Normalizing flow neural networks by JKO scheme

Chen Xu; Xiuyuan Cheng; Yao Xie

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arXiv · 2212.14424

Normalizing flow neural networks by JKO scheme

Chen Xu·Xiuyuan Cheng·Yao Xie

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Abstract

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

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Chen Xu, Xiuyuan Cheng, Yao Xie. 2022-12-29. Normalizing flow neural networks by JKO scheme. https://arxiv.org/abs/2212.14424

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