We present the Liouville Flow Importance Sampler (LFIS), an innovative flow-based model for generating samples from unnormalized density functions. LFIS learns a time-dependent velocity field that deterministically transports samples from a simple initial distribution to a complex target distribution, guided by a prescribed path of annealed distributions. The training of LFIS utilizes a unique method that enforces the structure of a derived partial differential equation to neural networks modeling velocity fields. By considering the neural velocity field as an importance sampler, sample weights can be computed through accumulating errors along the sample trajectories driven by neural velocity fields, ensuring unbiased and consistent estimation of statistical quantities. We demonstrate the effectiveness of LFIS through its application to a range of benchmark problems, on many of which LFIS achieved state-of-the-art performance.

我们提出了Liouville Flow Importance Sampler (LFIS)，这是一种创新的基于流的模型，用于从非归一化密度函数生成样本。通过将样本从简单的初始分布确定性地传送到复杂的目标分布，LFIS学习一种时间依赖的速度场，以预设的退火分布路径为指导。LFIS的训练采用了一种独特的方法，它将导数偏微分方程的结构强加于模拟速度场的神经网络。通过将神经速度场视为重要抽样器，可以通过沿着神经速度场驱动的样本轨迹累积误差来计算样本权重，确保对统计量进行无偏且一致的估计。通过在一系列基准问题上应用LFIS，我们展示了其有效性，其中LFIS在许多问题上都取得了最先进的性能。

Liouville流重要性取样器