Soft Metropolis-Hastings Correction for Generative Model Sampling

A bstract Molecular diffusion models suffer from systematic sampling biases that prevent optimal structure formation, resulting in chemically suboptimal molecules with metastable conformations trapped in local energy minima. We introduce Metropolis-Hastings (MH) correction to molecular diffusion models, providing a principled framework to address these systematic sampling biases. The traditional hard accept-reject Metropolis-Hastings corrector creates discontinuous trajectories incompatible with the continuous nature of molecular potential energy surfaces, disrupting proper structure assembly. To address this, we develop a soft Metropolis-Hastings correction that replaces binary acceptance with continuous interpolation weighted by acceptance probabilities, maintaining smooth navigation in the chemical space while providing principled bias correction. We design three molecular-specific variants and demonstrate through extensive experiments on small molecules, drug conformations, and therapeutic antibody CDR-H3 loops that our method consistently improves chemical validity, structural stability, and conformational quality across diverse molecular families. Our method establishes MH correction as a powerful component for molecular generation.