Soft Metropolis-Hastings Correction for 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 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.