None in this paper, which is just showing proofs of concept. But our follow-up paper does have SOTA density modeling among the class of efficiently-sample-able generative models. This is because the design of continuous flow models is less constrained than for discrete flows. But other than that, it's still early days for this whole model class.

You train these models in the same way you train a neural network, with stochastic gradient descent. For supervised learning, its main benefit is extra flexibility in the speed/precision tradeoff. For time-series problems, we expect this will ultimately allow us to handle data that's collected at irregular intervals - but we haven't yet moved past the prototype stage in that setting.