Latent Space Optimal Transport for Generative Models
This addresses the posterior collapse issue in VAEs and the optimization challenges in GANs for researchers in generative modeling, though it appears incremental as it builds on existing GAN-like frameworks.
The paper tackled the problem of preserving manifold structure in generative models by proposing a method that transforms a simple distribution to a latent-space data distribution using Optimal Transport, avoiding the difficult Min-Max optimization of GANs. Experimental results on MNIST and CelebA datasets validated its effectiveness, with specific tests on an eight-Gaussian dataset showing it can handle multi-cluster distributions.
Variational Auto-Encoders enforce their learned intermediate latent-space data distribution to be a simple distribution, such as an isotropic Gaussian. However, this causes the posterior collapse problem and loses manifold structure which can be important for datasets such as facial images. A GAN can transform a simple distribution to a latent-space data distribution and thus preserve the manifold structure, but optimizing a GAN involves solving a Min-Max optimization problem, which is difficult and not well understood so far. Therefore, we propose a GAN-like method to transform a simple distribution to a data distribution in the latent space by solving only a minimization problem. This minimization problem comes from training a discriminator between a simple distribution and a latent-space data distribution. Then, we can explicitly formulate an Optimal Transport (OT) problem that computes the desired mapping between the two distributions. This means that we can transform a distribution without solving the difficult Min-Max optimization problem. Experimental results on an eight-Gaussian dataset show that the proposed OT can handle multi-cluster distributions. Results on the MNIST and the CelebA datasets validate the effectiveness of the proposed method.