# Amortized Inference Regularization

arXiv: https://arxiv.org/abs/1805.08913 · HTML: https://mlsanity.com/paper/1805.08913/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 May 2018.

## Built on by (most cited first, 30 of 30)

- [FastSHAP: Real-Time Shapley Value Estimation](https://mlsanity.com/paper/2107.07436/) (2021)
- [Amortized Variational Inference: When and Why?](https://mlsanity.com/paper/2307.11018/) (2023)
- [Embrace the Gap: VAEs Perform Independent Mechanism Analysis](https://mlsanity.com/paper/2206.02416/) (2022)
- [I Don't Need u: Identifiable Non-Linear ICA Without Side Information](https://mlsanity.com/paper/2106.05238/) (2021)
- [On PAC-Bayesian reconstruction guarantees for VAEs](https://mlsanity.com/paper/2202.11455/) (2022)
- [Amortized Projection Optimization for Sliced Wasserstein Generative Models](https://mlsanity.com/paper/2203.13417/) (2022)
- [Adversarial robustness of amortized Bayesian inference](https://mlsanity.com/paper/2305.14984/) (2023)
- [Amortized Variational Inference: A Systematic Review](https://mlsanity.com/paper/2209.10888/) (2022)
- [Diffusion Prior-Based Amortized Variational Inference for Noisy Inverse Problems](https://mlsanity.com/paper/2407.16125/) (2024)
- [VAE Approximation Error: ELBO and Exponential Families](https://mlsanity.com/paper/2102.09310/) (2021)
- [An Introduction to Variational Inference](https://mlsanity.com/paper/2108.13083/) (2021)
- [Revisiting Structured Variational Autoencoders](https://mlsanity.com/paper/2305.16543/) (2023)
- [Generalization Gap in Amortized Inference](https://mlsanity.com/paper/2205.11640/) (2022)
- [Regularization-Agnostic Compressed Sensing MRI Reconstruction with Hypernetworks](https://mlsanity.com/paper/2101.02194/) (2021)
- [Partition Function Estimation: A Quantitative Study](https://mlsanity.com/paper/2105.11132/) (2021)
- [Computing Multiple Image Reconstructions with a Single Hypernetwork](https://mlsanity.com/paper/2202.11009/) (2022)
- [Improving VAE-based Representation Learning](https://mlsanity.com/paper/2205.14539/) (2022)
- [Input Dependent Sparse Gaussian Processes](https://mlsanity.com/paper/2107.07281/) (2021)
- [Revisiting Active Sets for Gaussian Process Decoders](https://mlsanity.com/paper/2209.04636/) (2022)
- [ADAVI: Automatic Dual Amortized Variational Inference Applied To Pyramidal Bayesian Models](https://mlsanity.com/paper/2106.12248/) (2021)
- [Deep Generative Modeling on Limited Data with Regularization by Nontransferable Pre-trained Models](https://mlsanity.com/paper/2208.14133/) (2022)
- [Langevin Autoencoders for Learning Deep Latent Variable Models](https://mlsanity.com/paper/2209.07036/) (2022)
- [Unsupervised learning of spatially varying regularization for diffeomorphic image registration](https://mlsanity.com/paper/2412.17982/) (2024)
- [Energy-Based Coarse-Graining in Molecular Dynamics: A Flow-Based Framework without Data](https://mlsanity.com/paper/2504.20940/) (2025)
- [A Note on Generalization in Variational Autoencoders: How Effective Is Synthetic Data & Overparameterization?](https://mlsanity.com/paper/2310.19653/) (2023)
- [Modeling Graph Node Correlations with Neighbor Mixture Models](https://mlsanity.com/paper/2103.15966/) (2021)
- [Variational Autoencoders: A Harmonic Perspective](https://mlsanity.com/paper/2105.14866/) (2021)
- [On The Finetuning of MLIPs Through the Lens of Iterated Maps With BPTT](https://mlsanity.com/paper/2512.01067/) (2025)
- [Independent Component Discovery in Temporal Count Data](https://mlsanity.com/paper/2601.21696/) (2026)
- [Instance-Adaptive Parametrization for Amortized Variational Inference](https://mlsanity.com/paper/2604.06796/) (2026)

## Abstract (arXiv)

The variational autoencoder (VAE) is a popular model for density estimation and representation learning. Canonically, the variational principle suggests to prefer an expressive inference model so that the variational approximation is accurate. However, it is often overlooked that an overly-expressive inference model can be detrimental to the test set performance of both the amortized posterior approximator and, more importantly, the generative density estimator. In this paper, we leverage the fact that VAEs rely on amortized inference and propose techniques for amortized inference regularization (AIR) that control the smoothness of the inference model. We demonstrate that, by applying AIR, it is possible to improve VAE generalization on both inference and generative performance. Our paper challenges the belief that amortized inference is simply a mechanism for approximating maximum likelihood training and illustrates that regularization of the amortization family provides a new direction for understanding and improving generalization in VAEs.