# NVAE: A Deep Hierarchical Variational Autoencoder

arXiv: https://arxiv.org/abs/2007.03898 · HTML: https://mlsanity.com/paper/2007.03898/

## Key facts

- Cited by 637 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jul 2020.

## Built on by (most cited first, 30 of 637)

- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [Mastering Diverse Domains through World Models](https://mlsanity.com/paper/2301.04104/) (2023)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [MaskGIT: Masked Generative Image Transformer](https://mlsanity.com/paper/2202.04200/) (2022)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [VideoGPT: Video Generation using VQ-VAE and Transformers](https://mlsanity.com/paper/2104.10157/) (2021)
- [Vector-quantized Image Modeling with Improved VQGAN](https://mlsanity.com/paper/2110.04627/) (2021)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [ILVR: Conditioning Method for Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2108.02938/) (2021)
- [NExT-GPT: Any-to-Any Multimodal LLM](https://mlsanity.com/paper/2309.05519/) (2023)
- [LION: Latent Point Diffusion Models for 3D Shape Generation](https://mlsanity.com/paper/2210.06978/) (2022)
- [Tackling the Generative Learning Trilemma with Denoising Diffusion GANs](https://mlsanity.com/paper/2112.07804/) (2021)
- [Make-A-Scene: Scene-Based Text-to-Image Generation with Human Priors](https://mlsanity.com/paper/2203.13131/) (2022)
- [Diffusion Models for Adversarial Purification](https://mlsanity.com/paper/2205.07460/) (2022)
- [Diffusion Autoencoders: Toward a Meaningful and Decodable Representation](https://mlsanity.com/paper/2111.15640/) (2021)
- [Improved Techniques for Training Consistency Models](https://mlsanity.com/paper/2310.14189/) (2023)
- [PhysDiff: Physics-Guided Human Motion Diffusion Model](https://mlsanity.com/paper/2212.02500/) (2022)
- [Knowledge Distillation in Iterative Generative Models for Improved Sampling Speed](https://mlsanity.com/paper/2101.02388/) (2021)
- [Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.06503/) (2022)
- [Rodin: A Generative Model for Sculpting 3D Digital Avatars Using Diffusion](https://mlsanity.com/paper/2212.06135/) (2022)
- [Perception Prioritized Training of Diffusion Models](https://mlsanity.com/paper/2204.00227/) (2022)
- [Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Models](https://mlsanity.com/paper/2103.04922/) (2021)
- [Score-Based Generative Modeling with Critically-Damped Langevin Diffusion](https://mlsanity.com/paper/2112.07068/) (2021)

## Abstract (arXiv)

Normalizing flows, autoregressive models, variational autoencoders (VAEs), and deep energy-based models are among competing likelihood-based frameworks for deep generative learning. Among them, VAEs have the advantage of fast and tractable sampling and easy-to-access encoding networks. However, they are currently outperformed by other models such as normalizing flows and autoregressive models. While the majority of the research in VAEs is focused on the statistical challenges, we explore the orthogonal direction of carefully designing neural architectures for hierarchical VAEs. We propose Nouveau VAE (NVAE), a deep hierarchical VAE built for image generation using depth-wise separable convolutions and batch normalization. NVAE is equipped with a residual parameterization of Normal distributions and its training is stabilized by spectral regularization. We show that NVAE achieves state-of-the-art results among non-autoregressive likelihood-based models on the MNIST, CIFAR-10, CelebA 64, and CelebA HQ datasets and it provides a strong baseline on FFHQ. For example, on CIFAR-10, NVAE pushes the state-of-the-art from 2.98 to 2.91 bits per dimension, and it produces high-quality images on CelebA HQ. To the best of our knowledge, NVAE is the first successful VAE applied to natural images as large as 256×256 pixels. The source code is available at https://github.com/NVlabs/NVAE .