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. Instead of the binary accept-reject step of hard MH, which fragments the denoising trajectory when a rejection still advances the diffusion time, our approach replaces binary acceptance with continuous interpolation weighted by a score-based acceptance weight. We show that this update is the conditional mean of the corresponding hard MH step: it reduces per-step variance but does not preserve the target distribution exactly, so we treat it as a sampling heuristic. 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 improves chemical validity and structural accuracy (RMSD, pLDDT) across diverse molecular families, in some settings at a cost in diversity. Soft MH correction is a simple, training-free, plug-and-play component for molecular generation.