Organizations: Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, China · Galaxea Inc., Beijing, China · Department of Computer Science, Princeton University, New Jersey, US
Diffusion models and flow matching have become a cornerstone of robotic imitation learning, yet they suffer from a structural inefficiency where inference is often bound to a fixed integration schedule that is agnostic to state complexity. This paradigm forces the policy to expend the same computational budget on trivial motions as it does on complex tasks. We introduce Generative Control as Optimization (GeCO), a time-unconditional framework that transforms action synthesis from trajectory integration into iterative optimization. GeCO learns a stationary velocity field in the action-sequence space where expert behaviors form stable attractors. Consequently, test-time inference becomes an adaptive process that allocates computation based on convergence--exiting early for simple states while refining longer for difficult ones. Furthermore, this stationary geometry yields an intrinsic, training-free safety signal, as the field norm at the optimized action serves as a robust out-of-distribution (OOD) detector, remaining low for in-distribution states while significantly increasing for anomalies. We validate GeCO on standard simulation benchmarks and demonstrate seamless scaling to pi0-series Vision-Language-Action (VLA) models. As a plug-and-play replacement for standard flow-matching heads, GeCO improves success rates and efficiency with an optimization-native mechanism for safe deployment. Video and code can be found at https://hrh6666.github.io/GeCO/
Figures & tables
Figure 1: Generative Control as Optimization (GeCO). (A) The Paradigm Shift: Unlike standard flow matching which relies on rigid, time-dependent integration schedules (top), GeCO learns a stationary velocity field where inference becomes an iterative optimization process toward stable attractors (bottom). (B) Adaptive Computation: This formulation enables the policy to dynamically allocate computational budget based on state complexity—exiting early for simple transit phases (Scenario 1) while performing deep refinement for precise manipulation (Scenario 2). (C) Intrinsic Safety: The stationary geometry provides a zero-shot safety mechanism. In-distribution (ID) states converge to low-energy equilibria ( ∣∣fθ∣∣≈0 ), whereas out-of-distribution (OOD) anomalies exhibit persistently high field norms ( ∣∣fθ∣∣≫0 ), enabling robust detection.
Figure 2: Computation Follows Task Complexity. We visualize the spatial distribution of inference effort along a single rollout. The first three panels (a–c) are sampled from LIBERO-Spatial, and the last three panels (d–f) are from LIBERO-Object. The color of each line encodes the number of function evaluations (NFE) required for convergence at that state, ranging from blue (NFE = 1) to red (NFE = 20). This visualization illustrates how GeCO allocates more computation to challenging states while using fewer steps in easier regions.
Method
Max
Success Rate (%)
Efficiency
Steps
Goal
Spat.
Obj.
Long
Avg.
NFE
Diff. Policy
100 (Fixed)
82.9
91.4
88.9
82.7
86.5
100.0
Rectified flow
20 (Fixed)
92.4
94.6
97.0
76.0
90.0
20.0
GeCO (Ours)
5
91.6
95.4
98.2
82.4
91.9
5.0
GeCO (Ours)
10
93.0
95.8
99.0
81.8
92.4
8.7
GeCO (Ours)
20
95.2
95.8
99.0
83.8
93.5
11.6
Table 1: Performance vs. Efficiency on LIBERO. GeCO achieves higher success rates by allowing adaptive refinement. By increasing the max step budget, GeCO refines actions for complex states, yet the average compute remains low compared to fixed-schedule baselines.
Method
Adjust Bottle
Beat Block Hammer
Blocks Ranking (Size)
Click Alarmclock
Click Bell
Avg.
Easy
Hard
Easy
Hard
Easy
Hard
Easy
Hard
Easy
Hard
Easy
Hard
ACT ( Zhao et al., 2023 )
97.0
23.0
56.0
3.0
0.0
0.0
32.0
4.0
58.0
3.0
49.0
7.0
π0 ( Black et al., 2024 )
90.0
56.0
43.0
21.0
7.0
1.0
63.0
11.0
44.0
3.0
49.0
18.0
π0 with GeCO
86.0
66.0
52.0
36.0
0.0
0.0
72.0
16.0
42.0
21.0
50.0
28.0
Table 2: Success rate (%) of different VLA methods on the RoboTwin 2.0 benchmark. Each task is evaluated under two difficulty levels: Easy and Hard . For every method we report the success rate for each task and difficulty level, together with the average performance across all five tasks. Higher values indicate better task completion ability. The best result in each column is highlighted in bold .
Method
Track 1
Track 2
Track 3
Track 4
Track 6
Avg.
π0
47.0
21.2
29.1
17.3
32.2
29.4
π0.5
40.6
22.6
18.0
16.1
25.6
24.5
π0 with GeCO
61.0
22.0
34.0
20.0
45.0
36.0
Table 3: VLA success rates (%) on VLABench tracks. We report track-wise success and the average over the listed tracks; higher is better.
Method
Goal
Spat.
Obj.
Long
Avg.
π0 + FAST ( Pertsch et al., 2025 )
88.6
96.4
96.8
60.2
85.5
π0 ( Black et al., 2024 )
95.8
96.8
98.8
85.2
94.2
π0.5 ( Intelligence et al., 2025 )
98.0
98.8
98.2
92.4
96.9
Ours ( π0 )
96.4
96.8
97.0
85.4
93.9
Ours ( π0.5 )
96.4
97.4
98.6
92.4
96.2
Table 4: VLA success rates (%) on LIBERO benchmark. We report track-wise success and the average over the listed tracks; higher is better.
Method
AUROC ( ↑ )
TNR(%)
TPR (%)
Time Saved(%)
Baseline (Moving Avg)
0.53
14.4
27.8
10.3
Ours (Moving Avg)
0.93
82.4
89.7
42.4
Ours (Leaky Bucket)
0.93
84.0
90.0
44.3
Table 5: OOD Detection on LIBERO Suite Shift (Goal → Spatial). We report planning-level AUROC for separating ID (Goal) and OOD (Spatial) using optimization-dynamics signals computed per planning call. At a fixed operating point, TPR is specificity on ID instances and TNR is recall on OOD instances. Time Saved is the average fraction of interaction time avoided on OOD episodes by early reporting, computed as 1−treport/Ttotal .
α
Object
Goal
Spatial
Long
Avg
α=0.0
0.984
0.946
0.934
0.770
0.909
α=0.2
0.968
0.954
0.958
0.802
0.921
α=0.4
0.982
0.934
0.956
0.782
0.914
α=0.6
0.982
0.942
0.956
0.778
0.915
α=0.8
0.978
0.940
0.960
0.810
0.922
α=1.0
0.932
0.840
0.898
0.558
0.807
Table 6: Ablation Study on Truncation Parameter α . We report the performance on the LIBERO benchmark across different values of α .
Figure 3: GeCO policy execution for the Nut Assembly task. The robot performs high-precision alignment and rotational insertion.
Figure 4: GeCO policy execution for the Chemistry Tube Arrangement task. The policy adaptively handles the tight-tolerance insertion of fragile tubes.
Method
Nut Assembly
Tube Arrangement
Success ( ↑ )
Avg. NFE ( ↓ )
Avg. Infer. Time ( ↓ )
Success ( ↑ )
Avg. NFE ( ↓ )
Avg. Infer. Time ( ↓ )
G0 Plus
30%
10.0
252.3
25%
10.0
254.6
G0 Plus + GeCO (Ours)
70%
5.06
172.4
80%
3.82
150.3
Table 7: Real-world performance on Galaxea R1 Lite. We report the success rate, average Number of Function Evaluations (NFE), and average inference time for each task.
Appendix figures & tables6 assets
Supplementary material from the paper’s appendix.
Appendix
Task
Track 1
Track 2
Track 3
Track 4
Track 6
π0
Ours
π0
Ours
π0
Ours
π0
Ours
π0
Ours
add_condiment
0.66
0.80
0.14
0.08
0.34
0.16
0.26
0.10
0.56
0.76
insert_flower
0.18
0.30
0.04
0.00
0.22
0.28
0.02
0.00
0.10
0.02
select_book
0.694
0.84
0.064
0.08
0.417
0.51
0.311
0.23
0.714
0.79
select_chemistry_tube
0.52
0.76
0.12
0.14
0.70
0.94
0.06
0.02
0.28
0.71
select_drink
0.52
0.78
0.224
0.30
0.08
0.10
0.10
0.04
0.44
0.66
Appendix
Table 8: Per-task success rates on VLABench primitive 10-task evaluation. We report success rates for the baseline π0 and π0 with GeCO (ours) across five tracks; higher is better. Track averages correspond to the averages over the 10 tasks in each track.
Figure 5: Task setups for the real-world robotic deployment, showing the configurations for both the Nut Assembly and the Chemistry Tube Arrangement tasks.
Figure 6: Adaptive computation during real-world execution. We visualize the per-step Number of Function Evaluations (NFE) and total inference time over time for representative physical rollouts of Nut Assembly and Tube Arrangement . For Nut Assembly , GeCO uses an average of 3.50 NFEs and 166.7 ms total inference time per decision. For Tube Arrangement , GeCO uses an average of 3.73 NFEs and 147.0 ms per decision. Rather than relying on a fixed computation budget, GeCO automatically increases computation during bottleneck phases, where the NFE rises to 9–10, and exits early during easier free-space motions, where the NFE drops to as low as 2–3. The corresponding inference-time traces mirror this behavior, showing that GeCO adaptively allocates computation according to task difficulty and thereby improves real-world inference efficiency.
α
Success Rate (%)
Goal
Spat.
Obj.
Long
Avg.
0.6
85.8
98.0
91.6
48.6
81.0
0.8
96.4
97.4
98.6
92.4
96.2
0.9
95.8
97.8
94.0
81.2
92.2
Appendix
Table 9: Ablation Study on Truncation Parameter α (VLA Architecture). We report the success rates (%) on the LIBERO benchmark across different values of α to demonstrate its impact on policy performance.
τ
LIBERO Object
LIBERO Goal
LIBERO Spatial
LIBERO Long
Avg
Avg. Steps
0.4
99.0
95.2
95.8
83.8
93.5
11.6
0.6
98.8
94.0
95.6
81.0
92.35
7.7
0.8
96.8
93.2
96.0
81.6
91.9
6.6
Appendix
Table 10: Ablation on the Early-Stop Threshold τ . We report the success rates (%) and the average number of inference steps across the LIBERO benchmark.
Step-size schedule
LIBERO Object
LIBERO Goal
LIBERO Spatial
LIBERO Long
Avg
0.015×20
97.0
92.0
94.8
77.2
90.3
0.02×20
98.0
94.8
95.4
84.0
93.1
0.025×20
98.4
95.0
94.2
80.4
92.0
0.035×20
98.0
95.0
95.0
77.4
91.4
Current schedule
99.0
95.2
95.8
83.8
93.5
Appendix
Table 11: Ablation on Fixed Step-Size Schedules. We compare our current adaptive schedule with several fixed step-size schedules (constant step size × total steps) on the LIBERO benchmark.
Learning long-horizon robotic manipulation requires jointly achieving expressive behavior modeling, real-time inference, and stable execution, which remains challenging for existing generative policies. Diffusion-based approaches offer strong modeling capacity but incur high inference latency, while flow matching enables fast, near-single-step generation yet often suffers from unstable execution when operating directly in the raw action space. We propose Continuous Latent Action Flow Policy (CoLA-Flow Policy), a trajectory-level imitation learning framework that performs flow matching in a continuous latent action space. By encoding action sequences into temporally coherent latent trajectories and learning an explicit latent-space flow, CoLA-Flow Policy decouples global motion structure from low-level control noise, enabling smooth and reliable long-horizon execution. The framework further integrates geometry-aware point cloud conditioning and execution-time multimodal modulation, using visual cues as a representative modality to enhance real-world robustness. Experiments in simulation and on real robots show that CoLA-Flow Policy achieves near-single-step inference, improves trajectory smoothness by up to 93.7% and task success by up to 25 percentage points over raw action-space flow baselines, while remaining significantly faster than diffusion-based policies.
Wu Songwei, Jiang Zhiduo, Sun Wandong +4
Harbin Institute of Technology, Harbin 150001, China · Honor Device Co., Ltd., Shenzhen, China
Generative Control Policies (GCPs) show immense promise in robotic manipulation but struggle to simultaneously model stable global motions and high-frequency local corrections. While modern architectures extract multi-scale spatial features, their underlying Probability Flow ODEs apply a uniform temporal integration schedule. Compressed to a single step for real-time Receding Horizon Control (RHC), uniform ODE solvers mathematically smooth over sparse, high-frequency transients entangled within low-frequency steady states. To decouple these dynamics without accumulating pipelined errors, we introduce KoopmanFlow, a parameter-efficient generative policy guided by a Koopman-inspired structural inductive bias. Operating in a unified multimodal latent space with visual context, KoopmanFlow bifurcates generation at the terminal stage. Because visual conditioning occurs before spectral decomposition, both branches are visually guided yet temporally specialized. A macroscopic branch anchors slow-varying trajectories via single-step Consistency Training, while a transient branch uses Flow Matching to isolate high-frequency residuals stimulated by sudden visual cues (e.g., contacts or occlusions). Guided by an explicit spectral prior and optimized via a novel asymmetric consistency objective, KoopmanFlow establishes a fused co-training mechanism. This allows the variant branch to absorb localized dynamics without multi-stage error accumulation. Extensive experiments show KoopmanFlow significantly outperforms state-of-the-art baselines in contact-rich tasks requiring agile disturbance rejection. By trading a surplus latency buffer for a richer structural prior, KoopmanFlow achieves superior control fidelity and parameter efficiency within real-time deployment limits.
Chengsi Yao, Ge Wang, Kai Kang +9
ISing AI · Future Network of Intelligence Institution, The Chinese University of Hong Kong, Shenzhen · Guangdong Polytechnic Normal University +1
Generative flow and diffusion models provide the continuous, multimodal action distributions needed for high-precision robotic policies. However, their reliance on iterative sampling introduces severe inference latency, degrading control frequency and harming performance in time-sensitive manipulation. To address this problem, we propose the One-Step Flow Policy (OFP), a from-scratch self-distillation framework for high-fidelity, single-step action generation without a pre-trained teacher. OFP unifies a self-consistency loss to enforce coherent transport across time intervals, and a self-guided regularization to sharpen predictions toward high-density expert modes. In addition, a warm-start mechanism leverages temporal action correlations to minimize the generative transport distance. Evaluations across 56 diverse simulated manipulation tasks demonstrate that a one-step OFP achieves state-of-the-art results, outperforming 100-step diffusion and flow policies while accelerating action generation by over 100×. We further integrate OFP into the π0.5 model on RoboTwin 2.0, where one-step OFP surpasses the original 10-step policy. These results establish OFP as a practical, scalable solution for highly accurate and low-latency robot control.
Shaolong Li, Lichao Sun, Yongchao Chen
CSE Department, University of Michigan · Lehigh University · College of AI, Tsinghua University