# Semi-Amortized Bayesian Inference with Reusable Local Posteriors

arXiv: https://arxiv.org/abs/2610.18945 · HTML: https://mlsanity.com/paper/2610.18945/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 42 references that are in the map.
- First posted on arXiv 13 Oct 2026.

## Builds on (most cited first, 24 of 24)

- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Revisiting Classifier Two-Sample Tests](https://mlsanity.com/paper/1610.06545/) (2016)
- [Analyzing Inverse Problems with Invertible Neural Networks](https://mlsanity.com/paper/1808.04730/) (2018)
- [BayesFlow: Learning complex stochastic models with invertible neural networks](https://mlsanity.com/paper/2003.06281/) (2020)
- [Validating Bayesian Inference Algorithms with Simulation-Based Calibration](https://mlsanity.com/paper/1804.06788/) (2018)
- [Rank-normalization, folding, and localization: An improved widehatR for assessing convergence of MCMC](https://mlsanity.com/paper/1903.08008/) (2019)
- [Covariances, Robustness, and Variational Bayes](https://mlsanity.com/paper/1709.02536/) (2017)
- [Inference Compilation and Universal Probabilistic Programming](https://mlsanity.com/paper/1610.09900/) (2016)
- [Faithful Inversion of Generative Models for Effective Amortized Inference](https://mlsanity.com/paper/1712.00287/) (2017)
- [Automatic structured variational inference](https://mlsanity.com/paper/2002.00643/) (2020)
- [HNPE: Leveraging Global Parameters for Neural Posterior Estimation](https://mlsanity.com/paper/2102.06477/) (2021)
- [Perturbation theory for Markov chains via Wasserstein distance](https://mlsanity.com/paper/1503.04123/) (2015)
- [Amortized Bayesian Multilevel Models](https://mlsanity.com/paper/2408.13230/) (2024)
- [Diffusion Models in Simulation-Based Inference: A Tutorial Review](https://mlsanity.com/paper/2512.20685/) (2025)
- [Hierarchical Neural Simulation-Based Inference Over Event Ensembles](https://mlsanity.com/paper/2306.12584/) (2023)
- [BayesFlow 2: Multi-Backend Amortized Bayesian Inference in Python](https://mlsanity.com/paper/2602.07098/) (2026)
- [Likelihood-free approximate Gibbs sampling](https://mlsanity.com/paper/1906.04347/) (2019)
- [Amortized Population Gibbs Samplers with Neural Sufficient Statistics](https://mlsanity.com/paper/1911.01382/) (2019)
- [Efficient Probabilistic Inference in the Quest for Physics Beyond the Standard Model](https://mlsanity.com/paper/1807.07706/) (2018)
- [ADAVI: Automatic Dual Amortized Variational Inference Applied To Pyramidal Bayesian Models](https://mlsanity.com/paper/2106.12248/) (2021)
- [Attention for Inference Compilation](https://mlsanity.com/paper/1910.11961/) (2019)
- [PAVI: Plate-Amortized Variational Inference](https://mlsanity.com/paper/2206.05111/) (2022)
- [Accelerating Metropolis-Hastings with Lightweight Inference Compilation](https://mlsanity.com/paper/2010.12128/) (2020)
- [Amortized Bayesian Inference on Multilevel Models of Arbitrary Structure](https://mlsanity.com/paper/2609.40024/) (2026)

## Abstract (arXiv)

Amortized Bayesian inference uses simulations to perform Bayesian estimation when likelihoods are expensive or analytically unavailable. However, learning the full joint posterior is challenging in high-dimensional models with complex dependencies. We introduce a semi-amortized method that divides parameters into smaller blocks, and uses conditional independence to identify the information needed to infer each block. We train neural estimators for blocks whose posterior updates are computationally expensive or frequently repeated. Each estimator learns from simulations of the relevant model components to approximate the block's full conditional posterior, given the relevant observations and the values of the variables on which it depends. A Markov chain then alternates direct draws from these estimators with conventional updates of the remaining variables. Each neural update uses the current conditioning values and requires neither likelihood evaluation nor an acceptance-rejection step. Where the same conditional structure recurs, one estimator can be reused across blocks and datasets, with an output dimension determined by the block rather than the full model. We illustrate the approach in high-dimensional and computationally expensive hierarchical and spatiotemporal models.