# A Coupled Flow Approach to Imitation Learning

arXiv: https://arxiv.org/abs/2305.00303 · HTML: https://mlsanity.com/paper/2305.00303/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for offline RL, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 44 of its 57 references that are in the map.
- First posted on arXiv 29 Apr 2023.

## Placed in

- Offline RL and imitation learning from data / [Diffusion and flow policies for offline RL](https://mlsanity.com/offlinerl/diffusion-and-flow-policies-for-offline-rl/)

## Builds on (most cited first, 30 of 44)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Generative Adversarial Imitation Learning](https://mlsanity.com/paper/1606.03476/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Off-Policy Deep Reinforcement Learning without Exploration](https://mlsanity.com/paper/1812.02900/) (2018)
- [Curiosity-driven Exploration by Self-supervised Prediction](https://mlsanity.com/paper/1705.05363/) (2017)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Learning Robust Rewards with Adversarial Inverse Reinforcement Learning](https://mlsanity.com/paper/1710.11248/) (2017)
- [MADE: Masked Autoencoder for Distribution Estimation](https://mlsanity.com/paper/1502.03509/) (2015)
- [Flow++: Improving Flow-Based Generative Models with Variational Dequantization and Architecture Design](https://mlsanity.com/paper/1902.00275/) (2019)
- [DualDICE: Behavior-Agnostic Estimation of Discounted Stationary Distribution Corrections](https://mlsanity.com/paper/1906.04733/) (2019)
- [Provably Efficient Maximum Entropy Exploration](https://mlsanity.com/paper/1812.02690/) (2018)
- [Breaking the Curse of Horizon: Infinite-Horizon Off-Policy Estimation](https://mlsanity.com/paper/1810.12429/) (2018)
- [Why Normalizing Flows Fail to Detect Out-of-Distribution Data](https://mlsanity.com/paper/2006.08545/) (2020)
- [Neural Autoregressive Flows](https://mlsanity.com/paper/1804.00779/) (2018)
- [Discriminator-Actor-Critic: Addressing Sample Inefficiency and Reward Bias in Adversarial Imitation Learning](https://mlsanity.com/paper/1809.02925/) (2018)
- [A Divergence Minimization Perspective on Imitation Learning Methods](https://mlsanity.com/paper/1911.02256/) (2019)
- [Efficient Exploration via State Marginal Matching](https://mlsanity.com/paper/1906.05274/) (2019)
- [Generative Adversarial Imitation from Observation](https://mlsanity.com/paper/1807.06158/) (2018)
- [Imitation Learning via Off-Policy Distribution Matching](https://mlsanity.com/paper/1912.05032/) (2019)
- [Imitation Learning as f-Divergence Minimization](https://mlsanity.com/paper/1905.12888/) (2019)
- [Primal Wasserstein Imitation Learning](https://mlsanity.com/paper/2006.04678/) (2020)
- [Variational Policy Gradient Method for Reinforcement Learning with General Utilities](https://mlsanity.com/paper/2007.02151/) (2020)

## Built on by (most cited first, 12 of 12)

- [AdaFlow: Imitation Learning with Variance-Adaptive Flow-Based Policies](https://mlsanity.com/paper/2402.04292/) (2024)
- [Deep Generative Models for Offline Policy Learning: Tutorial, Survey, and Perspectives on Future Directions](https://mlsanity.com/paper/2402.13777/) (2024)
- [Diffusion-Reward Adversarial Imitation Learning](https://mlsanity.com/paper/2405.16194/) (2024)
- [DiffAIL: Diffusion Adversarial Imitation Learning](https://mlsanity.com/paper/2312.06348/) (2023)
- [SEABO: A Simple Search-Based Method for Offline Imitation Learning](https://mlsanity.com/paper/2402.03807/) (2024)
- [Reward-free World Models for Online Imitation Learning](https://mlsanity.com/paper/2410.14081/) (2024)
- [A Simple Solution for Offline Imitation from Observations and Examples with Possibly Incomplete Trajectories](https://mlsanity.com/paper/2311.01329/) (2023)
- [Expert Proximity as Surrogate Rewards for Single Demonstration Imitation Learning](https://mlsanity.com/paper/2402.01057/) (2024)
- [Action-Constrained Imitation Learning](https://mlsanity.com/paper/2508.14379/) (2025)
- [Rethinking Adversarial Inverse Reinforcement Learning: Policy Imitation, Transferable Reward Recovery and Algebraic Equilibrium Proof](https://mlsanity.com/paper/2403.14593/) (2024)
- [Coupled Distributional Random Expert Distillation for World Model Online Imitation Learning](https://mlsanity.com/paper/2505.02228/) (2025)
- [SD2AIL: Adversarial Imitation Learning from Synthetic Demonstrations via Diffusion Models](https://mlsanity.com/paper/2512.18583/) (2025)

## Abstract (arXiv)

In reinforcement learning and imitation learning, an object of central importance is the state distribution induced by the policy. It plays a crucial role in the policy gradient theorem, and references to it--along with the related state-action distribution--can be found all across the literature. Despite its importance, the state distribution is mostly discussed indirectly and theoretically, rather than being modeled explicitly. The reason being an absence of appropriate density estimation tools. In this work, we investigate applications of a normalizing flow-based model for the aforementioned distributions. In particular, we use a pair of flows coupled through the optimality point of the Donsker-Varadhan representation of the Kullback-Leibler (KL) divergence, for distribution matching based imitation learning. Our algorithm, Coupled Flow Imitation Learning (CFIL), achieves state-of-the-art performance on benchmark tasks with a single expert trajectory and extends naturally to a variety of other settings, including the subsampled and state-only regimes.