# Approximate Inference with Amortised MCMC

arXiv: https://arxiv.org/abs/1702.08343 · HTML: https://mlsanity.com/paper/1702.08343/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Feb 2017.

## Built on by (most cited first, 23 of 23)

- [MCMC Variational Inference via Uncorrected Hamiltonian Annealing](https://mlsanity.com/paper/2107.04150/) (2021)
- [A Variational Perspective on Generative Flow Networks](https://mlsanity.com/paper/2210.07992/) (2022)
- [Sliced Wasserstein Variational Inference](https://mlsanity.com/paper/2207.13177/) (2022)
- [Nested Variational Inference](https://mlsanity.com/paper/2106.11302/) (2021)
- [Surrogate Likelihoods for Variational Annealed Importance Sampling](https://mlsanity.com/paper/2112.12194/) (2021)
- [Learning Energy-Based Prior Model with Diffusion-Amortized MCMC](https://mlsanity.com/paper/2310.03218/) (2023)
- [Fully Bayesian Autoencoders with Latent Sparse Gaussian Processes](https://mlsanity.com/paper/2302.04534/) (2023)
- [Learning Proposals for Probabilistic Programs with Inference Combinators](https://mlsanity.com/paper/2103.00668/) (2021)
- [Markov Chain Score Ascent: A Unifying Framework of Variational Inference with Markovian Gradients](https://mlsanity.com/paper/2206.06295/) (2022)
- [SPO: Sequential Monte Carlo Policy Optimisation](https://mlsanity.com/paper/2402.07963/) (2024)
- [Convergence Analysis of Stochastic Gradient Descent with MCMC Estimators](https://mlsanity.com/paper/2303.10599/) (2023)
- [Reparameterized Sampling for Generative Adversarial Networks](https://mlsanity.com/paper/2107.00352/) (2021)
- [Langevin Autoencoders for Learning Deep Latent Variable Models](https://mlsanity.com/paper/2209.07036/) (2022)
- [Conditional Sampling of Variational Autoencoders via Iterated Approximate Ancestral Sampling](https://mlsanity.com/paper/2308.09078/) (2023)
- [Structured Recognition for Generative Models with Explaining Away](https://mlsanity.com/paper/2209.05212/) (2022)
- [Bayesian Computation in Deep Learning](https://mlsanity.com/paper/2502.18300/) (2025)
- [Variational Rejection Particle Filtering](https://mlsanity.com/paper/2103.15343/) (2021)
- [High-Dimensional Inference in Bayesian Networks](https://mlsanity.com/paper/2112.09217/) (2021)
- [Accelerated Markov Chain Monte Carlo Using Adaptive Weighting Scheme](https://mlsanity.com/paper/2408.12888/) (2024)
- [Single-Step Consistent Diffusion Samplers](https://mlsanity.com/paper/2502.07579/) (2025)
- [Learning Extrapolative Sequence Transformations from Markov Chains](https://mlsanity.com/paper/2505.20251/) (2025)
- [Refinement-based Flow Policy Optimization](https://mlsanity.com/paper/2609.15123/) (2026)
- [Amortised Inference through One-Step Implicit Sampling](https://mlsanity.com/paper/2610.12679/) (2026)

## Abstract (arXiv)

We propose a novel approximate inference algorithm that approximates a target distribution by amortising the dynamics of a user-selected MCMC sampler. The idea is to initialise MCMC using samples from an approximation network, apply the MCMC operator to improve these samples, and finally use the samples to update the approximation network thereby improving its quality. This provides a new generic framework for approximate inference, allowing us to deploy highly complex, or implicitly defined approximation families with intractable densities, including approximations produced by warping a source of randomness through a deep neural network. Experiments consider image modelling with deep generative models as a challenging test for the method. Deep models trained using amortised MCMC are shown to generate realistic looking samples as well as producing diverse imputations for images with regions of missing pixels.