# Density-Informed VAE (DiVAE): Reliable Log-Prior Probability via Density Alignment Regularization

arXiv: https://arxiv.org/abs/2512.03928 · HTML: https://mlsanity.com/paper/2512.03928/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 21 references that are in the map.
- First posted on arXiv 3 Dec 2025.

## Builds on (most cited first, 11 of 11)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [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 Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Ladder Variational Autoencoders](https://mlsanity.com/paper/1602.02282/) (2016)
- [VAE with a VampPrior](https://mlsanity.com/paper/1705.07120/) (2017)
- [Variational Lossy Autoencoder](https://mlsanity.com/paper/1611.02731/) (2016)
- [PixelVAE: A Latent Variable Model for Natural Images](https://mlsanity.com/paper/1611.05013/) (2016)

## Abstract (arXiv)

We introduce Density-Informed VAE (DiVAE), a lightweight, data-driven regularizer that aligns the VAE log-prior probability log pZ(z) with a log-density estimated from data. Standard VAEs match latents to a simple prior, overlooking density structure in the data-space. DiVAE encourages the encoder to allocate posterior mass in proportion to data-space density and, when the prior is learnable, nudges the prior toward high-density regions. This is realized by adding a robust, precision-weighted penalty to the ELBO, incurring negligible computational overhead. On synthetic datasets, DiVAE (i) improves distributional alignment of latent log-densities to its ground truth counterpart, (ii) improves prior coverage, and (iii) yields better OOD uncertainty calibration. On MNIST, DiVAE improves alignment of the prior with external estimates of the density, providing better interpretability, and improves OOD detection for learnable priors.