Drifting to Boltzmann: Million-Fold Acceleration in Boltzmann Sampling with Force-Guided Drifting

Abstract: Sampling molecular conformations from the Boltzmann distribution is essential for computational chemistry, but iterative diffusion methods are prohibitively slow. Drifting Models offer one-step generation, yet their equilibrium matches the \emph{training} distribution, which may deviate from the true Boltzmann distribution due to sampling bias. We introduce Drifting Models to molecular conformation generation for the first time, establishing a theoretical bridge via the \emph{Drifting Score Identity}: for Gaussian kernels, the drifting field's attraction equals a kernel-weighted average of \emph{any} distribution's score function. Substituting molecular force labels -- which directly encode the Boltzmann score -- yields the \emph{Drifting Force Identity} and decomposes the field into standard drift plus a Boltzmann correction. We further discover a striking phenomenon unique to molecular systems: force incorporation's effectiveness \emph{reverses across representations}. In coordinate space, Force-Interpolated Drifting (FI) dominates by blending physical force directions with data displacements. In distance feature space, Force-Aligned Kernel (FK) achieves superior accuracy by modifying only kernel weights, thereby preserving the manifold of geometrically valid molecules. On MD17 Ethanol, both approaches achieve one-step generation with over 1000x speedup relative to recent score-matching methods with Boltzmann guiding, providing more than million-fold acceleration over traditional molecular dynamics, while ensuring perfect structural validity and distributional accuracy rivaling multi-step methods.