# Bridging Maximum Likelihood and Adversarial Learning via α-Divergence

arXiv: https://arxiv.org/abs/2007.06178 · HTML: https://mlsanity.com/paper/2007.06178/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jul 2020.

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

- [f-Divergence Minimization for Sequence-Level Knowledge Distillation](https://mlsanity.com/paper/2307.15190/) (2023)
- [Using Probabilistic Machine Learning to Better Model Temporal Patterns in Parameterizations: a case study with the Lorenz 96 model](https://mlsanity.com/paper/2203.14814/) (2022)
- [CoopInit: Initializing Generative Adversarial Networks via Cooperative Learning](https://mlsanity.com/paper/2303.11649/) (2023)
- [A Statistician Teaches Deep Learning](https://mlsanity.com/paper/2102.01194/) (2021)
- [Unified Perspective on Probability Divergence via Maximum Likelihood Density Ratio Estimation: Bridging KL-Divergence and Integral Probability Metrics](https://mlsanity.com/paper/2201.13127/) (2022)
- [Adaptive Symmetrization of the KL Divergence](https://mlsanity.com/paper/2511.11159/) (2025)

## Abstract (arXiv)

Maximum likelihood (ML) and adversarial learning are two popular approaches for training generative models, and from many perspectives these techniques are complementary. ML learning encourages the capture of all data modes, and it is typically characterized by stable training. However, ML learning tends to distribute probability mass diffusely over the data space, e.g., yielding blurry synthetic images. Adversarial learning is well known to synthesize highly realistic natural images, despite practical challenges like mode dropping and delicate training. We propose an α-Bridge to unify the advantages of ML and adversarial learning, enabling the smooth transfer from one to the other via the α-divergence. We reveal that generalizations of the α-Bridge are closely related to approaches developed recently to regularize adversarial learning, providing insights into that prior work, and further understanding of why the α-Bridge performs well in practice.