  Variational autoencoders (VAEs), as an important aspect of generative models,
have received a lot of research interests and reached many successful
applications. However, it is always a challenge to achieve the consistency
between the learned latent distribution and the prior latent distribution when
optimizing the evidence lower bound (ELBO), and finally leads to an
unsatisfactory performance in data generation. In this paper, we propose a
latent distribution consistency approach to avoid such substantial
inconsistency between the posterior and prior latent distributions in ELBO
optimizing. We name our method as latent distribution consistency VAE
(LDC-VAE). We achieve this purpose by assuming the real posterior distribution
in latent space as a Gibbs form, and approximating it by using our encoder.
However, there is no analytical solution for such Gibbs posterior in
approximation, and traditional approximation ways are time consuming, such as
using the iterative sampling-based MCMC. To address this problem, we use the
Stein Variational Gradient Descent (SVGD) to approximate the Gibbs posterior.
Meanwhile, we use the SVGD to train a sampler net which can obtain efficient
samples from the Gibbs posterior. Comparative studies on the popular image
generation datasets show that our method has achieved comparable or even better
performance than several powerful improvements of VAEs.
