# EBGAN-MDN: An Energy-Based Adversarial Framework for Multi-Modal Behavior Cloning

arXiv: https://arxiv.org/abs/2510.07562 · HTML: https://mlsanity.com/paper/2510.07562/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 13 references that are in the map.
- First posted on arXiv 8 Oct 2025.

## Builds on (most cited first, 7 of 7)

- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Generative Adversarial Imitation Learning](https://mlsanity.com/paper/1606.03476/) (2016)
- [Implicit Behavioral Cloning](https://mlsanity.com/paper/2109.00137/) (2021)
- [Imitation Learning as f-Divergence Minimization](https://mlsanity.com/paper/1905.12888/) (2019)
- [Learning Solution Manifolds for Control Problems via Energy Minimization](https://mlsanity.com/paper/2203.03432/) (2022)

## Abstract (arXiv)

Multi-modal behavior cloning faces significant challenges due to mode averaging and mode collapse, where traditional models fail to capture diverse input-output mappings. This problem is critical in applications like robotics, where modeling multiple valid actions ensures both performance and safety. We propose EBGAN-MDN, a framework that integrates energy-based models, Mixture Density Networks (MDNs), and adversarial training. By leveraging a modified InfoNCE loss and an energy-enforced MDN loss, EBGAN-MDN effectively addresses these challenges. Experiments on synthetic and robotic benchmarks demonstrate superior performance, establishing EBGAN-MDN as a effective and efficient solution for multi-modal learning tasks.