用轻量方法让扩散模型采样更准，不偏倚且快得多。
Efficient and Unbiased Sampling from Boltzmann Distributions via Variance-Tuned Diffusion Models
- 通过调节噪声协方差最小化分布差异，改进预训练扩散模型。
- 在多个分子系统上实现高达80%的有效样本率，计算开销极低。
- 适合需要高精度采样的分子模拟与统计物理研究者。
基于得分的扩散模型（SBDM）是贝叶斯分布的强大近似采样器；然而，得分估计不准确会引入下游蒙特卡洛估计偏差。经典重要性采样（IS）可纠正此偏差，但精确计算似然需求解概率流常微分方程（PF-ODE），该过程代价高昂且随维度增长而恶化。我们提出方差调优扩散重要性采样（VT-DIS），一种轻量级后训练方法，通过最小化前向扩散与反向去噪轨迹间的α-散度（α=2）来调整预训练SBDM的每步噪声协方差。VT-DIS为联合前向-反向过程分配单一轨迹重要性权重，在测试时实现无偏期望估计，计算开销几乎可忽略。在DW-4、LJ-13和丙氨酸二肽基准测试中，VT-DIS分别达到约80%、35%和3.5%的有效样本率，仅需极少计算资源，远低于传统扩散+IS或基于PF-ODE的IS方案。
原文摘要 · Abstract (English)
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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