# Source-Lifted Flow Matching for Intervenable Multimodal Imitation

arXiv: https://arxiv.org/abs/2607.10206 · HTML: https://mlsanity.com/paper/2607.10206/

## 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 25 of its 36 references that are in the map.
- First posted on arXiv 11 Jul 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, 25 of 25)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [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)
- [π0: A Vision-Language-Action Flow Model for General Robot Control](https://mlsanity.com/paper/2410.24164/) (2024)
- [π0.5: a Vision-Language-Action Model with Open-World Generalization](https://mlsanity.com/paper/2504.16054/) (2025)
- [D4RL: Datasets for Deep Data-Driven Reinforcement Learning](https://mlsanity.com/paper/2004.07219/) (2020)
- [GR00T N1: An Open Foundation Model for Generalist Humanoid Robots](https://mlsanity.com/paper/2503.14734/) (2025)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Implicit Behavioral Cloning](https://mlsanity.com/paper/2109.00137/) (2021)
- [Behavior Transformers: Cloning k modes with one stone](https://mlsanity.com/paper/2206.11251/) (2022)
- [Diffusion Policy Policy Optimization](https://mlsanity.com/paper/2409.00588/) (2024)
- [Multisample Flow Matching: Straightening Flows with Minibatch Couplings](https://mlsanity.com/paper/2304.14772/) (2023)
- [Imitating Human Behaviour with Diffusion Models](https://mlsanity.com/paper/2301.10677/) (2023)
- [Goal-Conditioned Imitation Learning using Score-based Diffusion Policies](https://mlsanity.com/paper/2304.02532/) (2023)
- [Flow Q-Learning](https://mlsanity.com/paper/2502.02538/) (2025)
- [Steering Your Diffusion Policy with Latent Space Reinforcement Learning](https://mlsanity.com/paper/2506.15799/) (2025)
- [ReinFlow: Fine-tuning Flow Matching Policy with Online Reinforcement Learning](https://mlsanity.com/paper/2505.22094/) (2025)
- [Towards Diverse Behaviors: A Benchmark for Imitation Learning with Human Demonstrations](https://mlsanity.com/paper/2402.14606/) (2024)
- [DynaGuide: Steering Diffusion Polices with Active Dynamic Guidance](https://mlsanity.com/paper/2506.13922/) (2025)
- [Designing a Conditional Prior Distribution for Flow-Based Generative Models](https://mlsanity.com/paper/2502.09611/) (2025)
- [RFS: Reinforcement Learning with Residual Flow Steering for Dexterous Manipulation](https://mlsanity.com/paper/2602.01789/) (2026)
- [VFP: Variational Flow-Matching Policy for Multi-Modal Robot Manipulation](https://mlsanity.com/paper/2508.01622/) (2025)
- [GoldenStart: Q-Guided Priors and Entropy Control for Distilling Flow Policies](https://mlsanity.com/paper/2603.14245/) (2026)
- [Controllable Motion Generation via Diffusion Modal Coupling](https://mlsanity.com/paper/2503.02353/) (2025)

## Abstract (arXiv)

Flow-matching policies are promising for imitation learning because they model complex multimodal action distributions. However, their stochasticity is largely passive: repeated sampling may yield diverse behaviors, but users cannot directly choose among valid continuations from the same state. We propose Source-Lifted Flow Matching (SL-FM), a source-intervenable flow-matching policy that exposes such a handle while keeping the velocity field shared and latent-free (without a separate discrete-handle input). The handle selects only the source endpoint of the conditional flow, not a mode-specific field, preserving the standard formulation while avoiding decomposition into separate mode-conditioned dynamics. The core mechanism is Orthogonal Source Lifting, designed to prevent path-crossing ambiguity. Instead of partitioning target actions by mode, SL-FM lifts handle-specific sources into auxiliary orthogonal coordinates and keeps targets in the original action subspace. This preserves the demonstrated action distribution while allowing one shared field to carry different branches without merging at crossings. To keep handles usable across states, we learn a state-dependent source mixture end to end and use a responsibility floor, giving each handle weak supervision and mitigating dead modes. Experiments on crossing-flow diagnostics and robot-control benchmarks show that SL-FM converts passive source randomness into an actionable intervention variable. It removes crossing-induced composite trajectories, changes future routes in 91.1% of matched-prefix interventions, and achieves strong free-deployment performance, with improvements in several benchmark settings. Overall, source geometry provides actionable multimodal control without conditioning the velocity field on the selected mode.