提出新方法实现高维玻尔兹曼采样无偏低方差雅可比估计
Flow Perturbation++: Multi-Step Unbiased Jacobian Estimation for High-Dimensional Boltzmann Sampling
- 将概率流微分方程离散化，分步无偏估计雅可比行列式
- 在1000维混合高斯和Chignolin蛋白上显著降低采样偏差
- 适合需要高精度采样的高维分子模拟与生成建模任务
连续归一化流（CNFs）在高维系统中进行无偏玻尔兹曼采样的可扩展性受限于雅可比行列式计算成本，需对流层进行D次反向传播。现有随机雅可比估计器如Hutchinson迹估计虽降低计算量但引入偏差，而近期的Flow Perturbation方法虽无偏却方差过高。本文提出Flow Perturbation++，通过离散化概率流常微分方程，在每一步积分中进行无偏雅可比估计，实现多步构造。该方法在保持无偏性的同时显著降低估计方差。集成至顺序蒙特卡洛框架后，相较于基于Hutchinson和单步Flow Perturbation的基线方法，其在1000维混合高斯模型和全原子Chignolin蛋白上的平衡采样性能均有显著提升。
原文摘要 · Abstract (English)
The scalability of continuous normalizing flows (CNFs) for unbiased Boltzmann sampling remains limited in high-dimensional systems due to the cost of Jacobian-determinant evaluation, which requires $D$ backpropagation passes through the flow layers. Existing stochastic Jacobian estimators such as the Hutchinson trace estimator reduce computation but introduce bias, while the recently proposed Flow Perturbation method is unbiased yet suffers from high variance. We present \textbf{Flow Perturbation++}, a variance-reduced extension of Flow Perturbation that discretizes the probability-flow ODE and performs unbiased stepwise Jacobian estimation at each integration step. This multi-step construction retains the unbiasedness of Flow Perturbation while achieves substantially lower estimator variance. Integrated into a Sequential Monte Carlo framework, Flow Perturbation++ achieves significantly improved equilibrium sampling on a 1000D Gaussian Mixture Model and the all-atom Chignolin protein compared with Hutchinson-based and single-step Flow Perturbation baselines.
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