# Augmented Normalizing Flows: Bridging the Gap Between Generative Flows and Latent Variable Models

arXiv: https://arxiv.org/abs/2002.07101 · HTML: https://mlsanity.com/paper/2002.07101/

## Key facts

- Cited by 66 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Feb 2020.

## Built on by (most cited first, 30 of 66)

- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [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)
- [Likelihood Training of Schr"odinger Bridge using Forward-Backward SDEs Theory](https://mlsanity.com/paper/2110.11291/) (2021)
- [Two for One: Diffusion Models and Force Fields for Coarse-Grained Molecular Dynamics](https://mlsanity.com/paper/2302.00600/) (2023)
- [Timewarp: Transferable Acceleration of Molecular Dynamics by Learning Time-Coarsened Dynamics](https://mlsanity.com/paper/2302.01170/) (2023)
- [Densely connected normalizing flows](https://mlsanity.com/paper/2106.04627/) (2021)
- [Deep Generative Models through the Lens of the Manifold Hypothesis: A Survey and New Connections](https://mlsanity.com/paper/2404.02954/) (2024)
- [CANF-VC: Conditional Augmented Normalizing Flows for Video Compression](https://mlsanity.com/paper/2207.05315/) (2022)
- [Learning Interpolations between Boltzmann Densities](https://mlsanity.com/paper/2301.07388/) (2023)
- [Resampling Base Distributions of Normalizing Flows](https://mlsanity.com/paper/2110.15828/) (2021)
- [SE(3) Equivariant Augmented Coupling Flows](https://mlsanity.com/paper/2308.10364/) (2023)
- [Flow-matching -- efficient coarse-graining of molecular dynamics without forces](https://mlsanity.com/paper/2203.11167/) (2022)
- [Where to Diffuse, How to Diffuse, and How to Get Back: Automated Learning for Multivariate Diffusions](https://mlsanity.com/paper/2302.07261/) (2023)
- [Implicit Normalizing Flows](https://mlsanity.com/paper/2103.09527/) (2021)
- [A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applications](https://mlsanity.com/paper/2403.00485/) (2024)
- [Rigid Body Flows for Sampling Molecular Crystal Structures](https://mlsanity.com/paper/2301.11355/) (2023)
- [Efficient-VDVAE: Less is more](https://mlsanity.com/paper/2203.13751/) (2022)
- [Free-form Flows: Make Any Architecture a Normalizing Flow](https://mlsanity.com/paper/2310.16624/) (2023)
- [Advances in machine-learning-based sampling motivated by lattice quantum chromodynamics](https://mlsanity.com/paper/2309.01156/) (2023)
- [ANFIC: Image Compression Using Augmented Normalizing Flows](https://mlsanity.com/paper/2107.08470/) (2021)
- [B-CANF: Adaptive B-frame Coding with Conditional Augmented Normalizing Flows](https://mlsanity.com/paper/2209.01769/) (2022)
- [A Review of Change of Variable Formulas for Generative Modeling](https://mlsanity.com/paper/2308.02652/) (2023)
- [Density estimation on low-dimensional manifolds: an inflation-deflation approach](https://mlsanity.com/paper/2105.12152/) (2021)
- [Semi-Discrete Normalizing Flows through Differentiable Tessellation](https://mlsanity.com/paper/2203.06832/) (2022)
- [Spatial Attention Kinetic Networks with E(n)-Equivariance](https://mlsanity.com/paper/2301.08893/) (2023)
- [Scalable Boltzmann Generators for equilibrium sampling of large-scale materials](https://mlsanity.com/paper/2509.25486/) (2025)
- [Latent Space Refinement for Deep Generative Models](https://mlsanity.com/paper/2106.00792/) (2021)
- [Automatic variational inference with cascading flows](https://mlsanity.com/paper/2102.04801/) (2021)
- [Designing losses for data-free training of normalizing flows on Boltzmann distributions](https://mlsanity.com/paper/2301.05475/) (2023)

## Abstract (arXiv)

In this work, we propose a new family of generative flows on an augmented data space, with an aim to improve expressivity without drastically increasing the computational cost of sampling and evaluation of a lower bound on the likelihood. Theoretically, we prove the proposed flow can approximate a Hamiltonian ODE as a universal transport map. Empirically, we demonstrate state-of-the-art performance on standard benchmarks of flow-based generative modeling.