  A normalizing flow (NF) is a mapping that transforms a chosen probability
distribution to a normal distribution. Such flows are a common technique used
for data generation and density estimation in machine learning and data
science. The density estimate obtained with a NF requires a change of variables
formula that involves the computation of the Jacobian determinant of the NF
transformation. In order to tractably compute this determinant, continuous
normalizing flows (CNF) estimate the mapping and its Jacobian determinant using
a neural ODE. Optimal transport (OT) theory has been successfully used to
assist in finding CNFs by formulating them as OT problems with a soft penalty
for enforcing the standard normal distribution as a target measure. A drawback
of OT-based CNFs is the addition of a hyperparameter, $\alpha$, that controls
the strength of the soft penalty and requires significant tuning. We present
JKO-Flow, an algorithm to solve OT-based CNF without the need of tuning
$\alpha$. This is achieved by integrating the OT CNF framework into a
Wasserstein gradient flow framework, also known as the JKO scheme. Instead of
tuning $\alpha$, we repeatedly solve the optimization problem for a fixed
$\alpha$ effectively performing a JKO update with a time-step $\alpha$. Hence
we obtain a "divide and conquer" algorithm by repeatedly solving simpler
problems instead of solving a potentially harder problem with large $\alpha$.
