MOSS: Mode-Oriented Source Shaping for Robot Flow Matching Policies
Organizations: MARS Lab, Nanyang Technological University · Tsinghua University
Abstract
In robotic manipulation, the same observation often admits multiple feasible actions. Generative policies such as diffusion and flow matching naturally capture such multimodal behaviors, yet which mode is executed is left to random sampling and cannot be actively controlled. We propose Mode-Oriented Source Shaping (MOSS), which turns mode selection into an explicit choice of where generation starts. We first reveal, both empirically and theoretically, that deterministic flow transport induces mode-dependent structure in the source space. Under ideal deterministic ODE transport, distinct behavioral modes have distinct source-space preimages, while practical approximation errors can blur their boundaries due to imbalanced data, limited model capacity, and few inference steps. Motivated by this source-space structure, MOSS constructs semantically aligned mode-specific Gaussian sources that encode mode identity in the initial noise. A modality-strength estimator predicts the local degree of multimodality, which adaptively controls the geometry of the mode-specific sources. It contracts them toward a shared Gaussian where behaviors are similar and separates them near behavioral branching points. During deployment, the desired behavior is selected at inference simply by sampling from the corresponding component. Across 6 simulated and 3 real-world manipulation tasks, MOSS steers to the target mode up to 100% of the time with high task success, recovers minority modes at over 90% guidance rate under a 10:90 imbalance dataset, and surpasses mode-conditioned flow policy by 43.3 points of guidance rate on real robots.
Figures & tables
| Push Cube | Grasp Eyeglasses | Stack Cube | Put Wine | |||||
| Method | Mode 1 | Mode 2 | Mode 1 | Mode 2 | Mode 1 | Mode 2 | Mode 1 | Mode 2 |
| Mode-Cond. FM | 0.86 / 0.96 | 0.94 / 1.00 | 1.00 / 1.00 | 1.00 / 1.00 | 0.96 / 0.96 | 0.94 / 0.94 | 0.92 / 0.92 | 0.94 / 0.96 |
| GMM-Sourced FM | 0.72 / 0.96 | 0.92 / 1.00 | 0.98 / 1.00 | 0.42 / 1.00 | 0.58 / 1.00 | 0.56 / 1.00 | 0.94 / 0.94 | 0.80 / 0.94 |
| MOSS | 0.99 / 0.99 | 1.00 / 1.00 | 1.00 / 1.00 | 1.00 / 1.00 | 0.98 / 0.98 | 0.96 / 0.96 | 0.92 / 0.94 | 0.86 / 0.94 |
| Method | SR | GR 1 | GR 2 |
|---|---|---|---|
| Place Cups | |||
| FM-DiT | 0.70 | – | – |
| Mode-conditioned FM | 0.70 | 0.15 | 0.85 |
| MOSS | 0.98 | 0.95 | 1.00 |
| Pick Veg | |||
| FM-DiT | 0.60 | – | – |
| Method | Push Cube | Grasp Eyeglasses | Stack Cube |
|---|---|---|---|
| MOSS (single Gaussian ) | 0.50 / 0.68 | 0.76 / 0.80 | 0.58 / 0.70 |
| MOSS (single-step separation) | 0.64 / 0.62 | 0.66 / 0.72 | 0.54 / 0.68 |
| MOSS (w/o adaptive) | 0.86 / 0.85 | 0.86 / 0.90 | 0.78 / 0.88 |
| MOSS (ours) | 0.99 / 1.00 | 1.00 / 1.00 | 0.98 / 0.96 |
Appendix figures & tables8 assets
Supplementary material from the paper’s appendix.
Appendix
| Target mean | Mode 1 | Mode 2 | Mode 3 | Mode 4 | Stuck | Target mode |
|---|---|---|---|---|---|---|
| (Mode 1) | 62 | 27 | 8 | 2 | 1 | 62% |
| (Mode 2) | 52 | 29 | 9 | 6 | 4 | 29% |
| (Mode 3) | 6 | 15 | 34 | 43 | 2 | 34% |
| (Mode 4) | 3 | 8 | 29 | 56 | 4 | 56% |
| Hyperparameter | Value |
| Observation/action history length | 8 / 8 |
| Future-action horizon | 8 |
| KNN projection dimension | 128 |
| Candidate/retained neighbors | 40 / 20 |
| MLP hidden dimensions | |
| Dropout | 0.1 |
| 0.0 | 1.0 | 1.25 | 2.5 | 1.0 | 0.25 | 1.0 | 0.5 |
| Task | Mode 1 | Mode 2 |
|---|---|---|
| Push Cube | Push around the left side | Push around the right side |
| Grasp Eyeglasses | Positive- approach | Negative- approach |
| Stack Cube | Cube A on Cube B | Cube B on Cube A |
| Place Cups | Grasp the left cup | Grasp the right cup |
| Pick Veg | Pick the left radish first | Pick the right corn first |
| Open Drawer | Open the lower blue drawer | Open the upper green drawer |
| Hyperparameter | Value |
|---|---|
| Observation history | steps |
| Predicted action horizon | steps |
| Actions executed per query | steps |
| Dropout | |
| FM integration steps | |
| Optimizer | AdamW |
| Task | Requested mode | SR | GR | |
|---|---|---|---|---|
| Place Cups | Mode 1 | |||
| Mode 1 | ||||
| Pick Veg | Mode 1 | |||
| Mode 1 | ||||
| Open Drawer | Mode 2 | |||
| Mode 2 |
| Task | Source | |||
|---|---|---|---|---|
| Push Cube | Fixed | |||
| Adaptive | ||||
| Grasp Eyeglasses | Fixed | |||
| Adaptive | ||||
| Stack Cube | Fixed | |||
| Adaptive |
Robot Policy Learning
Robot policy learning develops controllers that map sensory observations, task goals, and interaction history to actions for embodied robots.
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