Don't Throw Away the Solution: Reusing Denoising Trajectories for Fast Robot Control

Wu, Xianjin; Li, Xian; Tang, Jianxiang; Liang, Dingkang; Bai, Xiang

A flow-based robot policy denoises every action chunk from scratch and discards the solver trajectory at the next replan, although consecutive replans solve nearly the same problem. RePIC keeps it: shift it to the new horizon, re-align it to fresh noise in closed form, and let the pretrained network refine all states at once. Sequential calls per chunk drop from 10 to about 2.6.

Reuse the solve, then refine it in parallel

Comparison of action decoding schemes, with RePIC reusing the previous trajectory and denoising in parallel, and latency and success on RoboTwin 2.0 and LIBERO — **Overview.** RePIC carries the unexecuted part of the previous solve into the next replan and updates the whole window in batched calls.

One replan: transfer, refine, execute

RePIC pipeline in three stages: trajectory transfer, parallel refinement, and execute and cache

Trajectory transfer

Shift the cached trajectory by the executed prefix R_n−1 and re-align it to the fresh noise ε_n.

0 network calls
Parallel refinement

Refine a sliding window of p steps with batched fixed-point (Picard) updates. It advances by the longest stride whose residual on the executed prefix stays under τ²σ².

1 batched call per round
Execute and cache

Execute the first R_n actions and cache the refined trajectory. Optionally, the tail residual picks the next execution length.

0 network calls

Noise-aligned transfer

Eq. 7 x̃_s,h = x̄_s,q(h) + σ_s ( ε_n,h − x̄_0,q(h) )

Here q(h) maps position h to the matching step of the previous chunk. At σ = 1 the draft is the fresh noise; at σ = 0 it keeps the cached clean actions.

Try the transfer

Step through the noise levels and switch the alignment off to see what shifting alone leaves behind.

Noise level s

Executed prefix R 8 16 24

Align to fresh noise (Eq. 7)

Illustration with synthetic curves, horizon H = 32, computed with Eq. 6–7 and the S = 10, shift 5 schedule.

Noise-aligned transfer, sliding-window refinement with stride, and residual-guided commitment — **Three mechanisms.** Left: noise alignment. Middle: the stride of the sliding window. Right: residual-guided commitment of the next execution length `R`_n+1.

A reused trajectory starts close to the answer

On a RoboTwin 2.0 rollout, the 8 steps carried over from the previous chunk start 24× closer to the serial solution than a cold draft, and the remaining positions 4.4× closer. A closer draft means smaller residuals, longer strides and fewer calls.

Five consecutive replans with their cached trajectories and the draft error per action step for parallel-only and RePIC initialization — **Draft error.** Top: five consecutive replans. Bottom: draft error (DraftRMS) per action step, log scale.

Reuse only initializes: every refinement round re-evaluates the velocity field under the current observation.

Two replans of a place-burger-fries rollout where refinement redirects the reused trajectory toward the burger and into the tray — **Refinement corrects the reused trajectory.** In two replans of *place burger fries*, refinement (teal) redirects the reused trajectory (amber) toward the burger and into the tray.

Faster at comparable success

Latency drops 2.66× on RoboTwin 2.0 (91.8% success, unchanged) and 2.75× on LIBERO (97.55% to 97.35%). The same sampler gives 1.14× on π_0.5 and 1.68× on GR00T N1.5 without retraining.

Full results on RoboTwin 2.0

RoboTwin 2.0: 50 tasks, clean and randomized, 100 episodes each
Method	Size	Clean	Random	Avg.	Latency (ms)	Speed (×)
LingBot-VA	5.3B	92.9	91.6	92.2	9356.00	0.06
Motus	8.0B	88.7	87.0	87.8	2177.00	0.27
Fast-WAM (Joint)	6.0B	90.8	90.3	90.6	1122.00	0.52
Enfold	3.0B	91.6	91.9	91.8	253.00	2.28
ImageWAM	8.6B	93.2	93.6	93.4	351.00	1.65
Faster-WAM (FC)	~6B	92.8	92.3	92.6	493.00	1.17
AHA-WAM	7.23B	93.4	92.2	92.8	535.50	1.08
Faster-WAM (DoT)	5.05B	89.7	88.6	89.2	–	–
Fast-WAM	6.0B	91.9	91.8	91.8	578.00	1.00
C³ache	6.0B	91.0	89.7	90.4	314.13†	1.84
RePIC	6.0B	91.9	91.7	91.8	217.70	2.66
RePIC-Flash	6.0B	92.4	90.7	91.6	101.16	5.71

Success rate in %. Speed is relative to Fast-WAM. † Inferred from the reported speed-up and the reference latency.

Full results on LIBERO

LIBERO: four suites, 50 episodes per task
Method	Size	Spatial	Object	Goal	Long	Avg.	Latency (ms)	Speed (×)
Vision-language-action models
SmolVLA	0.45B	90.0	96.0	92.0	71.0	87.25	239.00	–
π_0.5	~3.35B	98.0	98.6	96.8	90.8	96.05	70.24	1.00
π_0.5 + RePIC	~3.35B	97.6	98.2	96.0	91.2	95.75	61.35	1.14
GR00T N1.5	3.0B	89.0	91.4	88.8	78.4	86.90	120.62	1.00
GR00T N1.5 + RePIC	3.0B	90.0	93.2	90.4	79.0	88.15	71.60	1.68
World action models
LingBot-VA	5.3B	98.5	99.6	97.2	98.5	98.45	8623.00	0.07
Fast-WAM (Joint)	6.0B	99.6	99.4	98.2	96.8	98.50	1146.00	0.49
Enfold	3.0B	97.0	100.0	96.8	97.4	97.80	268.00	2.10
ImageWAM	8.6B	97.0	99.4	98.2	96.8	97.85	373.00	1.51
Faster-WAM (FC)	~6B	98.8	100.0	98.4	97.2	98.60	488.00	1.16
Faster-WAM (DoT)	5.05B	98.4	100.0	97.0	97.8	98.30	176.20†	3.20
Fast-WAM	6.0B	98.0	99.6	97.2	95.4	97.55	563.85	1.00
C³ache	6.0B	97.6	99.6	96.0	95.2	97.10	224.64†	2.51
RePIC	6.0B	97.4	99.6	96.8	95.6	97.35	204.77	2.75
RePIC-Flash	6.0B	97.4	99.4	96.4	94.8	97.00	127.63	4.42

Success rate in %. Speed is relative to the same backbone (VLAs) or to Fast-WAM (WAMs). † Inferred from the reported speed-up and the reference latency.

What each part buys

Ablations on LIBERO with Fast-WAM; a batched call counts as one sequential call. Parallel refinement alone cuts calls from 10 to 4, and reuse brings them to 2.22.

Parallelism and reuse
Method	S	Success	Calls	ms
Baseline	10	97.55	10.00	563.85
Baseline	5	96.90	5.00	333.00
Baseline	3	96.60	3.00	236.30
Baseline	1	95.35	1.00	151.80
Parallel only	10	97.10	4.00	298.10
RePIC	10	97.35	2.22	204.77

What to reuse
Draft	Shift	Align	Success	Calls	ms
No reuse	–	–	97.10	4.00	298.10
Endpoint only	✓	–	97.05	2.88	234.70
Full trajectory	✗	✗	96.35	3.03	245.80
Full trajectory	✗	✓	96.40	3.01	243.90
Full trajectory	✓	✗	97.15	4.87	331.40
RePIC	✓	✓	97.35	2.22	204.77

Success, sequential calls and latency as the tolerance tau and the window size p vary — **Sensitivity.** A looser tolerance `τ` lowers calls and latency but also success; a smaller window `p` needs more calls. Defaults: `τ` = 0.05, `p` = 10.

RePIC applies to deterministic flow samplers whose states at different noise levels can be batched. It trades batched compute and memory for a shorter sequential path.

On a real robot and in simulation

We run Fast-WAM with and without RePIC on an Agilex Piper arm. RePIC succeeds in 62 of 80 trials (77.5%) versus 53 (66.3%), with higher success on three of four tasks. At 20 trials per task, the differences are within trial-to-trial variation.

Fast-WAM (left) and RePIC (right), real time.

Grab Roller

Fast-WAM

RePIC

Success over 20 trials: 70% → 100%

Move Card Away

Fast-WAM

RePIC

Success over 20 trials: 70% → 80%

Stack Three Bowls

Fast-WAM

RePIC

Success over 20 trials: 60% → 50%

Each clip is a single trial. The fourth task, Press Stapler, went from 65% to 80%.

Stack Three Bowls rollout and success rates on four real-world tasks for Fast-WAM and RePIC — **Real-world deployment.** Success over 20 trials per task: 66.3% for Fast-WAM, 77.5% with RePIC.

RoboTwin 2.0 rollouts

Place shoe

Lift pot

Place burger fries

Place object basket

Handover block

Stack blocks two

Open laptop

Stamp seal

Head-camera view of successful rollouts.

Cite RePIC

@misc{wu2026repic,
  title={Don't Throw Away the Solution: Reusing Denoising Trajectories for Fast Robot Control},
  author={Xianjin Wu and Xian Li and Jianxiang Tang and Dingkang Liang and Xiang Bai},
  year={2026},
  note={Preprint}
}

The main branch is built on Fast-WAM; please cite it as well.

Reuse the solve, then refine it in parallel

One replan: transfer, refine, execute

Trajectory transfer

Parallel refinement

Execute and cache

Noise-aligned transfer

A reused trajectory starts close to the answer

Faster at comparable success

What each part buys

On a real robot and in simulation

Grab Roller

Move Card Away

Stack Three Bowls

RoboTwin 2.0 rollouts

Cite RePIC