1 Introduction↩︎

Single-step generation has been a long-standing goal in diffusion modeling [1], [2]. In image generation, a class label or even text prompt leaves a high-dimensional, multimodal conditional distribution [3]. As a result, many one-step and few-step image generators add extra machinery, such as consistency training, distillation, shortcut models, mean-flow objectives, or flow-map learning [4]–[8].

VLA policies sit in a different condition-target regime. At each decision point, the model receives images, language, and proprioceptive state [9]–[11], and predicts an action chunk with dimension equal to action dimension times horizon, typically only tens to a few hundred scalars. The target is a relatively low-dimensional action chunk, not a high-dimensional sample. With a useful representation of the scene and task, the conditional action distribution can therefore be much simpler than the conditional image distribution.

This structure is closer to image-to-text than to text-to-image. We isolate the analogy with a controlled MNIST grid-to-sequence task inspired by continuous diffusion for language modeling [12]: a \(4\times4\) digit image grid is given as input, and the model generates the corresponding 16-token digit sequence. In this setting, a simple shift of the training time distribution toward high-noise states substantially improves one-step generation.

We then test the same idea in VLA. Across standard LIBERO [13], LIBERO-Plus [14], and LIBERO-Pro [15], a simple high-noise schedule often makes one-step action generation competitive with, and sometimes better than ten-step decoding for standard action-chunk policies, while keeping the standard flow-matching objective. A real-robot bimanual YAM RSS challenge evaluation [16] with a fine-tuned \(\pi_{0.5}\) policy [17] provides a small-sample cross-architecture check. Ablations over action horizon, observation inputs, and time distribution further support the condition-target view by changing the richness of the condition and the complexity of the target.

Our contributions are:

• We frame VLA action generation as a condition-target problem and design MNIST grid-to-sequence as a controlled probe of the same rich-observation, compact-target structure.

• We show that a simple high-noise training schedule can make standard flow matching produce strong one-step policies in the evaluated LIBERO-family settings; a real-robot bimanual YAM RSS challenge evaluation with a fine-tuned \(\pi_{0.5}\) policy provides cross-architecture evidence for the same sampler trend.

• We diagnose the learned velocity field and observe lower error and higher alignment near the noise endpoint where one-step inference starts. Systematic ablations over noise shift, observation inputs, and action horizon identify when this behavior holds.

2 Related Work↩︎

2.1 Autoregressive VLA Models↩︎

Autoregressive models are widely adopted in VLA [18]–[21]. They benefit from mature language-model infrastructure and scale naturally with discrete sequences. For continuous or perceptual outputs, however, autoregression requires choosing an ordering and often building a tokenizer. In image and video generation, learned visual tokenizers and autoregressive visual token hierarchies are major design components [22]–[24]; they add design and training cost, and can affect quality and latency. Action-tokenized VLAs extend this idea to robot actions [21], [25], making autoregressive action generation efficient but also turning continuous control into a separate discretization problem. Our alternative keeps the action target continuous and asks whether standard flow matching can decode the whole action chunk in one forward step.

2.2 Tokenization and latent Representation↩︎

Tokenization is also central outside autoregressive modeling. Latent diffusion models first map images into a learned continuous latent space, then train the generative model in that space [26], [27]. This reduces compute and can make the target easier to model. The latent representation, however, is not a neutral detail: it is usually trained by a reconstruction objective, and reconstruction-friendly latents may not be optimal for generation [28], [29]. For action generation, the target is already compact. This weakens the usual motivation for adding a tokenizer and motivates studying continuous action generation directly.

2.3 Diffusion VLA Architectures↩︎

Many diffusion VLA architectures couple heavy VLM encoders to action heads [9], [30]. Recent work questions this symmetry, adopting lightweight heads yet retaining multi-step diffusion [31] or adding complex adapter mechanisms for encoder-head fusion [32]. We share the lightweight-head direction with SimVLA [31], but ask a different question: when can such a head decode in one step? If the condition encoder already provides a useful scene and task representation [33]–[35], the remaining conditional action distribution can be much simpler than class- or text-conditioned image generation. In that case, a very light continuous action head can be sufficient for one-step decoding.

2.4 Few-Step and One-Step Diffusion↩︎

Few-step generation in image diffusion has spawned an active sub-field: rectified flows [36], consistency models [4], distribution matching distillation [5], shortcut models [6], mean-flow [7], and flow-map learning [8]. These methods were developed mainly for image generation, where the target is high-dimensional and the condition is relatively weak. They often require teacher models, auxiliary losses, or additional training stages. Recent robotics work has begun importing the same toolkit, applying consistency distillation to diffusion policies for 1–4-step action generation [37], [38]. Time-distribution design is a lighter intervention. High-noise shifts are already used in flow-based image generation [39]–[41]. These choices do not by themselves make one-step image synthesis easy. Our results show a direct VLA baseline: shifting the training time distribution toward higher noise can make the standard velocity objective work well for one-step action policies.

3 Method↩︎

3.1 Conditional Flow Matching↩︎

We follow the flow-matching convention [36], [42], [43]. Let \(x_1\sim p_{\text{data}}\) denote the target and \(x_0\sim\mathcal{N}(0,I)\) denote noise. With the linear interpolation \[x_t = t x_1 + (1-t)x_0,\qquad t\in[0,1],\] The target velocity is constant, \(v_t=x_1-x_0\), and the conditional velocity model is trained with \[\mathcal{L}_{\mathrm{CFM}} =\mathbb{E}_{t,x_0,x_1,c}\bigl\|v_\theta(x_t,t,c)-(x_1-x_0)\bigr\|^2 .\] The population optimum is the conditional mean velocity \[v^*(x,t,c)=\mathbb{E}\left[x_1-x_0 \mid x_t=x,\,t,\,c\right].\] One-step decoding is reliable only when that conditional target distribution is concentrated or simple to model; otherwise the model output averages incompatible actions.

The objective does not require \(t\) to be sampled uniformly. Given a base time sample \(u\in[0,1]\), we apply a simple noise shift [39] \[t = \frac{u}{1 + (\alpha-1)(1-u)}, \label{eq:noise95shift}\tag{1}\] where \(\alpha>1\) shifts samples toward \(t\to0\). As a stress test, we also use pure-noise training: replace \(x_t\) with independent Gaussian noise and predict the clean action from the condition. This probe asks whether the conditional action target is simple enough for a direct endpoint prediction.

3.2 Toy Example: MNIST Grid-to-Sequence↩︎

To isolate a rich-condition, compact-target setting, we use an image-to-text toy task inspired by continuous diffusion for language modeling [12]. A \(4\times4\) MNIST [44] grid is the condition, and the target is the 16-digit sequence in exact row-major order. This controlled task represents an idealized limit in which the condition largely specifies the target. It asks what happens when the condition carries most of the information needed for a structured low-dimensional target.

Figure 1 shows the motivating result: biasing training toward high-noise states substantially improves exact-match accuracy, especially for one-step decoding. Figure 2 gives the design diagnostics: stronger visual features raise the ceiling, larger decoders do not compensate for weak visual features, and pure-noise training is much less effective in a class-to-image loss diagnostic where the condition is weaker and the target is high-dimensional.

3.3 VLA Architecture Design↩︎

Our VLA architecture follows the same principle. A VLM encodes camera images and the language prompt; a lightweight action decoder then predicts velocities from VLM tokens, robot state, time, and noised action tokens (Figure 3). The design is close to SimVLA [31]: keep the condition encoder strong and the action head small. We build on OpenPI [9], using SigLIP [46] for vision and PaliGemma [47] for multimodal fusion.

For experiments we use two encoder scales. The tiny model slices the vision-language encoder for fast controlled ablations, while the full-encoder model restores the full SigLIP vision tower and pretrained first 4-layer PaliGemma multimodal fusion. Both keep the same lightweight action-head family; detailed hyperparameters are in Appendix 10.

4 Experiments↩︎

4.1 Standard LIBERO Controlled Study↩︎

We validate our design principles on LIBERO [13] across all four task suites: Spatial, Object, Goal, and Long (10 tasks for each suite). Unless stated otherwise, the action horizon is 10 steps (H10), the replanning interval¹ matches the trained action horizon, and evaluation uses Euler sampling with the reported number of flow steps. Tiny-model ablations use batch size 64 and 50k training steps; full-encoder validations use batch size 256 and 150k steps. The base training-time distribution is \(\mathrm{Beta}(1,1.5)\), a slightly high-noise biased time distribution. Each suite result averages 10 tasks with 50 episodes per task.

OpenPI uses a 32-dimensional action interface for compatibility across datasets, while LIBERO has seven physical action dimensions. We keep this interface, but do not supervise padded coordinates. We report both flow steps and replanning interval; Appendix 11 shows that replanning frequency materially affects closed-loop success.

4.1.1 Tiny-Model Ablations↩︎

4.1.1.1 Time schedule.

Table [tab:time95ablation] reports the H10 time-schedule controls and visualizes the suite-wise trends. The trend is clear: shifting training toward high-noise states improves one-step decoding, but the same bias can hurt ten-step decoding, and \(\alpha=8\) is already too aggressive. Pure-noise remains competitive as a one-step diagnostic, so we keep it as a control rather than the default recipe.²

4.1.1.2 Action horizon.

Action horizon changes the target while keeping the condition fixed: longer horizons ask the decoder to generate longer open-loop chunks from the same observation. Table [tab:horizon95ablation] shows the expected boundary. One-step success drops as the horizon grows, but high-noise schedules recover much of the loss at H20/H30 and can approach or exceed the uniform ten-step reference. At H40, the gap reappears, suggesting that very long chunks are harder to collapse into a single endpoint prediction. This is boundary evidence rather than a monotonic schedule claim: high-noise shifting is a simple way to expose strong one-step behavior under standard flow matching, but not a universal replacement for sampler and horizon choices.

4.1.1.3 Condition ablations.

We next weaken the condition by removing one input source at a time while keeping the H10 action target fixed. Table 1 shows that removing input sources generally hurts one-step success, and removing proprioceptive state nearly collapses the policy.

4.1.1.4 Action-loss supervision.

Although action-loss supervision is not our main claim, it is a natural ablation because OpenPI stores actions in a padded tensor. Table [tab:action95mask] shows a large effect for the tiny LIBERO-Long control, but the same pattern does not hold at full-encoder scale. We therefore use mask7 to keep the tiny ablations conceptually clean, not as a main claim.

The full-encoder block also shows that one-step decoding remains strong at larger scale under the same velocity objective, without distillation, consistency training, or a teacher model. Appendix 11 gives additional alpha-shift controls.

4.2 Velocity-Field Diagnostics↩︎

To understand why one-step inference can match or outperform ten-step inference, we directly inspect the learned velocity field. Across simulated and real-robot policies, MSE and cosine error decrease toward the noise endpoint. A CIFAR-10 class-to-image flow provides a contrast: its error is lowest near the middle of the interpolation, while tiny/full model and \(\pi_{0.5}\) errors keep improving toward the noise endpoint. Appendix 11 further analyzes action-horizon and condition-channel variants.

4.3 Beyond Standard LIBERO↩︎

4.3.0.1 LIBERO-Plus distribution shift.

We next run the same tiny-model study directly on LIBERO-Plus [14], a more varied LIBERO extension. We train LIBERO-Plus policies with different action horizons and noise shifts, then evaluate them on the four suites with 2000 episodes per suite.

4.3.0.2 LIBERO-Pro robustness probe.

Finally, we test the full-encoder standard-LIBERO checkpoint whose one-step LIBERO-Long success is 92.8% directly on LIBERO-Pro perturbations [15], without LIBERO-Pro training or selection. The sampler-step trend remains similar on this harder probe: one flow step gives 44.2% mean success and ten flow steps gives 43.5%, with 14 of 16 cells within 5 points.

4.4 Real-Robot Bimanual YAM RSS Evaluation↩︎

We also test bimanual YAM RSS real-robot specialist policies. Each policy starts from the official OpenPI \(\pi_{0.5}\) base checkpoint and is fine-tuned on the corresponding expert-data split from the RSS OpenPI-baseline repository [16]. At evaluation time, we change only the number of inference flow steps. Despite using the same checkpoint, one-step decoding matches or improves ten-step decoding on all three tasks (Table [tab:rss95real95robot]), giving a small-sample but useful cross-architecture check beyond our SimVLA-like models.

5 Limitations↩︎

First, our explanation for why one-step decoding can be better is still mostly intuitive. In CIFAR-10, points near the noise endpoint have high conditional variance over the clean image while our VLA diagnostics improve toward noise endpoint. Second, training time distribution strongly affects one-step performance, but we do not yet know how to choose the optimal shift parameter for a new horizon, condition set, or execution protocol.

6 Conclusion↩︎

This paper challenges the intuition that standard diffusion policies need many denoising steps to produce useful actions. From a condition-target view, VLA one-step generation can be easier than image generation when the encoder understands the observation, language, and state condition: the target is a compact action chunk rather than a high-dimensional image. Across standard LIBERO, LIBERO-Plus, LIBERO-Pro, and a real-robot bimanual YAM RSS evaluation, a simple high-noise time distribution can make standard flow matching produce strong one-step policies without distillation, teacher models, or auxiliary objectives. Before importing complex few-step diffusion machinery, VLA policies should first account for the condition-target structure of action generation.

7 Time Distribution↩︎

The main paper uses the flow-matching convention \(t=0\) for noise and \(t=1\) for clean data. The OpenPI implementation used by \(\pi_0\) [9] uses the opposite coordinate: \(t_{\mathrm{op}}=1\) denotes pure noise and \(t_{\mathrm{op}}=0\) denotes clean data. Its default base distribution is \(t_{\mathrm{op}}\sim\mathrm{Beta}(1.5,1)\), which becomes \(t\sim\mathrm{Beta}(1,1.5)\) under the main-paper coordinate. In that implementation coordinate, a high-noise shift is written as [39] \[t_{\mathrm{op,shifted}} = \frac{\alpha t_{\mathrm{op}}}{1 + (\alpha-1)t_{\mathrm{op}}}.\] This pushes samples toward \(t_{\mathrm{op}}\to1\), which is the same high-noise endpoint that corresponds to \(t\to0\) in Equation 1 . Applying the change of variables \(t=1-t_{\mathrm{op}}\) to both the input and output recovers the formula. Additional Beta and logit-normal schedules were less reliable in our runs; the reported noise-shift experiments use the shifted high-noise schedule specified by \(\alpha\).

8 Time-Condition Injection↩︎

We follow the OpenPI time-conditioning path: a sinusoidal embedding of \(t\) is concatenated with each action embedding along the channel dimension, then a two-layer MLP projects the result back to the model width.

9 Toy Example Implementation Details↩︎

Our training dataset size is 3750 and the test dataset size is 625.

We find cross-entropy helpful in continuous diffusion for text modeling [12], so the total loss is \[\mathcal{L} = \mathcal{L}_{\text{fm}} + \lambda \mathcal{L}_{\text{CE}}.\] We choose \(\lambda = 2\) as the default, convert to \(x_{\text{pred}}\) by \(x_{\text{pred}} = x_t + (1-t)v_{\text{pred}}\), then use \(x_{\text{pred}}\) to calculate the cross-entropy loss. Toy model training hyperparameters are listed in Table 2.

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We also train an AR model on this image-to-text task. A 4-layer AR model with \(d=256\) reaches about 25% exact-match accuracy. Scaling the AR model to \(d=512\) and 8 layers brings it to similar performance as the diffusion model.

10 LIBERO Training Hyperparameters↩︎

Model architecture and training hyperparameters are listed in Table 3 and Table 4. Tiny ablations use a 4-layer Gemma tiny backbone with a 4-layer SigLIP slice; the full-encoder validation keeps the same shallow Gemma action stack but restores the full SigLIP visual encoder. The action head is a standard shallow bidirectional Transformer: it concatenates condition tokens, state tokens, and action-time tokens, applies pre-LayerNorm self-attention and MLP blocks, and projects the action-token outputs to velocities.

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11 Additional LIBERO Controls↩︎

11.0.0.1 Action-loss masking.

LIBERO exposes seven physical action coordinates, while OpenPI keeps a 32-dimensional action tensor for cross-robot compatibility. Our controlled tiny-model experiments supervise only the seven physical coordinates. Table 5 reports the corresponding padded-dimension control. At full-encoder scale, Table [tab:action95mask] shows no clear gain from the mask, so we use mask7 to keep the tiny ablations clean.

11.0.0.2 Direct learned action start.

Because strong one-step action generation is possible under standard flow-matching training, a natural replacement is to replace the noise source with a learnable token and train a direct one-step regression objective. Table 6 shows that this direct baseline is viable, but remains below the stronger high-noise flow-matching runs in Table [tab:time95ablation]. This suggests that noised action tokens provide better training structure beyond merely reducing inference to one step.

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11.0.0.3 Replanning frequency.

LIBERO evaluation queries the policy for an action chunk and executes only the first replan_steps actions before querying again; we denote this interval by \(r\) below. Tables 7–9 and Figure 8 show that this closed-loop interval can strongly affect success: a capable checkpoint can look much worse under an unfavorable replanning choice. The longer-horizon rows are \(r\)-sensitivity ablations from the earlier full-action-loss horizon sweep and were not rerun with mask7. We report flow steps and replanning interval separately throughout the paper.

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11.0.0.4 Velocity diagnostics for horizon and condition controls.

Figures 9 and 10 report fixed-time velocity diagnostics for the same standard-LIBERO ablations.

12 LIBERO-Plus Full-Condition Sweep↩︎

Tables 10 and 11 report the full LIBERO-Plus sweep. Each cell averages four suites with 2000 episodes per suite.

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12.0.0.1 Decoder positional controls.

The deeper-head ablations use the same tiny-model training setup. The per-layer position variant adds a separate learned absolute position embedding inside each action-decoder block. Table 12 keeps train-time \(\alpha\) visible, while Table 13 reports the four-suite \(\alpha=4\) view. Across these ablations, deeper action heads bring no consistent success gain, and the one-step versus ten-step gap remains large.

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References↩︎

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1. The replanning interval is the number of environment steps executed before querying the policy again. It is separate from flow steps, which are solver steps inside one policy query.↩︎

2. Pure-noise replaces the interpolated action input with independent Gaussian noise, so ordinary multi-step Euler decoding over an interpolation trajectory is undefined.↩︎