Source-Lifted Flow Matching for Intervenable Multimodal Imitation

2026-07-11

AI Summary

While existing flow matching methods can model multimodal action distributions, their inherent randomness is passive and does not support user-driven intervention across multiple valid behavioral trajectories from the same state. This work proposes Source-Lifted Flow Matching (SL-FM), which introduces an intervention variable through orthogonal source lifting and a state-dependent source mixing mechanism—without altering the shared velocity field structure—to enable latent-free, controllable multimodal behavior generation. The approach effectively avoids trajectory crossing and mode collapse. Experimental results demonstrate that SL-FM achieves precise control over future trajectories with a 91.1% success rate in diagnostic and robotic control tasks, while significantly enhancing performance in free-deployment scenarios.

Abstract

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. 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 \textbf{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.

Problem

• flow matching
• multimodal imitation
• intervenable control
• action distribution
• source intervention

Innovation

• Source-Lifted Flow Matching
• Orthogonal Source Lifting
• Intervenable Imitation Learning
• Multimodal Policy
• Flow Matching