much where it does not.