# Diffusion Priors In Variational Autoencoders

arXiv: https://arxiv.org/abs/2106.15671 · HTML: https://mlsanity.com/paper/2106.15671/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 20 of its 23 references that are in the map.
- First posted on arXiv 29 Jun 2021.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 20 of 20)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Conditional Image Generation with PixelCNN Decoders](https://mlsanity.com/paper/1606.05328/) (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)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [Adversarial Autoencoders](https://mlsanity.com/paper/1511.05644/) (2015)
- [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)
- [Video Compression With Rate-Distortion Autoencoders](https://mlsanity.com/paper/1908.05717/) (2019)

## Built on by (most cited first, 25 of 25)

- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Diffusion Autoencoders: Toward a Meaningful and Decodable Representation](https://mlsanity.com/paper/2111.15640/) (2021)
- [From data to functa: Your data point is a function and you can treat it like one](https://mlsanity.com/paper/2201.12204/) (2022)
- [Single-Stage Diffusion NeRF: A Unified Approach to 3D Generation and Reconstruction](https://mlsanity.com/paper/2304.06714/) (2023)
- [Latent Diffusion Energy-Based Model for Interpretable Text Modeling](https://mlsanity.com/paper/2206.05895/) (2022)
- [DINOISER: Diffused Conditional Sequence Learning by Manipulating Noises](https://mlsanity.com/paper/2302.10025/) (2023)
- [Global Context with Discrete Diffusion in Vector Quantised Modelling for Image Generation](https://mlsanity.com/paper/2112.01799/) (2021)
- [On Analyzing Generative and Denoising Capabilities of Diffusion-based Deep Generative Models](https://mlsanity.com/paper/2206.00070/) (2022)
- [NVDiff: Graph Generation through the Diffusion of Node Vectors](https://mlsanity.com/paper/2211.10794/) (2022)
- [Deep Generative Models for Detector Signature Simulation: A Taxonomic Review](https://mlsanity.com/paper/2312.09597/) (2023)
- [Error bounds for particle gradient descent, and extensions of the log-Sobolev and Talagrand inequalities](https://mlsanity.com/paper/2403.02004/) (2024)
- [Making Reconstruction FID Predictive of Diffusion Generation FID](https://mlsanity.com/paper/2603.05630/) (2026)
- [Unified Generation, Reconstruction, and Representation: Generalized Diffusion with Adaptive Latent Encoding-Decoding](https://mlsanity.com/paper/2402.19009/) (2024)
- [Diffusion Models with Deterministic Normalizing Flow Priors](https://mlsanity.com/paper/2309.01274/) (2023)
- [Training Latent Diffusion Models with Interacting Particle Algorithms](https://mlsanity.com/paper/2505.12412/) (2025)
- [Text Diffusion with Reinforced Conditioning](https://mlsanity.com/paper/2402.14843/) (2024)
- [Denoising Diffusion Variational Inference: Diffusion Models as Expressive Variational Posteriors](https://mlsanity.com/paper/2401.02739/) (2024)
- [VAE-QWGAN: Addressing Mode Collapse in Quantum GANs via Autoencoding Priors](https://mlsanity.com/paper/2409.10339/) (2024)
- [Discouraging posterior collapse in hierarchical Variational Autoencoders using context](https://mlsanity.com/paper/2302.09976/) (2023)
- [Diffusion Autoencoders with Perceivers for Long, Irregular and Multimodal Astronomical Sequences](https://mlsanity.com/paper/2510.20595/) (2025)
- [VaeDiff-DocRE: End-to-end Data Augmentation Framework for Document-level Relation Extraction](https://mlsanity.com/paper/2412.13503/) (2024)
- [Disentangled representations via score-based variational autoencoders](https://mlsanity.com/paper/2512.17127/) (2025)
- [VAMP-Diff: VampPrior Latent Diffusion for Photoplethysmography Modeling](https://mlsanity.com/paper/2605.22851/) (2026)
- [BattVAE-GP: Generative Modeling of Long-Horizon Battery Degradation with Uncertainty Quantification](https://mlsanity.com/paper/2607.11943/) (2026)

## Abstract (arXiv)

Among likelihood-based approaches for deep generative modelling, variational autoencoders (VAEs) offer scalable amortized posterior inference and fast sampling. However, VAEs are also more and more outperformed by competing models such as normalizing flows (NFs), deep-energy models, or the new denoising diffusion probabilistic models (DDPMs). In this preliminary work, we improve VAEs by demonstrating how DDPMs can be used for modelling the prior distribution of the latent variables. The diffusion prior model improves upon Gaussian priors of classical VAEs and is competitive with NF-based priors. Finally, we hypothesize that hierarchical VAEs could similarly benefit from the enhanced capacity of diffusion priors.