Title: PaddingFlow: Improving Normalizing Flows with Padding-Dimensional Noise

Abstract: Normalizing flow is a generative modeling approach with efficient sampling. However, Flow-based models suffer two issues, which are manifold and discrete data. If the target distribution is a manifold, which means the dimension of the latent target distribution and the dimension of the data distribution are unmatched, flow-based models might perform badly. Discrete data makes flow-based models collapse into a degenerate mixture of point masses. In this paper, to sidestep such two issues we propose PaddingFlow, a novel dequantization method, which improves normalizing flows with padding-dimensional noise. PaddingFlow is easy to implement, computationally cheap, widely suitable for various tasks, and generates samples that are unbiased estimations of the data. Especially, our method can overcome the limitation of existing dequantization methods that have to change the data distribution, which might degrade performance. We validate our method on the main benchmarks of unconditional density estimation, including five tabular datasets and four image datasets for VAE models, and the IK experiments which are conditional density estimation. The results show that PaddingFlow can provide improvement on all tasks in this paper.