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

• URL: http://arxiv.org/abs/2505.21005v1
• Date: Tue, 27 May 2025 10:37:48 GMT
• Title: Efficient and Unbiased Sampling from Boltzmann Distributions via Variance-Tuned Diffusion Models
• Authors: Fengzhe Zhang, Laurence I. Midgley, José Miguel Hernández-Lobato,
• Abstract summary: Variance-Tuned Diffusion Sampling (VT-DIS) is a lightweight method that adapts the per-step noise covariance of a pretrained score-based diffusion model.<n>VT-DIS achieves effective sample sizes of approximately 80 %, 35 %, and 3.5 %, respectively, on the DW-4, LJ-13, and alanine-dipeptide benchmarks.
• Score: 29.531531253864753
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $\alpha$-divergence ($\alpha=2$) 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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