One-Step Sampler for Boltzmann Distributions via Drifting
This addresses the computational bottleneck of iterative sampling for Boltzmann distributions in physics and machine learning, though it appears incremental as it builds on existing drifting and score-based methods.
The paper tackles the problem of amortized sampling from Boltzmann distributions with unknown normalization constants by developing a drifting-based framework that trains a one-step neural generator. The method achieves mean error 0.0754, covariance error 0.0425, and RBF MMD 0.0020 on a Gaussian-mixture target, demonstrating effective single-pass sampling.
We present a drifting-based framework for amortized sampling of Boltzmann distributions defined by energy functions. The method trains a one-step neural generator by projecting samples along a Gaussian-smoothed score field from the current model distribution toward the target Boltzmann distribution. For targets specified only up to an unknown normalization constant, we derive a practical target-side drift from a smoothed energy and use two estimators: a local importance-sampling mean-shift estimator and a second-order curvature-corrected approximation. Combined with a mini-batch Gaussian mean-shift estimate of the sampler-side smoothed score, this yields a simple stop-gradient objective for stable one-step training. On a four-mode Gaussian-mixture Boltzmann target, our sampler achieves mean error $0.0754$, covariance error $0.0425$, and RBF MMD $0.0020$. Additional double-well and banana targets show that the same formulation also handles nonconvex and curved low-energy geometries. Overall, the results support drifting as an effective way to amortize iterative sampling from Boltzmann distributions into a single forward pass at test time.