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Normalizing flow is a class of deep generative models for efficient samplingand likelihood estimation, which achieves attractive performance, particularlyin high dimensions. The flow is often implemented using a sequence ofinvertible residual blocks. Existing works adopt special network architecturesand regularization of flow trajectories. In this paper, we develop a neural ODEflow network called JKO-iFlow, inspired by the Jordan-Kinderleherer-Otto (JKO)scheme, which unfolds the discrete-time dynamic of the Wasserstein gradientflow. The proposed method stacks residual blocks one after another, allowingefficient block-wise training of the residual blocks, avoiding sampling SDEtrajectories and score matching or variational learning, thus reducing thememory load and difficulty in end-to-end training. We also develop adaptivetime reparameterization of the flow network with a progressive refinement ofthe induced trajectory in probability space to improve the model accuracyfurther. Experiments with synthetic and real data show that the proposedJKO-iFlow network achieves competitive performance compared with existing flowand diffusion models at a significantly reduced computational and memory cost.

Normalizing flow neural networks by JKO scheme