# MetFlow: A New Efficient Method for Bridging the Gap between Markov Chain Monte Carlo and Variational Inference

arXiv: https://arxiv.org/abs/2002.12253 · HTML: https://mlsanity.com/paper/2002.12253/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Feb 2020.

## Built on by (most cited first, 7 of 7)

- [Annealed Flow Transport Monte Carlo](https://mlsanity.com/paper/2102.07501/) (2021)
- [From Risk to Uncertainty: Generating Predictive Uncertainty Measures via Bayesian Estimation](https://mlsanity.com/paper/2402.10727/) (2024)
- [The Free Energy Principle for Perception and Action: A Deep Learning Perspective](https://mlsanity.com/paper/2207.06415/) (2022)
- [Disentangling impact of capacity, objective, batchsize, estimators, and step-size on flow VI](https://mlsanity.com/paper/2412.08824/) (2024)
- [Variational Learning of Gaussian Process Latent Variable Models through Stochastic Gradient Annealed Importance Sampling](https://mlsanity.com/paper/2408.06710/) (2024)
- [Optimization of Annealed Importance Sampling Hyperparameters](https://mlsanity.com/paper/2209.13226/) (2022)
- [Learning variational autoencoders via MCMC speed measures](https://mlsanity.com/paper/2308.13731/) (2023)

## Abstract (arXiv)

In this contribution, we propose a new computationally efficient method to combine Variational Inference (VI) with Markov Chain Monte Carlo (MCMC). This approach can be used with generic MCMC kernels, but is especially well suited to textitMetFlow, a novel family of MCMC algorithms we introduce, in which proposals are obtained using Normalizing Flows. The marginal distribution produced by such MCMC algorithms is a mixture of flow-based distributions, thus drastically increasing the expressivity of the variational family. Unlike previous methods following this direction, our approach is amenable to the reparametrization trick and does not rely on computationally expensive reverse kernels. Extensive numerical experiments show clear computational and performance improvements over state-of-the-art methods.