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.

翻译：本文提出Liouville Flow重要性采样器（LFIS），一种基于流的创新模型，用于从非归一化密度函数中生成样本。LFIS学习一个依赖于时间的速度场，该速度场在预设的退火分布路径引导下，将样本从简单初始分布确定性传输至复杂目标分布。LFIS的训练采用独特方法，将推导出的偏微分方程的结构强制应用于建模速度场的神经网络中。通过将神经速度场视为重要性采样器，可沿神经速度场驱动的样本轨迹累积误差来计算样本权重，确保统计量的无偏且一致估计。我们通过将LFIS应用于一系列基准问题来验证其有效性，在多个问题上LFIS取得了最先进的性能表现。