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arXiv · 2505.21005

Efficient and Unbiased Sampling from Boltzmann Distributions via Variance-Tuned Diffusion Models

Fengzhe Zhang·Laurence I. Midgley·José Miguel Hernández-Lobato
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Abstract

Score-based diffusion models (SBDMs) are powerful amortized samplers for Boltzmann distributions; however, imperfect score estimates bias downstream Monte Carlo estimates. Classical importance sampling (IS) can correct this bias, but computing exact likelihoods requires solving the probability-flow ordinary differential equation (PF-ODE), a procedure that is prohibitively costly and scales poorly with dimensionality. We introduce Variance-Tuned Diffusion Importance Sampling (VT-DIS), a lightweight post-training method that adapts the per-step noise covariance of a pretrained SBDM by minimizing the $α$-divergence ($α=2$) between its forward diffusion and reverse denoising trajectories. VT-DIS assigns a single trajectory-wise importance weight to the joint forward-reverse process, yielding unbiased expectation estimates at test time with negligible overhead compared to standard sampling. On the DW-4, LJ-13, and alanine-dipeptide benchmarks, VT-DIS achieves effective sample sizes of approximately 80 %, 35 %, and 3.5 %, respectively, while using only a fraction of the computational budget required by vanilla diffusion + IS or PF-ODE-based IS.

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Fengzhe Zhang, Laurence I. Midgley, José Miguel Hernández-Lobato. 2025-11-07. Efficient and Unbiased Sampling from Boltzmann Distributions via Variance-Tuned Diffusion Models. https://arxiv.org/abs/2505.21005

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