# BayesFlow: Amortized Bayesian Workflows With Neural Networks

arXiv: https://arxiv.org/abs/2306.16015 · HTML: https://mlsanity.com/paper/2306.16015/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 39 references that are in the map.
- First posted on arXiv 28 Jun 2023.

## Builds on (most cited first, 23 of 23)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows](https://mlsanity.com/paper/1805.07226/) (2018)
- [Automatic Posterior Transformation for Likelihood-Free Inference](https://mlsanity.com/paper/1905.07488/) (2019)
- [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)
- [TensorFlow Distributions](https://mlsanity.com/paper/1711.10604/) (2017)
- [Bayesian Workflow](https://mlsanity.com/paper/2011.01808/) (2020)
- [Detecting Model Misspecification in Amortized Bayesian Inference with Neural Networks](https://mlsanity.com/paper/2112.08866/) (2021)
- [JANA: Jointly Amortized Neural Approximation of Complex Bayesian Models](https://mlsanity.com/paper/2302.09125/) (2023)
- [Truncated Marginal Neural Ratio Estimation](https://mlsanity.com/paper/2107.01214/) (2021)
- [Graphical Test for Discrete Uniformity and its Applications in Goodness of Fit Evaluation and Multiple Sample Comparison](https://mlsanity.com/paper/2103.10522/) (2021)
- [Reliable amortized variational inference with physics-based latent distribution correction](https://mlsanity.com/paper/2207.11640/) (2022)
- [Amortized Bayesian model comparison with evidential deep learning](https://mlsanity.com/paper/2004.10629/) (2020)
- [OutbreakFlow: Model-based Bayesian inference of disease outbreak dynamics with invertible neural networks and its application to the COVID-19 pandemics in Germany](https://mlsanity.com/paper/2010.00300/) (2020)
- [Toward a principled Bayesian workflow in cognitive science](https://mlsanity.com/paper/1904.12765/) (2019)
- [Some models are useful, but how do we know which ones? Towards a unified Bayesian model taxonomy](https://mlsanity.com/paper/2209.02439/) (2022)
- [A Deep Learning Method for Comparing Bayesian Hierarchical Models](https://mlsanity.com/paper/2301.11873/) (2023)
- [ELFI: Engine for Likelihood-Free Inference](https://mlsanity.com/paper/1708.00707/) (2017)
- [Meta-Uncertainty in Bayesian Model Comparison](https://mlsanity.com/paper/2210.07278/) (2022)
- [Neural Superstatistics for Bayesian Estimation of Dynamic Cognitive Models](https://mlsanity.com/paper/2211.13165/) (2022)
- [Variational inference of fractional Brownian motion with linear computational complexity](https://mlsanity.com/paper/2203.07961/) (2022)
- [A Bayesian brain model of adaptive behavior: An application to the Wisconsin Card Sorting Task](https://mlsanity.com/paper/2003.07394/) (2020)

## Built on by (most cited first, 30 of 32)

- [Neural Methods for Amortized Inference](https://mlsanity.com/paper/2404.12484/) (2024)
- [Simulation-Based Inference: A Practical Guide](https://mlsanity.com/paper/2508.12939/) (2025)
- [sbi reloaded: a toolkit for simulation-based inference workflows](https://mlsanity.com/paper/2411.17337/) (2024)
- [Consistency Models for Scalable and Fast Simulation-Based Inference](https://mlsanity.com/paper/2312.05440/) (2023)
- [Sensitivity-Aware Amortized Bayesian Inference](https://mlsanity.com/paper/2310.11122/) (2023)
- [Amortized Bayesian Multilevel Models](https://mlsanity.com/paper/2408.13230/) (2024)
- [Does Unsupervised Domain Adaptation Improve the Robustness of Amortized Bayesian Inference? A Systematic Evaluation](https://mlsanity.com/paper/2502.04949/) (2025)
- [BayesFlow 2: Multi-Backend Amortized Bayesian Inference in Python](https://mlsanity.com/paper/2602.07098/) (2026)
- [Detecting Model Misspecification in Amortized Bayesian Inference with Neural Networks: An Extended Investigation](https://mlsanity.com/paper/2406.03154/) (2024)
- [ALINE: Joint Amortization for Bayesian Inference and Active Data Acquisition](https://mlsanity.com/paper/2506.07259/) (2025)
- [Multilevel neural simulation-based inference](https://mlsanity.com/paper/2506.06087/) (2025)
- [Improving the Accuracy of Amortized Model Comparison with Self-Consistency](https://mlsanity.com/paper/2508.20614/) (2025)
- [Demonstrating the power and flexibility of variational assumptions for amortized neural posterior estimation in environmental applications](https://mlsanity.com/paper/2404.10899/) (2024)
- [Fast, accurate and lightweight sequential simulation-based inference using Gaussian locally linear mappings](https://mlsanity.com/paper/2403.07454/) (2024)
- [Amortized Bayesian Workflow](https://mlsanity.com/paper/2409.04332/) (2024)
- [Posterior SBC: Simulation-Based Calibration Checking Conditional on Data](https://mlsanity.com/paper/2502.03279/) (2025)
- [Meta-Statistical Learning: Supervised Learning of Statistical Estimators](https://mlsanity.com/paper/2502.12088/) (2025)
- [Variational Autoencoders for Efficient Simulation-Based Inference](https://mlsanity.com/paper/2411.14511/) (2024)
- [MetaMolGen: A Neural Graph Motif Generation Model for De Novo Molecular Design](https://mlsanity.com/paper/2504.15587/) (2025)
- [ConDiSim: Conditional Diffusion Models for Simulation Based Inference](https://mlsanity.com/paper/2505.08403/) (2025)
- [metabeta -- A fast neural model for Bayesian mixed-effects regression](https://mlsanity.com/paper/2510.07473/) (2025)
- [From Mice to Trains: Amortized Bayesian Inference on Graph Data](https://mlsanity.com/paper/2601.02241/) (2026)
- [Expert-elicitation method for non-parametric joint priors using normalizing flows](https://mlsanity.com/paper/2411.15826/) (2024)
- [Uncertainty-Aware Surrogate-based Amortized Bayesian Inference for Computationally Expensive Models](https://mlsanity.com/paper/2505.08683/) (2025)
- [MIST: Mutual Information Estimation Via Supervised Training](https://mlsanity.com/paper/2511.18945/) (2025)
- [An Introduction to Bayesian and Frequentist Simulation-Based Inference with Machine Learning](https://mlsanity.com/paper/2607.21702/) (2026)
- [Amortized Bayesian Inference on Multilevel Models of Arbitrary Structure](https://mlsanity.com/paper/2609.40024/) (2026)
- [Preconditioned Robust Neural Posterior Estimation for Misspecified Simulators](https://mlsanity.com/paper/2602.18004/) (2026)
- [Unsupervised Continual Learning for Amortized Bayesian Inference](https://mlsanity.com/paper/2602.22884/) (2026)
- [ForwardFlow: Simulation only statistical inference using deep learning](https://mlsanity.com/paper/2603.10991/) (2026)

## Abstract (arXiv)

Modern Bayesian inference involves a mixture of computational techniques for estimating, validating, and drawing conclusions from probabilistic models as part of principled workflows for data analysis. Typical problems in Bayesian workflows are the approximation of intractable posterior distributions for diverse model types and the comparison of competing models of the same process in terms of their complexity and predictive performance. This manuscript introduces the Python library BayesFlow for simulation-based training of established neural network architectures for amortized data compression and inference. Amortized Bayesian inference, as implemented in BayesFlow, enables users to train custom neural networks on model simulations and re-use these networks for any subsequent application of the models. Since the trained networks can perform inference almost instantaneously, the upfront neural network training is quickly amortized.