Efficient and Unbiased Sampling from Boltzmann Distributions via Variance-Tuned Diffusion Models
This addresses the challenge of unbiased Monte Carlo estimation in computational chemistry and physics, offering a more efficient alternative to existing methods, though it is incremental as it builds on prior diffusion and importance sampling techniques.
The paper tackles the problem of biased sampling from Boltzmann distributions using score-based diffusion models by introducing VT-DIS, a method that corrects bias via variance tuning and importance sampling, achieving effective sample sizes of up to 80% on benchmarks with reduced computational cost.
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.