# An AI-powered Bayesian Generative Modeling Approach for Arbitrary Conditional Inference

arXiv: https://arxiv.org/abs/2601.05355 · HTML: https://mlsanity.com/paper/2601.05355/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 39 references that are in the map.
- First posted on arXiv 8 Jan 2026.

## Builds on (most cited first, 17 of 17)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming](https://mlsanity.com/paper/1309.5549/) (2013)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Variational Dropout and the Local Reparameterization Trick](https://mlsanity.com/paper/1506.02557/) (2015)
- [Hands-on Bayesian Neural Networks -- a Tutorial for Deep Learning Users](https://mlsanity.com/paper/2007.06823/) (2020)
- [Predictive inference with the jackknife+](https://mlsanity.com/paper/1905.02928/) (2019)
- [Flipout: Efficient Pseudo-Independent Weight Perturbations on Mini-Batches](https://mlsanity.com/paper/1803.04386/) (2018)
- [Bayesian Neural Networks: An Introduction and Survey](https://mlsanity.com/paper/2006.12024/) (2020)
- [Localized Conformal Prediction: A Generalized Inference Framework for Conformal Prediction](https://mlsanity.com/paper/2106.08460/) (2021)
- [TensorFlow Distributions](https://mlsanity.com/paper/1711.10604/) (2017)
- [Variational Autoencoder with Arbitrary Conditioning](https://mlsanity.com/paper/1806.02382/) (2018)
- [Flow Models for Arbitrary Conditional Likelihoods](https://mlsanity.com/paper/1909.06319/) (2019)
- [Arbitrary Conditional Distributions with Energy](https://mlsanity.com/paper/2102.04426/) (2021)
- [An AI-powered Bayesian generative modeling approach for causal inference in observational studies](https://mlsanity.com/paper/2501.00755/) (2025)

## Built on by (most cited first, 2 of 2)

- [BGM-IV: AI-Powered Bayesian Generative Modeling for Instrumental Variable Regression with High-Dimensional Covariates](https://mlsanity.com/paper/2605.07029/) (2026)
- [BayesNDE: Bayesian Generative Modeling for Neural Density Estimation](https://mlsanity.com/paper/2609.39843/) (2026)

## Abstract (arXiv)

Modern data analysis increasingly requires flexible conditional inference P(X_B | X_A) where (X_A, X_B) is an arbitrary partition of observed variable X. Existing approaches are either restricted to a fixed conditioning structure or depend strongly on the distribution of conditioning masks during training. To address these limitations, we introduce Bayesian generative modeling (BGM), a unified framework for arbitrary conditional inference. BGM learns a generative model of X via a stochastic iterative Bayesian updating algorithm in which model parameters and latent variables are updated until convergence. Once trained, any conditional distribution can be obtained without retraining. Empirically, BGM achieves superior predictive performance with posterior predictive intervals, demonstrating that a single learned model can serve as a universal engine for conditional prediction with principled uncertainty quantification. We provide theoretical guarantees for convergence of the stochastic iterative algorithm, statistical consistency, and conditional risk bounds. The proposed BGM framework leverages modern AI to capture complex relationships among variables while adhering to Bayesian principles, offering a promising approach for a wide range of applications in modern data science. Code for BGM is available at https://github.com/liuq-lab/bayesgm. Document of BGM is available at https://bayesgm.readthedocs.io.