# Preventing Oversmoothing in VAE via Generalized Variance Parameterization

arXiv: https://arxiv.org/abs/2102.08663 · HTML: https://mlsanity.com/paper/2102.08663/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 39 references that are in the map.
- First posted on arXiv 17 Feb 2021.

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

- [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)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Generating Diverse High-Fidelity Images with VQ-VAE-2](https://mlsanity.com/paper/1906.00446/) (2019)
- [InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets](https://mlsanity.com/paper/1606.03657/) (2016)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)
- [Generating Sentences from a Continuous Space](https://mlsanity.com/paper/1511.06349/) (2015)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [PixelCNN++: Improving the PixelCNN with Discretized Logistic Mixture Likelihood and Other Modifications](https://mlsanity.com/paper/1701.05517/) (2017)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [Adversarial Autoencoders](https://mlsanity.com/paper/1511.05644/) (2015)
- [How Does Batch Normalization Help Optimization?](https://mlsanity.com/paper/1805.11604/) (2018)
- [Ladder Variational Autoencoders](https://mlsanity.com/paper/1602.02282/) (2016)
- [Very Deep VAEs Generalize Autoregressive Models and Can Outperform Them on Images](https://mlsanity.com/paper/2011.10650/) (2020)
- [Diagnosing and Enhancing VAE Models](https://mlsanity.com/paper/1903.05789/) (2019)
- [Cyclical Annealing Schedule: A Simple Approach to Mitigating KL Vanishing](https://mlsanity.com/paper/1903.10145/) (2019)
- [From Variational to Deterministic Autoencoders](https://mlsanity.com/paper/1903.12436/) (2019)
- [Lagging Inference Networks and Posterior Collapse in Variational Autoencoders](https://mlsanity.com/paper/1901.05534/) (2019)
- [Don't Blame the ELBO! A Linear VAE Perspective on Posterior Collapse](https://mlsanity.com/paper/1911.02469/) (2019)
- [Preventing Posterior Collapse with delta-VAEs](https://mlsanity.com/paper/1901.03416/) (2019)
- [Spherical Latent Spaces for Stable Variational Autoencoders](https://mlsanity.com/paper/1808.10805/) (2018)
- [The Usual Suspects? Reassessing Blame for VAE Posterior Collapse](https://mlsanity.com/paper/1912.10702/) (2019)
- [MAE: Mutual Posterior-Divergence Regularization for Variational AutoEncoders](https://mlsanity.com/paper/1901.01498/) (2019)
- [Variational Autoencoders with Normalizing Flow Decoders](https://mlsanity.com/paper/2004.05617/) (2020)
- [ControlVAE: Controllable Variational Autoencoder](https://mlsanity.com/paper/2004.05988/) (2020)

## Built on by (most cited first, 15 of 15)

- [HQ-VAE: Hierarchical Discrete Representation Learning with Variational Bayes](https://mlsanity.com/paper/2401.00365/) (2023)
- [PID: Physics-Informed Diffusion Model for Infrared Image Generation](https://mlsanity.com/paper/2407.09299/) (2024)
- [Amortized Variational Inference: A Systematic Review](https://mlsanity.com/paper/2209.10888/) (2022)
- [VCT: Training Consistency Models with Variational Noise Coupling](https://mlsanity.com/paper/2502.18197/) (2025)
- [Flow Matching Meets Biology and Life Science: A Survey](https://mlsanity.com/paper/2507.17731/) (2025)
- [Learning Physics for Unveiling Hidden Earthquake Ground Motions via Conditional Generative Modeling](https://mlsanity.com/paper/2407.15089/) (2024)
- [How to train your VAE](https://mlsanity.com/paper/2309.13160/) (2023)
- [Denoising Multi-Beta VAE: Representation Learning for Disentanglement and Generation](https://mlsanity.com/paper/2507.06613/) (2025)
- [Causal Dynamic Variational Autoencoder for Counterfactual Regression in Longitudinal Data](https://mlsanity.com/paper/2310.10559/) (2023)
- [Reasoning-guided Collaborative Filtering with Language Models for Explainable Recommendation](https://mlsanity.com/paper/2602.05544/) (2026)
- [Teacher-free Latent Self-distillation and Class-separable Representations for Lightweight IoT Attack Detection](https://mlsanity.com/paper/2403.15509/) (2024)
- [DiffKnock: Diffusion-based Knockoff Statistics for Neural Networks Inference](https://mlsanity.com/paper/2510.01418/) (2025)
- [Mutual Information Collapse Explains Disentanglement Failure in β-VAEs](https://mlsanity.com/paper/2602.09277/) (2026)
- [No Free Lunch for Synthetic Images under Data Scarcity Conditions](https://mlsanity.com/paper/2606.07640/) (2026)
- [K-IPO: Kendall-constrained Importance Preserving Oversampling for Imbalanced Tabular Data](https://mlsanity.com/paper/2607.16478/) (2026)

## Abstract (arXiv)

Variational autoencoders (VAEs) often suffer from posterior collapse, which is a phenomenon in which the learned latent space becomes uninformative. This is often related to the hyperparameter resembling the data variance. It can be shown that an inappropriate choice of this hyperparameter causes the oversmoothness in the linearly approximated case and can be empirically verified for the general cases. Moreover, determining such appropriate choice becomes infeasible if the data variance is non-uniform or conditional. Therefore, we propose VAE extensions with generalized parameterizations of the data variance and incorporate maximum likelihood estimation into the objective function to adaptively regularize the decoder smoothness. The images generated from proposed VAE extensions show improved Fr'echet inception distance (FID) on MNIST and CelebA datasets.