Diamond Maps for Protein Binder Design: Inference-Time Scaling Survives Stochastic Flow Map Distillation

Conditional protein generative models rely on inference-time scaling techniques such as Sequential Monte Carlo and reward-guided sampling to achieve competitive binder design performance. These techniques estimate a value function over candidate trajectories, which requires many evaluations of expensive pretrained models. Flow map distillation could relieve this bottleneck, but standard flow maps are deterministic and yield biased value-function estimates, collapsing the inference-time scaling that makes generative methods competitive with hallucination in the first place. We apply Posterior Diamond Maps to Proteina-Complexa, distilling its joint latent and C$\alpha$ flow into a single-step stochastic sampler of the posterior $p_{1|t}(z \mid x_t)$ that admits consistent, low-cost value-function estimation. We pair the distilled model with Sequential Monte Carlo using AlphaFold-Multimer interface confidence as the reward, and use the PD-L1 binder design problem as proof of concept. On a 5K-step student, deterministic higher-order integration of the teacher saturates well short of FK-steering, while a $(P, K)$ search-width sweep with the distilled SMC monotonically improves every tail metric tracked. These results are consistent with stochastic flow map distillation preserving the inference-time scaling behavior of the underlying generative model.