# KAN We Flow? Advancing Robotic Manipulation with 3D Flow Matching via KAN & RWKV

arXiv: https://arxiv.org/abs/2602.01115 · HTML: https://mlsanity.com/paper/2602.01115/

## 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 35 of its 41 references that are in the map.
- First posted on arXiv 1 Feb 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, 30 of 35)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Meta-World: A Benchmark and Evaluation for Multi-Task and Meta Reinforcement Learning](https://mlsanity.com/paper/1910.10897/) (2019)
- [What Matters in Learning from Offline Human Demonstrations for Robot Manipulation](https://mlsanity.com/paper/2108.03298/) (2021)
- [Learning Complex Dexterous Manipulation with Deep Reinforcement Learning and Demonstrations](https://mlsanity.com/paper/1709.10087/) (2017)
- [Implicit Behavioral Cloning](https://mlsanity.com/paper/2109.00137/) (2021)
- [U-KAN Makes Strong Backbone for Medical Image Segmentation and Generation](https://mlsanity.com/paper/2406.02918/) (2024)
- [FlowPolicy: Enabling Fast and Robust 3D Flow-based Policy via Consistency Flow Matching for Robot Manipulation](https://mlsanity.com/paper/2412.04987/) (2024)
- [Vision-RWKV: Efficient and Scalable Visual Perception with RWKV-Like Architectures](https://mlsanity.com/paper/2403.02308/) (2024)
- [Hierarchical Diffusion Policy for Kinematics-Aware Multi-Task Robotic Manipulation](https://mlsanity.com/paper/2403.03890/) (2024)
- [Controllable Generation with Text-to-Image Diffusion Models: A Survey](https://mlsanity.com/paper/2403.04279/) (2024)
- [Teach a Robot to FISH: Versatile Imitation from One Minute of Demonstrations](https://mlsanity.com/paper/2303.01497/) (2023)
- [The Ingredients for Robotic Diffusion Transformers](https://mlsanity.com/paper/2410.10088/) (2024)
- [A Survey on Kolmogorov-Arnold Network](https://mlsanity.com/paper/2411.06078/) (2024)
- [DexArt: Benchmarking Generalizable Dexterous Manipulation with Articulated Objects](https://mlsanity.com/paper/2305.05706/) (2023)
- [ManiCM: Real-time 3D Diffusion Policy via Consistency Model for Robotic Manipulation](https://mlsanity.com/paper/2406.01586/) (2024)
- [AdaFlow: Imitation Learning with Variance-Adaptive Flow-Based Policies](https://mlsanity.com/paper/2402.04292/) (2024)
- [Diffusion-RWKV: Scaling RWKV-Like Architectures for Diffusion Models](https://mlsanity.com/paper/2404.04478/) (2024)
- [RISE: 3D Perception Makes Real-World Robot Imitation Simple and Effective](https://mlsanity.com/paper/2404.12281/) (2024)
- [Diffusion Transformer Policy](https://mlsanity.com/paper/2410.15959/) (2024)
- [Dexterous Functional Grasping](https://mlsanity.com/paper/2312.02975/) (2023)
- [3DFlowAction: Learning Cross-Embodiment Manipulation from 3D Flow World Model](https://mlsanity.com/paper/2506.06199/) (2025)
- [rKAN: Rational Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.14495/) (2024)
- [MP1: MeanFlow Tames Policy Learning in 1-step for Robotic Manipulation](https://mlsanity.com/paper/2507.10543/) (2025)
- [FP3: A 3D Foundation Policy for Robotic Manipulation](https://mlsanity.com/paper/2503.08950/) (2025)
- [Embodied AI: From LLMs to World Models](https://mlsanity.com/paper/2509.20021/) (2025)
- [Mamba Policy: Towards Efficient 3D Diffusion Policy with Hybrid Selective State Models](https://mlsanity.com/paper/2409.07163/) (2024)
- [3D FlowMatch Actor: Unified 3D Policy for Single- and Dual-Arm Manipulation](https://mlsanity.com/paper/2508.11002/) (2025)
- [DiffAIL: Diffusion Adversarial Imitation Learning](https://mlsanity.com/paper/2312.06348/) (2023)

## Abstract (arXiv)

Diffusion-based visuomotor policies excel at modeling action distributions but are inference-inefficient, since recursively denoising from noise to policy requires many steps and heavy UNet backbones, which hinders deployment on resource-constrained robots. Flow matching alleviates the sampling burden by learning a one-step vector field, yet prior implementations still inherit large UNet-style architectures. In this work, we present KAN-We-Flow, a flow-matching policy that draws on recent advances in Receptance Weighted Key Value (RWKV) and Kolmogorov-Arnold Networks (KAN) from vision to build a lightweight and highly expressive backbone for 3D manipulation. Concretely, we introduce an RWKV-KAN block: an RWKV first performs efficient time/channel mixing to propagate task context, and a subsequent GroupKAN layer applies learnable spline-based, groupwise functional mappings to perform feature-wise nonlinear calibration of the action mapping on RWKV outputs. Moreover, we introduce an Action Consistency Regularization (ACR), a lightweight auxiliary loss that enforces alignment between predicted action trajectories and expert demonstrations via Euler extrapolation, providing additional supervision to stabilize training and improve policy precision. Without resorting to large UNets, our design reduces parameters by 86.8%, maintains fast runtime, and achieves state-of-the-art success rates on Adroit, Meta-World, and DexArt benchmarks. Our project page can be viewed in hrefhttps://zhihaochen-2003.github.io/KAN-We-Flow.github.io/textcolorredlink