# Explicitly Minimizing the Blur Error of Variational Autoencoders

arXiv: https://arxiv.org/abs/2304.05939 · HTML: https://mlsanity.com/paper/2304.05939/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 31 references that are in the map.
- First posted on arXiv 12 Apr 2023.

## Builds on (most cited first, 21 of 21)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [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)
- [Autoencoding beyond pixels using a learned similarity metric](https://mlsanity.com/paper/1512.09300/) (2015)
- [A General and Adaptive Robust Loss Function](https://mlsanity.com/paper/1701.03077/) (2017)
- [Stochastic Latent Actor-Critic: Deep Reinforcement Learning with a Latent Variable Model](https://mlsanity.com/paper/1907.00953/) (2019)
- [Focal Frequency Loss for Image Reconstruction and Synthesis](https://mlsanity.com/paper/2012.12821/) (2020)
- [Flows for simultaneous manifold learning and density estimation](https://mlsanity.com/paper/2003.13913/) (2020)
- [Improved Conditional VRNNs for Video Prediction](https://mlsanity.com/paper/1904.12165/) (2019)
- [Sylvester Normalizing Flows for Variational Inference](https://mlsanity.com/paper/1803.05649/) (2018)
- [Rectangular Flows for Manifold Learning](https://mlsanity.com/paper/2106.01413/) (2021)
- [Blind Image Deconvolution using Deep Generative Priors](https://mlsanity.com/paper/1802.04073/) (2018)
- [A Loss Function for Generative Neural Networks Based on Watson's Perceptual Model](https://mlsanity.com/paper/2006.15057/) (2020)
- [MR image reconstruction using deep density priors](https://mlsanity.com/paper/1711.11386/) (2017)
- [Modelling the Distribution of 3D Brain MRI using a 2D Slice VAE](https://mlsanity.com/paper/2007.04780/) (2020)

## Built on by (most cited first, 30 of 31)

- [PID: Physics-Informed Diffusion Model for Infrared Image Generation](https://mlsanity.com/paper/2407.09299/) (2024)
- [Flow Matching Meets Biology and Life Science: A Survey](https://mlsanity.com/paper/2507.17731/) (2025)
- [Tree Variational Autoencoders](https://mlsanity.com/paper/2306.08984/) (2023)
- [FELLE: Autoregressive Speech Synthesis with Token-Wise Coarse-to-Fine Flow Matching](https://mlsanity.com/paper/2502.11128/) (2025)
- [BiPO: Bidirectional Partial Occlusion Network for Text-to-Motion Synthesis](https://mlsanity.com/paper/2412.00112/) (2024)
- [Diffusion Prior Interpolation for Flexibility Real-World Face Super-Resolution](https://mlsanity.com/paper/2412.16552/) (2024)
- [Synergy Between Sufficient Changes and Sparse Mixing Procedure for Disentangled Representation Learning](https://mlsanity.com/paper/2503.00639/) (2025)
- [Blind Image Deconvolution by Generative-based Kernel Prior and Initializer via Latent Encoding](https://mlsanity.com/paper/2407.14816/) (2024)
- [TreeDiffusion: Hierarchical Generative Clustering for Conditional Diffusion](https://mlsanity.com/paper/2410.16910/) (2024)
- [GUIDE-VAE: Advancing Data Generation with User Information and Pattern Dictionaries](https://mlsanity.com/paper/2411.03936/) (2024)
- [Text-to-Events: Synthetic Event Camera Streams from Conditional Text Input](https://mlsanity.com/paper/2406.03439/) (2024)
- [Variational Rank Reduction Autoencoders](https://mlsanity.com/paper/2505.09458/) (2025)
- [Guided Unconditional and Conditional Generative Models for Super-Resolution and Inference of Quasi-Geostrophic Turbulence](https://mlsanity.com/paper/2507.00719/) (2025)
- [Content-Style Identification via Differential Independence](https://mlsanity.com/paper/2605.17827/) (2026)
- [Short-Time Fourier Transform for deblurring Variational Autoencoders](https://mlsanity.com/paper/2401.03166/) (2024)
- [Motion Free B-frame Coding for Neural Video Compression](https://mlsanity.com/paper/2411.17160/) (2024)
- [A new pathway to generative artificial intelligence by minimizing the maximum entropy](https://mlsanity.com/paper/2502.13287/) (2025)
- [Diffusion-Based Authentication of Copy Detection Patterns: A Multimodal Framework with Printer Signature Conditioning](https://mlsanity.com/paper/2603.08998/) (2026)
- [Cross Modality Image Translation In Medical Imaging Using Generative Frameworks](https://mlsanity.com/paper/2605.13686/) (2026)
- [Structured Generations: Using Hierarchical Clusters to guide Diffusion Models](https://mlsanity.com/paper/2407.06124/) (2024)
- [3D Nephrographic Image Synthesis in CT Urography with the Diffusion Model and Swin Transformer](https://mlsanity.com/paper/2502.19623/) (2025)
- [Likelihood-Free Variational Autoencoders](https://mlsanity.com/paper/2504.17622/) (2025)
- [Learning Extrapolative Sequence Transformations from Markov Chains](https://mlsanity.com/paper/2505.20251/) (2025)
- [Generative Latent Kernel Modeling for Blind Motion Deblurring](https://mlsanity.com/paper/2507.09285/) (2025)
- [Structure-Preserving Unpaired Image Translation to Photometrically Calibrate JunoCam with Hubble Data](https://mlsanity.com/paper/2511.22668/) (2025)
- [mViSE: A Visual Search Engine for Analyzing Multiplex IHC Brain Tissue Images](https://mlsanity.com/paper/2512.11745/) (2025)
- [Unified Control for Inference-Time Guidance of Denoising Diffusion Models](https://mlsanity.com/paper/2512.12339/) (2025)
- [Deep Neural Networks as Iterated Function Systems and a Generalization Bound](https://mlsanity.com/paper/2601.19958/) (2026)
- [Rare-Aware Autoencoding: Reconstructing Spatially Imbalanced Data](https://mlsanity.com/paper/2604.02031/) (2026)
- [Conditional Flow Matching for Generation of 3D Multi-variable Instantaneous Urban Microclimate Fields](https://mlsanity.com/paper/2610.10430/) (2026)

## Abstract (arXiv)

Variational autoencoders (VAEs) are powerful generative modelling methods, however they suffer from blurry generated samples and reconstructions compared to the images they have been trained on. Significant research effort has been spent to increase the generative capabilities by creating more flexible models but often flexibility comes at the cost of higher complexity and computational cost. Several works have focused on altering the reconstruction term of the evidence lower bound (ELBO), however, often at the expense of losing the mathematical link to maximizing the likelihood of the samples under the modeled distribution. Here we propose a new formulation of the reconstruction term for the VAE that specifically penalizes the generation of blurry images while at the same time still maximizing the ELBO under the modeled distribution. We show the potential of the proposed loss on three different data sets, where it outperforms several recently proposed reconstruction losses for VAEs.