Motivated by the computational difficulties incurred by popular deep learning algorithms for the generative modeling of temporal densities, we propose a cheap alternative which requires minimal hyperparameter tuning and scales favorably to high dimensional problems. In particular, we use a projection-based optimal transport solver [Meng et al., 2019] to join successive samples and subsequently use transport splines [Chewi et al., 2020] to interpolate the evolving density. When the sampling frequency is sufficiently high, the optimal maps are close to the identity and are thus computationally efficient to compute. Moreover, the training process is highly parallelizable as all optimal maps are independent and can thus be learned simultaneously. Finally, the approach is based solely on numerical linear algebra rather than minimizing a nonconvex objective function, allowing us to easily analyze and control the algorithm. We present several numerical experiments on both synthetic and real-world datasets to demonstrate the efficiency of our method. In particular, these experiments show that the proposed approach is highly competitive compared with state-of-the-art normalizing flows conditioned on time across a wide range of dimensionalities.

本文提出了一种用于生成模型的廉价替代方案，该方案使用投影优化器以及输运样条来加入连续的样本并插值演变密度，比起基于时间而条件的现有流模型具有高度的竞争力，适用于一系列高维度问题。

最优传输与投影寻踪下的时间相关密度生成建模