# AdvNF: Reducing Mode Collapse in Conditional Normalising Flows using Adversarial Learning

arXiv: https://arxiv.org/abs/2401.15948 · HTML: https://mlsanity.com/paper/2401.15948/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 62 references that are in the map.
- First posted on arXiv 29 Jan 2024.

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

- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [NIPS 2016 Tutorial: Generative Adversarial Networks](https://mlsanity.com/paper/1701.00160/) (2016)
- [A Review on Generative Adversarial Networks: Algorithms, Theory, and Applications](https://mlsanity.com/paper/2001.06937/) (2020)
- [VEEGAN: Reducing Mode Collapse in GANs using Implicit Variational Learning](https://mlsanity.com/paper/1705.07761/) (2017)
- [Learning Likelihoods with Conditional Normalizing Flows](https://mlsanity.com/paper/1912.00042/) (2019)
- [Stochastic Normalizing Flows](https://mlsanity.com/paper/2002.06707/) (2020)
- [Flow-based generative models for Markov chain Monte Carlo in lattice field theory](https://mlsanity.com/paper/1904.12072/) (2019)
- [Mode Seeking Generative Adversarial Networks for Diverse Image Synthesis](https://mlsanity.com/paper/1903.05628/) (2019)
- [Mode Regularized Generative Adversarial Networks](https://mlsanity.com/paper/1612.02136/) (2016)
- [Equivariant flow-based sampling for lattice gauge theory](https://mlsanity.com/paper/2003.06413/) (2020)
- [A Generative Model For Zero Shot Learning Using Conditional Variational Autoencoders](https://mlsanity.com/paper/1709.00663/) (2017)
- [Unsupervised learning of phase transitions: from principal component analysis to variational autoencoders](https://mlsanity.com/paper/1703.02435/) (2017)
- [Resampling Base Distributions of Normalizing Flows](https://mlsanity.com/paper/2110.15828/) (2021)
- [Greedification Operators for Policy Optimization: Investigating Forward and Reverse KL Divergences](https://mlsanity.com/paper/2107.08285/) (2021)
- [Normalizing flows for atomic solids](https://mlsanity.com/paper/2111.08696/) (2021)
- [Deep Generative Stochastic Networks Trainable by Backprop](https://mlsanity.com/paper/1306.1091/) (2013)
- [Evaluating generative models in high energy physics](https://mlsanity.com/paper/2211.10295/) (2022)
- [Flow-based sampling for fermionic lattice field theories](https://mlsanity.com/paper/2106.05934/) (2021)
- [Flow-based sampling for multimodal and extended-mode distributions in lattice field theory](https://mlsanity.com/paper/2107.00734/) (2021)
- [MGGAN: Solving Mode Collapse using Manifold Guided Training](https://mlsanity.com/paper/1804.04391/) (2018)
- [Flow-based sampling in the lattice Schwinger model at criticality](https://mlsanity.com/paper/2202.11712/) (2022)
- [Physics-informed deep generative models](https://mlsanity.com/paper/1812.03511/) (2018)
- [Machine Learning of Thermodynamic Observables in the Presence of Mode Collapse](https://mlsanity.com/paper/2111.11303/) (2021)
- [Self-Supervised Learning of Generative Spin-Glasses with Normalizing Flows](https://mlsanity.com/paper/2001.00585/) (2020)
- [Towards meaningful physics from generative models](https://mlsanity.com/paper/1705.09524/) (2017)

## Built on by (most cited first, 6 of 6)

- [Physics-Conditioned Diffusion Models for Lattice Gauge Theory](https://mlsanity.com/paper/2502.05504/) (2025)
- [SCORENF: Score-based Normalizing Flows for Sampling Unnormalized distributions](https://mlsanity.com/paper/2510.21330/) (2025)
- [MAGIC-Flow: Multiscale Adaptive Conditional Flows for Generation and Interpretable Classification](https://mlsanity.com/paper/2510.22070/) (2025)
- [Accurate Sampling from Diffusion Models](https://mlsanity.com/paper/2609.29902/) (2026)
- [SIMANF: Sample Free Learning of Unnormalized Distributions via Simulated Annealing in Normalizing Flows](https://mlsanity.com/paper/2609.32279/) (2026)
- [FUND: Density Flow for Sampling Unnormalised Distributions](https://mlsanity.com/paper/2609.32296/) (2026)

## Abstract (arXiv)

Deep generative models complement Markov-chain-Monte-Carlo methods for efficiently sampling from high-dimensional distributions. Among these methods, explicit generators, such as Normalising Flows (NFs), in combination with the Metropolis Hastings algorithm have been extensively applied to get unbiased samples from target distributions. We systematically study central problems in conditional NFs, such as high variance, mode collapse and data efficiency. We propose adversarial training for NFs to ameliorate these problems. Experiments are conducted with low-dimensional synthetic datasets and XY spin models in two spatial dimensions.