BLOCS: Scalable Block-Conditional Generative Proposals with Exact Local Metropolis–Hastings Correction

Generative molecular samplers propose large conformational changes, but full-system statistical correction becomes inefficient as proposal mismatch accumulates across molecular degrees of freedom. We introduce BLOCS, a transferable block-conditional proposal model for accelerating local equilibrium transitions. Each learned torsional block receives an exact full-system Metropolis–Hastings correction using the molecular energy, coordinate measure, and forward/reverse proposal densities. A state-dependent Hastings-score diagnostic connects correction difficulty to stationary proposal-pair overlap. In controlled scaling, global-proposal acceptance falls from $2.0\times 10^{-3}$ at $N=20$ to $3.1\times 10^{-9}$ at $N=76$, whereas fixed-scope block correction remains usable; complete-pool scans show that moved dimension has a substantially larger effect on acceptance than total protein size. The residual autoregressive proposal, trained on proteins with $N\le 36$, transfers zero-shot to proteins with up to 250 residues. Under the canonical $m=12$, $r=100$ fixed setting, end-to-end ESS/GPU-s improves by $2.69$–$3.34\times$ over Rotamer MH across six proteins, with a median gain of $3.07\times$. On the five-system common-pool thermodynamic benchmark, gains over a matched-data Robin-style autoregressive control are $1.67$–$1.91\times$. In a paired protein-scale exact-composition benchmark with Metropolized dynamics, the gains remain $2.79$–$2.87\times$ over Rotamer MH and $1.57$–$1.68\times$ over the matched learned control. Acceptance calibration on frozen primary and prospective pools reaches $4.8\%$ median relative error.