Langevin Autoencoders for Learning Deep Latent Variable Models

Markov chain Monte Carlo (MCMC), such as Langevin dynamics, is valid for approximating intractable distributions. However, its usage is limited in the context of deep latent variable models owing to costly datapoint-wise sampling iterations and slow convergence. This paper proposes the amortized Langevin dynamics (ALD), wherein datapoint-wise MCMC iterations are entirely replaced with updates of an encoder that maps observations into latent variables. This amortization enables efficient posterior sampling without datapoint-wise iterations. Despite its efficiency, we prove that ALD is valid as an MCMC algorithm, whose Markov chain has the target posterior as a stationary distribution under mild assumptions.