Soft Metropolis-Hastings Correction for Generative Model Sampling

Hanqi Feng, Peng Qiu, Meng-Chun Zhang, You Fan, Yiran Tao, Barnabas Poczos

Keywords: Generative Model, Markov Process, Efficiency

Abstract:

Molecular diffusion models suffer from systematic sampling biases that prevent
optimal structure formation, resulting in chemically suboptimal molecules with
incomplete hydrogen bonding networks and metastable conformations trapped in
local energy minima. We introduce Metropolis-Hastings correction to molecular
diffusion models for the first time, providing a principled framework to address
these systematic sampling biases. However, traditional hard accept-reject deci-
sions create discontinuous trajectories incompatible with the continuous nature
of molecular potential energy surfaces, disrupting proper structure assembly. To
address this, we develop soft Metropolis-Hastings correction that replaces binary
acceptance with continuous interpolation weighted by acceptance probabilities,
maintaining smooth navigation of chemical space while providing principled bias
correction. We design three molecular-specific variants: global correction pre-
serving geometric equivariance (E(3)/SE(3)), local adaptive correction account-
ing for heterogeneous atomic environments, and distribution matching operating
in whitened space to decouple structural correlations. Extensive experiments on
small molecules, Drugs conformations, and therapeutic antibody CDR-H3 loops
demonstrate consistent improvements in chemical validity, structural stability, and
conformational quality across diverse molecular families. Our method establishes
MH correction as a powerful component for molecular generation.

Primary Area: generative models

Submission Number: 8227