# VFP: Variational Flow-Matching Policy for Multi-Modal Robot Manipulation

arXiv: https://arxiv.org/abs/2508.01622 · HTML: https://mlsanity.com/paper/2508.01622/

## Key facts

- Cited by 9 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 28 of its 33 references that are in the map.
- First posted on arXiv 3 Aug 2025.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)
- Mixture-of-experts / [MoE in reinforcement learning and robotics](https://mlsanity.com/moe/moe-in-reinforcement-learning-and-robotics/)

## Builds on (most cited first, 28 of 28)

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [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)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Meta-World: A Benchmark and Evaluation for Multi-Task and Meta Reinforcement Learning](https://mlsanity.com/paper/1910.10897/) (2019)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Learning Complex Dexterous Manipulation with Deep Reinforcement Learning and Demonstrations](https://mlsanity.com/paper/1709.10087/) (2017)
- [Perceiver-Actor: A Multi-Task Transformer for Robotic Manipulation](https://mlsanity.com/paper/2209.05451/) (2022)
- [Relay Policy Learning: Solving Long-Horizon Tasks via Imitation and Reinforcement Learning](https://mlsanity.com/paper/1910.11956/) (2019)
- [MimicPlay: Long-Horizon Imitation Learning by Watching Human Play](https://mlsanity.com/paper/2302.12422/) (2023)
- [DexPilot: Vision Based Teleoperation of Dexterous Robotic Hand-Arm System](https://mlsanity.com/paper/1910.03135/) (2019)
- [Consistency Flow Matching: Defining Straight Flows with Velocity Consistency](https://mlsanity.com/paper/2407.02398/) (2024)
- [FlowPolicy: Enabling Fast and Robust 3D Flow-based Policy via Consistency Flow Matching for Robot Manipulation](https://mlsanity.com/paper/2412.04987/) (2024)
- [One-Step Diffusion Policy: Fast Visuomotor Policies via Diffusion Distillation](https://mlsanity.com/paper/2410.21257/) (2024)
- [Augmented Normalizing Flows: Bridging the Gap Between Generative Flows and Latent Variable Models](https://mlsanity.com/paper/2002.07101/) (2020)
- [Multi-Modal Imitation Learning from Unstructured Demonstrations using Generative Adversarial Nets](https://mlsanity.com/paper/1705.10479/) (2017)
- [Riemannian Flow Matching Policy for Robot Motion Learning](https://mlsanity.com/paper/2403.10672/) (2024)
- [ManiCM: Real-time 3D Diffusion Policy via Consistency Model for Robotic Manipulation](https://mlsanity.com/paper/2406.01586/) (2024)
- [Sparse Diffusion Policy: A Sparse, Reusable, and Flexible Policy for Robot Learning](https://mlsanity.com/paper/2407.01531/) (2024)
- [Affordance-based Robot Manipulation with Flow Matching](https://mlsanity.com/paper/2409.01083/) (2024)
- [Towards Diverse Behaviors: A Benchmark for Imitation Learning with Human Demonstrations](https://mlsanity.com/paper/2402.14606/) (2024)
- [Variational Rectified Flow Matching](https://mlsanity.com/paper/2502.09616/) (2025)
- [Flow Matching Imitation Learning for Multi-Support Manipulation](https://mlsanity.com/paper/2407.12381/) (2024)
- [Gaussian Mixture Flow Matching Models](https://mlsanity.com/paper/2504.05304/) (2025)
- [Efficient Flow Matching using Latent Variables](https://mlsanity.com/paper/2505.04486/) (2025)

## Built on by (most cited first, 9 of 9)

- [IntentVLA: Short-Horizon Intent Modeling for Aliased Robot Manipulation](https://mlsanity.com/paper/2605.14712/) (2026)
- [Flow Matching for Tabular Data Synthesis](https://mlsanity.com/paper/2512.00698/) (2025)
- [Action Hallucination in Generative Vision-Language-Action Models](https://mlsanity.com/paper/2602.06339/) (2026)
- [Ada3Drift: Adaptive Training-Time Drifting for One-Step 3D Visuomotor Robotic Manipulation](https://mlsanity.com/paper/2603.11984/) (2026)
- [DreamFlow: Local Navigation Beyond Observation via Conditional Flow Matching in the Latent Space](https://mlsanity.com/paper/2603.02976/) (2026)
- [CoFreeVLA: Short-Horizon Collision-Free Dual-Arm Manipulation via Vision-Language-Action Model and Risk Estimation](https://mlsanity.com/paper/2601.21712/) (2026)
- [Source-Lifted Flow Matching for Intervenable Multimodal Imitation](https://mlsanity.com/paper/2607.10206/) (2026)
- [PAVE: Predictive Alignment and Value-Guided Evolution for World-Action Policies](https://mlsanity.com/paper/2608.30378/) (2026)
- [Online Evolution Strategy for Flow-Matching VLA Policies via Self-Supervised Trajectory Distribution Optimization](https://mlsanity.com/paper/2609.38855/) (2026)

## Abstract (arXiv)

Flow-matching-based policies have recently emerged as a promising approach for learning-based robot manipulation, offering significant acceleration in action sampling compared to diffusion-based policies. However, conventional flow-matching methods struggle with multi-modality, often collapsing to averaged or ambiguous behaviors in complex manipulation tasks. To address this, we propose the Variational Flow-Matching Policy (VFP), which introduces a variational latent prior for mode-aware action generation and effectively captures both task-level and trajectory-level multi-modality. VFP further incorporates Kantorovich Optimal Transport (K-OT) for distribution-level alignment and utilizes a Mixture-of-Experts (MoE) decoder for mode specialization and efficient inference. We comprehensively evaluate VFP on 41 simulated tasks and 3 real-robot tasks, demonstrating its effectiveness and sampling efficiency in both simulated and real-world settings. Results show that VFP achieves a 49% relative improvement in task success rate over standard flow-based baselines in simulation, and further outperforms them on real-robot tasks, while still maintaining fast inference and a compact model size. More details are available on our project page: https://sites.google.com/view/varfp/