# BayesFlow 2: Multi-Backend Amortized Bayesian Inference in Python

arXiv: https://arxiv.org/abs/2602.07098 · HTML: https://mlsanity.com/paper/2602.07098/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 66 of its 98 references that are in the map.
- First posted on arXiv 6 Feb 2026.

## Builds on (most cited first, 30 of 66)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Transformers in Time Series: A Survey](https://mlsanity.com/paper/2202.07125/) (2022)
- [Improved Techniques for Training Consistency Models](https://mlsanity.com/paper/2310.14189/) (2023)
- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [Black Box Variational Inference](https://mlsanity.com/paper/1401.0118/) (2013)
- [Understanding Diffusion Objectives as the ELBO with Simple Data Augmentation](https://mlsanity.com/paper/2303.00848/) (2023)
- [Revisiting Classifier Two-Sample Tests](https://mlsanity.com/paper/1610.06545/) (2016)
- [Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows](https://mlsanity.com/paper/1805.07226/) (2018)
- [Validating Bayesian Inference Algorithms with Simulation-Based Calibration](https://mlsanity.com/paper/1804.06788/) (2018)
- [On Contrastive Learning for Likelihood-free Inference](https://mlsanity.com/paper/2002.03712/) (2020)
- [Simulation Intelligence: Towards a New Generation of Scientific Methods](https://mlsanity.com/paper/2112.03235/) (2021)
- [Likelihood-free inference with emulator networks](https://mlsanity.com/paper/1805.09294/) (2018)
- [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)
- [Learning Robust Statistics for Simulation-based Inference under Model Misspecification](https://mlsanity.com/paper/2305.15871/) (2023)
- [Robust Neural Posterior Estimation and Statistical Model Criticism](https://mlsanity.com/paper/2210.06564/) (2022)

## Built on by (most cited first, 9 of 9)

- [Amortized Bayesian Inference on Multilevel Models of Arbitrary Structure](https://mlsanity.com/paper/2609.40024/) (2026)
- [Unsupervised Continual Learning for Amortized Bayesian Inference](https://mlsanity.com/paper/2602.22884/) (2026)
- [Identifiability and amortized inference limitations in Kuramoto models](https://mlsanity.com/paper/2603.21752/) (2026)
- [Inverting Foundation Models of Brain Function with Simulation-Based Inference](https://mlsanity.com/paper/2604.23865/) (2026)
- [Conservative neural posterior estimation via distributionally robust training](https://mlsanity.com/paper/2605.28516/) (2026)
- [Divide-and-Conquer: Towards Generalizable Amortized Bayesian Inference for the Drift Diffusion Model](https://mlsanity.com/paper/2608.03566/) (2026)
- [High-Dimensional Simulation-Based Inference in Latent Spaces](https://mlsanity.com/paper/2609.37381/) (2026)
- [Joint Neural Posterior Estimation and Model Selection for Chemical Reaction Networks](https://mlsanity.com/paper/2610.18825/) (2026)
- [Semi-Amortized Bayesian Inference with Reusable Local Posteriors](https://mlsanity.com/paper/2610.18945/) (2026)

## Abstract (arXiv)

Modern Bayesian inference involves a mixture of computational methods for estimating, validating, and drawing conclusions from probabilistic models as part of principled workflows. An overarching motif of many Bayesian methods is that they are relatively slow, which often becomes prohibitive when fitting complex models to large data sets. Amortized Bayesian inference (ABI) offers a path to solving the computational challenges of Bayes. ABI trains neural networks on model simulations, rewarding users with rapid inference of any model-implied quantity, such as point estimates, likelihoods, or full posterior distributions. In this work, we present the Python library BayesFlow, Version 2.0, for general-purpose ABI. Along with direct posterior, likelihood, and ratio estimation, the software includes support for multiple popular deep learning backends, a rich collection of generative networks for sampling and density estimation, complete customization and high-level interfaces, as well as new capabilities for hyperparameter optimization, design optimization, and hierarchical modeling. Using a case study on dynamical system parameter estimation, combined with comparisons to similar software, we show that our streamlined, user-friendly workflow has strong potential to support broad adoption.