BayesNDE: Bayesian Generative Modeling for Neural Density Estimation
Abstract
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.
Related
- BGM-IV: AI-Powered Bayesian Generative Modeling for Instrumental Variable Regression with High-Dimensional Covariates
- Dirichlet Process Mixtures within Semiparametric Bayesian Networks: A Novel Conditional Density Estimation Approach
- Generative SDEs with Trainable Diffusion and Density-Based Losses
- Generative modeling via hierarchical tensor sketching
- Generative modelling meets Bayesian inference: a new paradigm for inverse problems
BibTeX
@misc{li2026bayesnde,
title = {{BayesNDE: Bayesian Generative Modeling for Neural Density Estimation}},
author = {Chenglin Li and Qiao Liu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.39843},
eprint = {2609.39843},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.39843},
}
RIS
TY - UNPB
TI - BayesNDE: Bayesian Generative Modeling for Neural Density Estimation
AU - Chenglin Li
AU - Qiao Liu
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.39843
UR - https://arxiv.org/abs/2609.39843
AB - 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.
ER -