Coupled Variational Autoencoder

TL;DR

The paper introduces the Coupled Variational Auto-Encoder (C-VAE), a novel model that addresses low-quality sample generation in VAEs by framing the problem as an Optimal Transport task, improving sample fidelity and latent representations.

Contribution

It formulates VAE as an Optimal Transport problem, enabling flexible priors and solving the prior hole issue through coupling and OT optimization methods.

Findings

C-VAE outperforms VAE, WAE, and InfoVAE in sample quality.

C-VAE improves latent representation quality.

C-VAE enhances data fidelity in generated samples.

Abstract

Variational auto-encoders are powerful probabilistic models in generative tasks but suffer from generating low-quality samples which are caused by the holes in the prior. We propose the Coupled Variational Auto-Encoder (C-VAE), which formulates the VAE problem as one of Optimal Transport (OT) between the prior and data distributions. The C-VAE allows greater flexibility in priors and natural resolution of the prior hole problem by enforcing coupling between the prior and the data distribution and enables flexible optimization through the primal, dual, and semi-dual formulations of entropic OT. Simulations on synthetic and real data show that the C-VAE outperforms alternatives including VAE, WAE, and InfoVAE in fidelity to the data, quality of the latent representation, and in quality of generated samples.