text: The authors try to use continuous time generalizations of normalizing flows for improving upon VAE-like models or for standard density estimation problems. Clarity: the text is mathematically very sloppy / hand-wavy. 1. I do not understand proposition (1).  I do not think that the proof is correct  (e.g. the generator L needs to be applied to a function  -- the notation L(x) does not make too much sense):  indeed, in the case when the volatility is zero (or very small), this proposition would imply that any vector field induces a volume preserving transformation, which is indeed false. 2. I do not really see how the sequence of minimization Eq(5) helps in practice.  The Wasserstein term is difficult to hand. 3. in Equation (6), I do not really understand what $\log(\bar{\rho})$ is if $\bar{\rho}$ is an empirical distribution.  One really needs $\bar{\rho}$ to be a probability density to make sense of that.