  Variational autoencoder (VAE) is a very popular and well-investigated
generative model in neural learning research. To leverage VAE in practical
tasks dealing with a massive dataset of large dimensions, it is required to
deal with the difficulty of building low variance evidence lower bounds (ELBO).
Markov Chain Monte Carlo (MCMC) is an effective approach to tighten the ELBO
for approximating the posterior distribution and Hamiltonian Variational
Autoencoder (HVAE) is an effective MCMC inspired approach for constructing a
low-variance ELBO that is amenable to the reparameterization trick. The HVAE
adapted the Hamiltonian dynamic flow into variational inference that
significantly improves the performance of the posterior estimation. We propose
in this work a Langevin dynamic flow-based inference approach by incorporating
the gradients information in the inference process through the Langevin dynamic
which is a kind of MCMC based method similar to HVAE. Specifically, we employ a
quasi-symplectic integrator to cope with the prohibit problem of the Hessian
computing in naive Langevin flow. We show the theoretical and practical
effectiveness of the proposed framework with other gradient flow-based methods.
