# Liquid Networks with Mixture Density Heads for Efficient Imitation Learning

arXiv: https://arxiv.org/abs/2603.27058 · HTML: https://mlsanity.com/paper/2603.27058/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models.
- Builds on 12 of its 15 references that are in the map.
- First posted on arXiv 28 Mar 2026.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)
- Offline RL and imitation learning from data / [Robot manipulation imitation learning](https://mlsanity.com/offlinerl/robot-manipulation-imitation-learning/)

## Builds on (most cited first, 12 of 12)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [D4RL: Datasets for Deep Data-Driven Reinforcement Learning](https://mlsanity.com/paper/2004.07219/) (2020)
- [Consistency Policy: Accelerated Visuomotor Policies via Consistency Distillation](https://mlsanity.com/paper/2405.07503/) (2024)
- [Liquid Time-constant Networks](https://mlsanity.com/paper/2006.04439/) (2020)
- [One-Step Diffusion Policy: Fast Visuomotor Policies via Diffusion Distillation](https://mlsanity.com/paper/2410.21257/) (2024)
- [Streaming Diffusion Policy: Fast Policy Synthesis with Variable Noise Diffusion Models](https://mlsanity.com/paper/2406.04806/) (2024)
- [Mamba Policy: Towards Efficient 3D Diffusion Policy with Hybrid Selective State Models](https://mlsanity.com/paper/2409.07163/) (2024)
- [On-Device Diffusion Transformer Policy for Efficient Robot Manipulation](https://mlsanity.com/paper/2508.00697/) (2025)
- [Compose Your Policies! Improving Diffusion-based or Flow-based Robot Policies via Test-time Distribution-level Composition](https://mlsanity.com/paper/2510.01068/) (2025)
- [Fast Visuomotor Policy for Robotic Manipulation](https://mlsanity.com/paper/2510.12483/) (2025)

## Abstract (arXiv)

We compare liquid neural networks with mixture density heads against diffusion policies on Push-T, RoboMimic Can, and PointMaze under a shared-backbone comparison protocol that isolates policy-head effects under matched inputs, training budgets, and evaluation settings. Across tasks, liquid policies use roughly half the parameters (4.3M vs. 8.6M), achieve 2.4x lower offline prediction error, and run 1.8 faster at inference. In sample-efficiency experiments spanning 1% to 46.42% of training data, liquid models remain consistently more robust, with especially large gains in low-data and medium-data regimes. Closed-loop results on Push-T and PointMaze are directionally consistent with offline rankings but noisier, indicating that strong offline density modeling helps deployment while not fully determining closed-loop success. Overall, liquid recurrent multimodal policies provide a compact and practical alternative to iterative denoising for imitation learning.