Soft Metropolis-Hastings Correction for Molecular Generative Model Sampling

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 soft Metropolis-Hastings (soft MH) correction to address these biases. Unlike the traditional hard accept-reject mechanism, which creates discontinuous trajectories incompatible with smooth molecular potential energy surfaces, our approach replaces binary acceptance with continuous interpolation weighted by acceptance probabilities, maintaining smooth navigation of chemical space. 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 accuracy (RMSD, pLDDT), and molecular diversity across diverse molecular families. Our method establishes soft MH correction as a powerful plug-and-play component for molecular generation.