GeCO: Generative Control as Optimization

01 Overview

Instead of integrating a time-conditioned flow along a fixed schedule, GeCO learns a stationary velocity field over action sequences and optimizes until it converges. Easy states exit after a few steps and hard ones refine longer. The leftover field norm doubles as a free out-of-distribution detector.

3070%

Real-world success
Nut Assembly

2580%

Real-world success
Tube Arrangement

−41%

Real-world inference
latency

−75%

Compute vs. Rectified Flow
at higher success (LIBERO)

0.93

OOD AUROC,
training-free

GeCO overview: paradigm shift, adaptive computation, intrinsic safety — **Overview.** **(A)** Standard flow matching integrates along a rigid time schedule, while GeCO optimizes an action sequence in a stationary field until \(f_\theta \to 0\). **(B)** Simple transit converges in a few steps and grasping uses more. **(C)** In-distribution states settle into low-norm attractors. OOD states keep a high field norm, so anomalies can be detected at zero extra cost.

Abstract

Diffusion and flow-based generators are increasingly used in robot policies to produce action chunks from visual observations, proprioception, and language instructions. However, closed-loop robot control requires solving action-generation problems of varying difficulty, whereas standard diffusion and flow-matching inference typically follows a fixed integration schedule. We introduce Generative Control as Optimization (GeCO), a time-unconditional framework that turns action synthesis from fixed-time integration into iterative optimization. GeCO learns a stationary velocity field over action sequences and refines actions until the field norm becomes small. This enables adaptive computation at each planning call: simple states can terminate early, while difficult states can use additional refinement. The same field norm also provides a lightweight signal for non-convergent action generation under distribution shift. GeCO can be instantiated in both diffusion-transformer policies and flow-matching Vision-Language-Action (VLA) systems without changing the surrounding policy interface. Across simulation benchmarks and real-world tasks, GeCO matches or improves task performance while enabling convergence-based inference as a plug-and-play replacement for standard time-conditioned action generators.

02 Method

From integrating through time to optimizing to equilibrium

Before

Time-conditioned flow matching

\[ a \leftarrow a + \Delta t \, v_\theta(a, t, z), \quad t: 0 \to 1 \]

Fixed number of steps regardless of state difficulty
No intrinsic signal for when an action is "done"
Uncertainty estimation needs ensembles or extra passes

GeCO

Time-unconditional optimization

\[ a^{(k+1)} = a^{(k)} - \eta_k \, f_\theta(a^{(k)}, z) \]

Stop when \(\|f_\theta\| \le \tau_{\text{opt}}\), so compute follows difficulty
Expert actions are stable attractors of a single field
Final \(\|f_\theta\|\) is a free OOD score

01

Train a stationary field

Interpolate \(x_\gamma = \gamma a + (1-\gamma)\varepsilon\) but never give \(\gamma\) to the model. Regress the velocity-rescaled target \(g^\star = (\varepsilon - a)\,c(\gamma)\), where \(c(1)=0\), so the field vanishes on demonstrations.

02

Optimize, don't integrate

At each planning call, descend the field from a prior sample. Exit early once the field norm falls below \(\tau_{\text{opt}}\), or stop at \(K_{\max}\). Execute the first \(H\) actions and replan (receding horizon).

03

Read the residual

In-distribution states converge to \(\|f_\theta\|\approx 0\). Anomalous states stay high. \(\mathrm{Score}(o_t) = \|f_\theta(\hat a_t, z_t)\|\) flags OOD with essentially no overhead.

Plug-and-play for VLAs. For π₀-style flow-matching heads, set the time input to \(t=0\) during fine-tuning. The same pre-trained weights then learn a stationary field, with no change to architecture, action representation, or control API.

03 Real-World Deployment

Millimeter-precision manipulation on the Galaxea R1 Lite

We swap the flow-matching action head of Galaxea G0 Plus for GeCO and fine-tune both on the same teleoperated demonstrations with the same training budget. We evaluate two contact-rich tasks over 20 physical trials each, with object positions randomized.

Nut assembly NFE and inference time over the episode

Per-call NFE spikes to 9–10 during alignment and threading, then drops to 2–3 in free-space transit (mean 3.50 NFE, 166.7 ms).

Success rate↑

G0 Plus

30%

+ GeCO

70%

Avg. NFE↓

G0 Plus

10.0

+ GeCO

5.06

Avg. inference time (ms)↓

G0 Plus

252.3

+ GeCO

172.4

Tube arrangement NFE and inference time over the episode

The episode starts with deep refinement (NFE 10) to lock onto the tube, then early-exits for most of the motion (mean 3.73 NFE, 147.0 ms).

Success rate↑

G0 Plus

25%

+ GeCO

80%

Avg. NFE↓

G0 Plus

10.0

+ GeCO

3.82

Avg. inference time (ms)↓

G0 Plus

254.6

+ GeCO

150.3

04 Adaptive Computation

Computation follows task complexity

Each line is one planned action chunk along a rollout, colored by the number of function evaluations GeCO needed to converge at that state. Free-space transit converges almost immediately. Effort concentrates at bottlenecks such as pre-grasp alignment and placement, and at the episode start when the policy must ground the instruction among distractors.

NFE = 1

NFE = 20

LIBERO-Spatial rollout colored by NFE — **LIBERO-Spatial** · motion-planning bottlenecks

LIBERO-Object rollout colored by NFE — **LIBERO-Object** · semantic grounding at episode onset

05 Simulation Benchmarks

Better success–latency trade-offs, from DiT policies to VLAs

With a budget of only 5 steps, GeCO already beats 20-step Rectified Flow (91.9% vs. 90.0%) using 75% less compute. Its peak of 93.5% uses only 11.6 NFE on average.

Method	Max steps	Goal	Spatial	Object	Long	Avg.	NFE ↓
Diffusion Policy	100	82.9	91.4	88.9	82.7	86.5	100.0
Rectified Flow	20	92.4	94.6	97.0	76.0	90.0	20.0
GeCO	5	91.6	95.4	98.2	82.4	91.9	5.0
GeCO	10	93.0	95.8	99.0	81.8	92.4	8.7
GeCO	20	95.2	95.8	99.0	83.8	93.5	11.6
GeCO	30	93.6	95.2	98.8	84.8	93.1	12.8

Bimanual manipulation. Hard adds clutter, texture, lighting, and table-height randomization. GeCO raises the π₀ Hard average from 18% to 28%.

Method	Adjust Bottle		Beat Block Hammer		Blocks Ranking		Click Alarmclock		Click Bell		Avg.
Method	Easy	Hard	Easy	Hard	Easy	Hard	Easy	Hard	Easy	Hard	Easy	Hard
ACT	97	23	56	3	0	0	32	4	58	3	49	7
π₀	90	56	43	21	7	1	63	11	44	3	49	18
π₀ + GeCO	86	66	52	36	0	0	72	16	42	21	50	28

Long-horizon, language-conditioned manipulation. The largest gains are on Track 1 (in-distribution skills) and Track 6 (unseen textures and visual variation).

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
π_0.5	40.6	22.6	18.0	16.1	25.6	24.5
π₀ + GeCO	61.0	22.0	34.0	20.0	45.0	36.4

06 Intrinsic Safety

The field norm is a training-free OOD detector

We train on LIBERO-Goal and deploy on LIBERO-Spatial, an unseen workspace layout. The final field norm of each planning call serves as the anomaly score. When a lightweight leaky-bucket filter triggers, the episode is stopped before the robot wastes time on a doomed execution.

The baseline, Diff-DAgger's flow-matching loss signal, is close to chance. GeCO separates ID from OOD almost perfectly and needs no extra network, ensemble, or timestep sampling.

AUROC

Diff-DAgger

0.53

GeCO

0.93

OOD detected (TPR)

Diff-DAgger

14.4%

GeCO

82.6%

OOD execution time saved

Diff-DAgger

10.3%

GeCO

43.2%

GeCO (Leaky Bucket) at TNR 90.5%. Diff-DAgger (Moving Avg) TNR is 27.8%.

07 Citation

BibTeX

@article{zhang2026generative,
  title={Generative Control as Optimization: Time Unconditional Flow Matching for Adaptive and Robust Robotic Control},
  author={Zhang, Zunzhe and Huang, Runhan and Liu, Yicheng and Zhu, Shaoting and Mou, Linzhan and Zhao, Hang},
  journal={arXiv preprint arXiv:2603.17834},
  year={2026}
}