Reinforcement Learning Team

When One Step Is Enough:
An Empirical Study of Euler Integration
in Flow-Matching Policies

Shivakanth Sujit*, Luca Nunziante*, Rousslan Dossa, Kai Arulkumaran

Araya Inc., Tokyo, Japan

* Equal contribution

Accepted at the 10th Conference on Robot Learning (CoRL 2026)

arXiv OpenReview Dataset BibTeX

Overview

For large, sufficiently trained vision-language-action models, a single Euler step largely matches multi-step task success, with 1.6× to 4.8× faster action generation across the evaluated VLAs. No retraining, distillation, or auxiliary objectives are required.

We evaluate SmolVLA (450M), X-VLA (900M), FLOWER (947M), π₀.₅ (3.3B), LAP (3.3B), and XR-0 (4.7B), plus a 211M DiT baseline. Benchmarks sets span LIBERO, LIBERO+, CALVIN ABC→D, RoboTwin 2.0, our real-world Franka dataset, and D3IL Avoiding.

Paper Figure 1: four scatter plots of one-step versus reference-step success rates for LIBERO and LIBERO+, RoboTwin, CALVIN, and the real-world suite. Most points lie on or near the equality diagonal; the share of cells within 3 percentage points is 80%, 74%, 93%, and 67% respectively.
Fig. 1 One-step vs. reference-step success rates across every (model, benchmark) cell. Points near the diagonal indicate a negligible gap Δ = SRref − SR1. For the three largest models (π₀.₅, LAP, XR-0), all gaps are small and either statistically equivalent or inconclusive with one step ahead. In the real world, pooled gaps are at most 3.7 pp, with some task-level differences. View full size ↗

Motivation

Flow matching is now the dominant approach for vision-language-action (VLA) robot policies, thanks to its expressiveness and simple training objective. Models such as π₀.₅, X-VLA, and SmolVLA pair a pretrained vision-language backbone with a flow matching action head.

The action head learns a velocity field that moves a Gaussian noise sample toward an action chunk, conditioned on camera images, robot state, and a language instruction. VLAs are trained with the rectified flow objective: the network regresses its velocity onto the straight line from the noise sample to a demonstrated action. At inference, the learned field is integrated from noise to action with N Euler steps, each a forward pass of the action head. Published VLAs use 4 to 10 steps, and every step adds latency, limiting control frequency and fluid motion in dynamic or contact-rich tasks.

A single step is exact only if the learned flow is straight. Although each training target is a straight line, these lines cross, so the learned paths are generally curved. In image generation, collapsing such flows to one or a few steps sharply degrades sample quality, which has motivated additional methods to recover single-step generation (e.g., distillation, consistency).

Robot actions, however, are not images. Given the current observation, the action distribution may differ substantially from the image setting. The few-step methods applied to robotics were evaluated on small policies, where single-step inference is indeed substantially worse. Whether this degradation persists for large VLAs has not been thoroughly investigated.

We therefore ask: can large VLAs trained with the standard rectified flow objective, without additional regularization, generate actions with a single Euler step without losing performance?

Experimental Results

We compare six publicly released VLAs, spanning 450M to 4.7B parameters, and a 211M DiT baseline across four simulation benchmarks. For each model and benchmark, we use the same checkpoint and matched seeds, changing only the number of Euler integration steps. Apart from the DiT baseline, which we train ourselves, simulation results use the authors' publicly released checkpoints as-is, so not every model has results on every benchmark.

Across 36 simulation test cells, TOST (two one-sided tests) checks whether one-step and multi-step inference are equivalent, rather than merely failing to find a difference. We compute the 90% confidence interval of the gap Δ = SRref - SR1. If it lies entirely within ±3 pp, the two are equivalent; if entirely outside, the difference is relevant; otherwise the test is inconclusive. finds 23 equivalent, 4 favoring multi-step, 2 favoring one-step, and 7 inconclusive. Equivalence uses a ±3 percentage-point margin for success rates; point estimates alone do not establish equivalence. Hover to visualize the 90% confidence interval (CI) for the success rate (SR) gap Δ = SRref - SR1.

Reference steps 1 step
MODEL SUCCESS RATE (%) 1 STEP / REF. TOST

SGO aggregates the Spatial, Goal, and Object suites.

Real-World Evaluation

We evaluate four kitchen-style tasks with a Franka Emika Panda arm using paired, blinded A/B testing. The suite includes 4,800 rollouts, with 100 trials per task for each model and inference variant. Models are fine-tuned on our in-house dataset, and the policy noise is seeded within each pair.

Spoon → drawer
Open drawer
Open oven
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Real-world Franka suite · successful one-step π₀.₅ rollouts

Multi-step inference confers no systematic advantage. Only 3 of 24 task–model comparisons show a significant McNemar's test is a statistical test on paired data: in this case we compare one-step and multi-step inference on the same matched initial conditions and noise streams. A small p-value means that one condition is significantly better than the other. difference, and they run in both directions: the reference is better on Close Oven for π₀.₅ and FLOWER, while one step is better for FLOWER on Open Drawer. Pooled per-model gaps are small and bidirectional,with LAP being the only model showing a constant benefit from multi-step inference. Select Real world in the benchmark explorer above to see real-world results.

Inference Latency

A single Euler step reduces per-chunk inference latency for the six VLAs by 1.6× to 4.8× on an NVIDIA A100. Speedups depend on the relative cost of the VLM backbone and action head.

Inference latency from Table 1 of the paper
Model Reference 1 step Speedup
DiT 30 ms 15 ms 2.0×
SmolVLA 436 ms 91 ms 4.8×
X-VLA 215 ms 70 ms 3.1×
FLOWER 140 ms 60 ms 2.3×
π₀.₅ 80 ms 50 ms 1.6×
LAP 60 ms 35 ms 1.7×
XR-0 170 ms 90 ms 1.9×

Speedups depend on the relative cost of the VLM backbone and action head. The largest speedup is for SmolVLA, whose success rates are not consistently step-equivalent.

Trajectory Analysis

A binary success rate does not capture how the robot moves. We therefore ask two further questions: does one-step inference make the executed motion less smooth, and does it narrow the range of behaviors a policy produces?

Trajectory Smoothness

We compare the RMS joint jerk of paired real-world rollouts in which both variants succeed, since failures produce different jerk profiles. There is no consistent smoothness cost to one-step inference: the multi-step reference is meaningfully smoother only for the two sub-1B models (DiT, FLOWER), while for every model above 1B, one-step motion is marginally smoother. This mirrors the scale dependence of the success-rate results.

Paper Figure 3: violin plots of the paired log-ratio of reference-step to one-step jerk. DiT and FLOWER lie left of zero (multi-step smoother); X-VLA, π₀.₅, LAP, and XR-0 lie right of zero (one step smoother).
Fig. 3 Paired jerk-RMS comparison of real-world rollouts. Positive values of log(dref/d1) mean the one-step rollout is smoother. Boxes give quartiles with 5–95% whiskers; the colored line is the median; n counts pairs where both runs succeed. View full size ↗

Trajectory Diversity

D3IL Avoiding is a multimodal control task with 24 valid ways to succeed. We built a visual version of the task and run 200 episodes per model with matched initial states and policy noise. One-step inference improves success for DiT and FLOWER, lowers it for X-VLA, and never hurts the larger models. It does, however, reduce behavior diversity: under one step, DiT, FLOWER, and LAP each collapse onto a single successful strategy while keeping at least 99.5% success, and π₀.₅ drops from 19 observed successful strategies to 8.

Paper Figure 4a: bar charts of D3IL Avoiding success rate and normalized strategy entropy for one step and reference steps. One step reaches 100% success for DiT, FLOWER, and LAP but has lower entropy for every model except X-VLA.
Paper Figure 4b: π₀.₅ end-effector paths around obstacles. With one step, paths concentrate on a few routes; with ten steps they spread across many routes.
Fig. 4 D3IL Avoiding. Top: success rate with 95% CIs (* marks a significant McNemar difference, p < 0.05) and normalized strategy entropy. Bottom: trajectories executed by the selected model with 1 step and its reference step count (10, except FLOWER 4 and XR-0 5); grey lines are failed rollouts.

Takeaway. For models above 1B parameters, one-step inference costs neither task success nor smoothness, but it concentrates behavior on fewer strategies. Where behavioral diversity matters, success rate alone hides this difference.

Ablations

The main results show that multi-step inference does not guarantee higher success rates. To understand when step-equivalence emerges, we train models on LIBERO from different initializations and evaluate checkpoints throughout training. LIBERO pairs the short-horizon Spatial, Goal, and Object (SGO) suites with the long-horizon LIBERO-10 suite, where most gaps appear. We ask two research questions:

Answering the Research Questions

Q1 Larger models with pretrained vision-language features reach step-equivalence, and robot-action pretraining is not required. We trained π₀.₅ and X-VLA from scratch, from a generic VLM (PaliGemma2 or Florence) or the VLA's own VLM backbone with a randomly initialized action expert, and from the full pretrained VLA. All three pretrained initializations reach step-equivalence on SGO, with near-zero gaps by the final checkpoint. Pretrained features alone are not enough, though: the 211M DiT, built on pretrained CLIP encoders, develops a multi-step advantage on LIBERO-10 that grows to 15 pp. It remains open whether training from scratch eventually reaches step-equivalence: a randomly initialized π₀.₅ still favors one-step inference at the final checkpoint, although its SGO gap narrows from −20 to −3 pp.

Q2 Where multi-step inference helps, the benefit fades with training. We evaluated every run at checkpoints throughout training. π₀.₅ is step-equivalent on SGO from the earliest checkpoint. For X-VLA, extra Euler steps hurt early in training, and that gap collapses by the end. FLOWER's multi-step benefit is confined to LIBERO-10 at early and intermediate checkpoints and disappears at the final one. Its residual gap in Table 2 therefore reflects the authors' early-stopped release checkpoint, not the model's scale or architecture.

Paper Figure 5: the success-rate gap between reference-step and one-step inference over training, in four columns (VLM initialization, X-VLA variants, π₀.₅ variants, pretrained VLAs) and two rows (LIBERO-10, LIBERO SGO). SGO gaps stay near zero; LIBERO-10 gaps are larger early and mostly fade with training, except for DiT, whose gap grows to about 15 points.
Fig. 5 Step-count gap Δ = SRref − SR1 over training on LIBERO, with shaded 90% CIs. Multi-step gains, when present, are concentrated on LIBERO-10 and fade with training; the short-horizon suites stay close to step-invariant throughout. View full size ↗

Takeaway. Step-equivalence is favoured by larger models, generic VLM pretraining, and longer fine-tuning. When one of these properties is missing, tasks with longer horizons tend to show step-dependence.

Key Findings

Citation

@inproceedings{sujit2026when,
  title={When One Step Is Enough: An Empirical Study of Euler Integration in Flow-Matching Policies},
  author={Sujit, Shivakanth and Nunziante, Luca and Dossa, Rousslan Fernand Julien and Arulkumaran, Kai},
  booktitle={Conference on Robot Learning},
  year={2026},
  organization={PMLR}
}

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