# A Flow Matching Framework for Soft-Robot Inverse Dynamics

arXiv: https://arxiv.org/abs/2604.03006 · HTML: https://mlsanity.com/paper/2604.03006/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models.
- Builds on 7 of its 31 references that are in the map.
- First posted on arXiv 3 Apr 2026.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)

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

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Data-driven Methods Applied to Soft Robot Modeling and Control: A Review](https://mlsanity.com/paper/2305.12137/) (2023)
- [Efficient Jacobian-Based Inverse Kinematics with Sim-to-Real Transfer of Soft Robots by Learning](https://mlsanity.com/paper/2012.13965/) (2020)
- [Adaptive Model-Predictive Control of a Soft Continuum Robot Using a Physics-Informed Neural Network Based on Cosserat Rod Theory](https://mlsanity.com/paper/2508.12681/) (2025)
- [Lightweight Dynamic Modeling of Cable-Driven Continuum Robots Based on Actuation-Space Energy Formulation](https://mlsanity.com/paper/2512.13271/) (2025)

## Built on by (most cited first, 1 of 1)

- [Whole-Body Semantic-to-Actuation Grounding of Elephant-Inspired Soft-Trunk Motion via Lightweight Flow Matching](https://mlsanity.com/paper/2607.11018/) (2026)

## Abstract (arXiv)

Learning the inverse dynamics of soft continuum robots remains challenging due to high-dimensional nonlinearities and complex actuation coupling. Conventional feedback-based controllers often suffer from control chattering due to corrective oscillations, while deterministic regression-based learners struggle to capture the complex nonlinear mappings required for accurate dynamic tracking. Motivated by these limitations, we propose an inverse-dynamics framework for open-loop feedforward control that learns the system's differential dynamics as a generative transport map. Specifically, inverse dynamics is reformulated as a conditional flow-matching problem, and Rectified Flow (RF) is adopted as a lightweight instance to generate physically consistent control inputs rather than conditional averages. Two variants are introduced to further enhance physical consistency: RF-Physical, utilizing a physics-based prior for residual modeling; and RF-FWD, integrating a forward-dynamics consistency loss during flow matching. Extensive evaluations demonstrate that our framework reduces trajectory tracking RMSE by over 50% compared to standard regression baselines (MLP, LSTM, Transformer). The system sustains stable open-loop execution at a peak end-effector velocity of 1.14 m/s with sub-millisecond inference latency (0.995 ms). This work demonstrates flow matching as a robust, high-performance paradigm for learning differential inverse dynamics in soft robotic systems.