  We propose the tensorizing flow method for estimating high-dimensional
probability density functions from the observed data. The method is based on
tensor-train and flow-based generative modeling. Our method first efficiently
constructs an approximate density in the tensor-train form via solving the
tensor cores from a linear system based on the kernel density estimators of
low-dimensional marginals. We then train a continuous-time flow model from this
tensor-train density to the observed empirical distribution by performing a
maximum likelihood estimation. The proposed method combines the
optimization-less feature of the tensor-train with the flexibility of the
flow-based generative models. Numerical results are included to demonstrate the
performance of the proposed method.
