# BayesNDE: Bayesian Generative Modeling for Neural Density Estimation

arXiv: https://arxiv.org/abs/2609.39843 · HTML: https://mlsanity.com/paper/2609.39843/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 31 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## Builds on (most cited first, 12 of 12)

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [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)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Residual Flows for Invertible Generative Modeling](https://mlsanity.com/paper/1906.02735/) (2019)
- [Rank-normalization, folding, and localization: An improved widehatR for assessing convergence of MCMC](https://mlsanity.com/paper/1903.08008/) (2019)
- [Normalizing Constant Estimation with Gaussianized Bridge Sampling](https://mlsanity.com/paper/1912.06073/) (2019)
- [An AI-powered Bayesian generative modeling approach for causal inference in observational studies](https://mlsanity.com/paper/2501.00755/) (2025)
- [An AI-powered Bayesian Generative Modeling Approach for Arbitrary Conditional Inference](https://mlsanity.com/paper/2601.05355/) (2026)
- [Missingness-aware Data Imputation via AI-powered Bayesian Generative Modeling](https://mlsanity.com/paper/2605.01676/) (2026)

## Abstract (arXiv)

Density estimation is a fundamental problem in statistics and machine learning. In this work, we introduce BayesNDE, a neural density estimator based on Bayesian generative modeling. BayesNDE learns a Bayesian generative model and evaluates its density without requiring invertible networks or Jacobian-determinant computation. For each observation, it infers a sample-specific latent posterior to construct an adaptive proposal that focuses computation on regions contributing most to its density. Bridge sampling then combines samples from this proposal with separate posterior samples to estimate the density. Experiments on nonlinear and multimodal synthetic datasets show improved estimation of density values and better recovery of the density structure compared to the state-of-the-art neural density estimators. Applications to real-world datasets further demonstrate improved anomaly detection. Together, these results highlight BayesNDE as a flexible and effective neural density estimator, demonstrating how posterior inference can turn generative models into tools for density estimation. The code and tutorials are available at https://github.com/liuq-lab/BayesNDE.