用于从玻尔兹曼密度采样的迭代基于能量的流匹配
Iterated Energy-based Flow Matching for Sampling from Boltzmann Densities
AI总结：
针对从未归一化密度训练生成器的问题，提出首个离策略方法iEFM，通过无仿真的基于能量的流匹配目标训练CNF模型，在GMM和DW-4上优于现有方法，适用于高维系统。
摘要：
在这项工作中，我们考虑从能量函数或未归一化密度的评估中训练生成器的问题。这是概率推断中的一个基本问题，对于学习分子3D坐标分布等科学应用至关重要。为解决此问题，我们提出了迭代基于能量的流匹配（iEFM），这是首个从未归一化密度训练连续正则化流（CNF）模型的离策略方法。我们引入了无仿真的基于能量的流匹配目标，训练模型预测由已知能量函数构建的边缘向量场的蒙特卡洛估计。我们的框架具有通用性，可扩展至方差爆炸（VE）和最优传输（OT）条件概率路径。我们在二维高斯混合模型（GMM）和八维四粒子双井势（DW-4）能量函数上评估了iEFM。结果表明，iEFM优于现有方法，展示了其在复杂高维系统中实现高效且可扩展概率建模的潜力。
英文摘要：
In this work, we consider the problem of training a generator from evaluations of energy functions or unnormalized densities. This is a fundamental problem in probabilistic inference, which is crucial for scientific applications such as learning the 3D coordinate distribution of a molecule. To solve this problem, we propose iterated energy-based flow matching (iEFM), the first off-policy approach to train continuous normalizing flow (CNF) models from unnormalized densities. We introduce the simulation-free energy-based flow matching objective, which trains the model to predict the Monte Carlo estimation of the marginal vector field constructed from known energy functions. Our framework is general and can be extended to variance-exploding (VE) and optimal transport (OT) conditional probability paths. We evaluate iEFM on a two-dimensional Gaussian mixture model (GMM) and an eight-dimensional four-particle double-well potential (DW-4) energy function. Our results demonstrate that iEFM outperforms existing methods, showcasing its potential for efficient and scalable probabilistic modeling in complex high-dimensional systems.
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