Learning Deep Latent Variable Models via Amortized Langevin Dynamics

How can we perform posterior inference for deep latent variable models in an efficient and flexible manner? Markov chain Monte Carlo (MCMC) methods, such as Langevin dynamics, provide sample approximations of such posteriors with an asymptotic convergence guarantee. However, it is difficult to apply these methods to large-scale datasets owing to their slow convergence and datapoint-wise iterations. In this study, we propose amortized Langevin dynamics, wherein datapoint-wise MCMC iterations are replaced with updates of an inference model that maps observations into latent variables. The amortization enables scalable inference from large-scale datasets. Developing a latent variable model and an inference model with neural networks, yields Langevin autoencoders (LAEs), a novel Langevin-based framework for deep generative models. Moreover, if we define a latent prior distribution with an unnormalized energy function for more flexible generative modeling, LAEs are extended to a more general framework, which we refer to as contrastive Langevin autoencoders (CLAEs). We experimentally show that LAEs and CLAEs can generate sharp image samples. Moreover, we report their performance of unsupervised anomaly detection.