WAVE-0: Bridging VLA Policies and WAMs with Lightweight Latent Future Prediction

WAVE-0: Bridging VLA Policies and WAMs with Lightweight Latent Future Prediction Haomin Wang1

Anqiong Ji1,3 Ke Wang2,4 Zhongshan Liu3 Ran Zheng3 Zhipeng Zhang1†

Ru Ying3

arXiv:2610.18568v1 [cs.RO] 13 Oct 2026

1 AutoLab, School of Artificial Intelligence, Shanghai Jiao Tong University

2 Awaken Robotics

3 Baidu AI Cloud

4 Zhejiang University

† Corresponding Author

Abstract

Vision–language–action (VLA) policies excel at generalist robotic manipulation but generate actions without explicitly modeling their environmental consequences. World action models (WAMs) incorporate future prediction, yet most rely on costly video generation, while latent alternatives either use predicted futures only as auxiliary targets or infer latent actions from suboptimal visual transitions through costly large-scale video pretraining. We introduce WAVE-0 (World-model-Augmented VLA Execution), a framework that bridges VLAs and WAMs through a lightweight latent world model. By connecting the semantic understanding of pretrained VLAs with explicit future prediction, WAVE-0 allows anticipated action consequences to directly guide action generation. Built on a pretrained VLA, its 257M world model translates VLM-generated latent action plans into predicted future representations that condition the action expert, unifying latent planning, future prediction, and action generation. The world model is trained directly on ground-truth robot actions with a counterfactual ranking objective, requiring neither pixel reconstruction nor large-scale video pretraining. WAVE-0 achieves success rates of 91.47% on RoboTwin 2.0 and 98.7% on LIBERO, along with 88.0%, 61.4%, and 75.0% on LIBERO-Plus, LIBERO-Pro, and LIBERO-Para, respectively. On real-world tasks, it improves the success rate of 𝜋0.5 from 38.3% to 73.3%. These results demonstrate strong manipulation performance and generalization across diverse distribution shifts. Project Page: https://hmwang2002.github.io/release/wave0/ GitHub Repo: https://github.com/AutoLab-SAI-SJTU/WAVE-0

Introduction

Vision–language–action (VLA) policies have made substantial progress in general robotic manipulation by combining the semantic knowledge of pretrained vision–language models with action supervision from robot demonstrations [5– 8, 15, 17, 26]. While effective, this direct observation-to-action mapping does not explicitly capture how actions transform the environment and thereby shape subsequent decisions. World action models (WAMs) address this limitation by incorporating environmental dynamics into action generation, enabling policies to anticipate the future consequences of their actions [4, 21, 38]. Most existing WAMs build on large-scale video generation models, whose pixel-level prediction spends substantial computation on visual details irrelevant to action selection and limits inference efficiency. Recent efforts have tried to reduce this overhead [10, 39], but they still rely on video generation backbones that devote considerable capacity to visual reconstruction.

A promising alternative is to model environmental dynamics in a compact latent space, allowing future prediction to focus on information relevant to action selection rather than visual reconstruction. VLA-JEPA [31] learns latent actions through future-state prediction, while JEPA-WAM [24] uses a shared predictor to model state transitions and generate actions. However, neither approach explicitly conditions action generation on predicted future states, leaving future prediction and action selection only loosely connected. LaWAM [11] guides action generation with predicted latent visual subgoals, but learns its latent actions indirectly from visual transitions through inverse dynamics. While this formulation enables world model pretraining on large-scale videos without action annotations, the inferred latent actions may summarize realized transitions rather than the executable actions that caused them. Consequently, a representation that explains an observed transition may be misaligned with the action a policy must generate before the transition occurs. Moreover, LaWAM pretrains its world model on approximately 4,500 hours of videos, followed by policy-integration pretraining and additional benchmark-specific training, resulting in substantial training costs. This raises a natural question: when domain-specific demonstrations already provide ground-truth executable actions, is such large-scale, indirect pretraining truly more effective than directly training the world model with those actions? We answer this question by grounding future prediction directly in the ground-truth actions of robot trajectories. Our key insight is that demonstrations already pair each action sequence with its resulting observations, providing direct supervision on how actions change the environment. A world model trained with this supervision predicts futures tied to the executed actions rather than to latent actions inferred after the transition occurs, and requires no large-scale pretraining. Moreover, since a pretrained VLA already provides rich semantic understanding and a visual representation space, the world model only needs to predict how this representation evolves under a given action plan, which keeps it lightweight and avoids reconstructing future images. We therefore view semantic understanding in VLAs and future prediction in WAMs as complementary, where the former determines action intent and the latter anticipates its consequences. Building on this view, we introduce WAVE-0 (World-model-Augmented VLA Execution), a framework that bridges VLAs and WAMs through action-grounded latent future prediction. As shown in Figure 1, our latent world model transforms VLM-generated latent action plans into predicted future visual representations that explicitly condition the action expert, yielding a unified pipeline of latent planning, future prediction, and action generation. WAVE-0 follows a two-stage training strategy. In the first stage, we train the latent world model on action-labeled trajectories to predict future visual representations from current observations and ground-truth actions. Besides future and latent delta objectives, a counterfactual ranking objective encourages the model to distinguish the consequences of different action plans. In the second stage, we integrate the frozen world model into pretrained 𝜋0.5 [15] and align VLM-generated latent plans with the learned action representation space. The world model predicts future representations from these plans, and a lightweight resampler compresses them into future-conditioning tokens for the action expert. The planning branch guides action generation only through these predictions, while the expert retains access to the original VLM context. This design allows anticipated action consequences to explicitly guide action generation during both training and inference. On RoboTwin 2.0 [12] and LIBERO [25], WAVE-0 achieves average success rates of 91.47% and 98.7%, improving over 𝜋0.5 by 11.09 and 1.8 percentage points, respectively. On the more challenging LIBERO-Plus [13] and LIBERO-Pro [45], which introduce variations in objects, layouts, camera viewpoints, and instructions, WAVE-0 achieves 88.0% and 61.4%, outperforming all compared methods. On LIBERO-Para [16], it exceeds 𝜋0.5 by 3.6 percentage points under instruction paraphrasing. These gains extend to three real-world tasks, where WAVE-0 improves the average success rate of 𝜋0.5 from 38.3% to 73.3%. Compared with LaWAM, WAVE-0 is also more training-efficient, processing far fewer training examples across RoboTwin 2.0 and real-world tasks. Together, these results demonstrate that action-grounded latent future prediction not only improves a strong VLA with modest cost, but also substantially enhances its robustness to visual, spatial, and language distribution shifts. Our contributions are threefold: (1) We introduce WAVE-0, a framework that connects VLA semantic understanding with WAM future prediction through a 257M lightweight latent world model, enabling anticipated action consequences to guide action generation during training and inference. (2) We develop a two-stage training strategy that learns action-dependent latent dynamics from ground-truth robot actions using counterfactual ranking, then integrates the frozen world model into a pretrained VLA through an explicit prediction bottleneck.

(1) VLA Policy KV Cache

VLM

Noised Visual Tokens

Learnable Action Queries

Noised Action Tokens

Visual Tokens

Text Tokens

Predicted Action Tokens

(3) World Model as Supervisor

Action DiT

Training Only Losswm

GT Future

World Model Predicted Future

(2) Video-generation WAM cross-attn

Text Encoder

Video DiT

KV Cache

KV Cache

VLM

Action DiT

Action DiT

(4) WAVE-0: Bridging VLAs and WAMs

Latent World Model latent action plans (a) Current Observation

VLM Planner (c) Predicted Consequences

future tokens

(b) Latent Action Plans

KV Cache

Action DiT

(d) Executed Actions

Figure 1 Comparison of representative robot policy paradigms. (1) Standard VLAs map vision-language context directly to actions. (2) Video-based WAMs model dynamics through costly video generation. (3) A world model provides auxiliary supervision by predicting the consequences of generated actions during training, leaving the inference pathway unchanged. (4) WAVE-0 translates VLM-generated latent action plans into predicted future representations with a lightweight latent world model, conditioning the action expert during both training and inference.

(3) Evaluations on RoboTwin 2.0, LIBERO, and its generalization benchmarks demonstrate WAVE-0’s effectiveness and generalization under visual and language distribution shifts. Real-world experiments further demonstrate substantial improvements over 𝜋0.5 across three manipulation tasks.

Related Works

2.1

Vision-Language-Action Policies

Vision-language-action (VLA) policies have advanced generalist robotic manipulation by combining pretrained visionlanguage knowledge with robot action supervision [7, 8, 17, 18, 32, 35]. Diffusion-based and flow-based policies further support expressive continuous action generation across diverse tasks and embodiments [5, 6, 15, 26, 33]. Beyond action generation, embodied reasoning and explicit spatial representations have also been explored to enhance VLA policies [30, 40]. Another line of work learns task-centric latent action representations from videos, enabling VLA pretraining across embodiments with reduced reliance on action annotations [9, 34, 37]. Despite these advances, VLAs primarily map observations and instructions to actions, leaving action-dependent environmental dynamics implicit. This motivates integrating explicit future prediction into VLAs, allowing anticipated action consequences to directly guide action generation.

2.2

Visual Generation-Based World Action Models

World action models (WAMs) incorporate future-state prediction into action generation to explicitly model how robot actions affect the environment. Most existing WAMs build on pretrained video models that jointly predict future observations and actions [4, 19, 21–23, 28, 38]. However, large backbones, modeling of action-irrelevant visual details, and iterative denoising incur substantial computational cost and latency. To reduce this cost, Fast-WAM [39] and GigaWorld-Policy [36] retain visual prediction only as training supervision and skip future generation at inference, while other methods reuse future information through asynchronous execution, sparse interactions, or single-pass 3

caching [10, 42, 44]. Beyond video generation, BagelVLA [14] builds on a unified model for understanding and generation to extract predictive visual features through single-step denoising, while ImageWAM [43] guides action generation using denoising features from an image-editing model without decoding future images at inference. However, visual generation backbones remain computationally demanding, motivating lightweight dynamics models that directly predict future visual representations without pixel-level reconstruction.

2.3

Latent World Action Models

Joint-embedding predictive architecture (JEPA) offers a framework for latent world action modeling by predicting representations without pixel reconstruction [1, 2, 20, 27]. VLA-JEPA [31] learns action-relevant latent representations from action-free human videos through world prediction, and then adapts them to robot control. JEPA-WAM [24] uses spatially structured targets that jointly encode current and future observations, providing dense transition supervision for policy learning. However, both methods use predictive supervision to shape policy representations without directly conditioning action generation on predicted visual representations. LaWAM [11] learns latent actions through visual inverse dynamics and uses them to predict visual subgoals that guide action generation. We posit that semantic understanding in pretrained VLAs and future prediction in WAMs are complementary capabilities that should jointly guide action generation. WAVE-0 bridges these paradigms through a lightweight latent world model that learns to predict world state transitions from labeled robot action sequences. It translates VLM-generated latent action plans into future representations that explicitly guide the action expert during both training and inference.

Method

3.1

Problem Formulation

We consider robot manipulation conditioned on a current observation and a task instruction. At time 𝑡, the robot receives an observation 𝑜 𝑡 = (𝐼𝑡, 𝑠𝑡 ), where 𝐼𝑡 = {𝐼𝑡(𝑐) }𝐶 𝑐=1 contains images from 𝐶 cameras and 𝑠 𝑡 is the proprioceptive state. Given an instruction ℓ, the robot generates a continuous action chunk with an action horizon of 𝐻: 𝐴𝑡 = (𝑎 𝑡, . . ., 𝑎 𝑡+𝐻 −1 ),

𝑎 𝑡 ∈ R 𝑑𝑎 .

(1)

We learn a policy from demonstrations to generate actions conditioned on the current observation and instruction: 𝐴𝑡 ∼ 𝜋 𝜃 (· | 𝑜 𝑡, ℓ).

(2)

WAVE-0 decomposes this process into latent action planning, future world state prediction, and future-conditioned action generation. Let 𝑆𝑡 = E (𝐼𝑡 ) denote the world state representation in a fixed visual embedding space. AVLM planner 𝑓 𝜂 produces a latent action plan, a world model 𝑔 𝜙 predicts its consequences, and an action expert 𝑝 𝜓 generates actions using both the original context and the predicted future: b𝑎 = 𝑓 𝜂 (𝑜 𝑡, ℓ), 𝑍

b𝑎 ), 𝑆b𝑡+ℎ = 𝑔 𝜙 (𝑆𝑡, 𝑠𝑡, 𝑍

𝐴𝑡 ∼ 𝑝 𝜓 (· | 𝑜 𝑡, ℓ, 𝑆b𝑡+ℎ ),

(3)

where ℎ denotes the future observation offset.

3.2

Model Architecture

Built on pretrained 𝜋0.5 [15], WAVE-0 combines vision-language understanding with explicit dynamics prediction through latent action planning, future world state prediction, and future-conditioned action generation. The training procedure is conducted in two sequential stages. In the first stage, the latent world model jointly learns action representations and latent dynamics from visual observations, proprioceptive states, and ground-truth action sequences to predict future world states in a fixed visual embedding space. In the second stage, we integrate the frozen world model into 𝜋0.5 and train the VLM to produce latent action plans aligned with the learned action representation space. The world model converts these plans into predicted future visual representations, which condition the action expert alongside the original vision-language context. Latent World Model. We learn action-conditioned latent dynamics in a fixed visual embedding space. We obtain

𝑆𝑡 = E (𝐼𝑡 ) and 𝑆𝑡+ℎ = E (𝐼𝑡+ℎ ) using the frozen SigLIP [41] encoder and visual projector from pretrained 𝜋0.5, followed 4

Stage 1: Latent World Model Training

Stage 2: Future-Conditioned Policy Fine-tuning

SigLIP Future Images

SigLIP

GT Future

Future & Residual Supervision Current Images

GT Actions

Action Encoder

Latent World Model

Current Images

Robot State

State Encoder

GT Actions

Action Encoder

Latent World Model

Resampler

Alignment

Latent Action Plans

Future Tokens

Noise

Predicted Future

PaliGemma VLM Planner

State Encoder

KV

Action Expert

Robot State

Same Current Observation

Mismatched Actions

Counterfactual Ranking

World Model

GT & Predicted Future

Language Instruction

Negative Future

Learnable Action Queries

Actions

Figure 2 Overview of WAVE-0. Stage 1: The latent world model learns action-conditioned dynamics in a fixed visual embedding space, trained with future-representation prediction, latent residual supervision, and counterfactual action ranking. Stage 2: The VLM generates latent action plans aligned with the representations from the frozen action encoder. The frozen world model predicts the visual consequences of these plans, and a resampler compresses them into future tokens that condition the action expert alongside the original VLM context.

by spatial pooling. An action encoder embeds the ground-truth action sequence conditioned on the current proprioceptive state, yielding 𝑍 𝑎 = E 𝑎 ( 𝐴𝑡, 𝑠𝑡 ), while a state encoder produces 𝑧 𝑠 = E 𝑠 (𝑠𝑡 ). A Transformer with action-conditioned AdaLN-Zero blocks [29] predicts a latent residual, which is added to the current representation to obtain the predicted future: b Δ𝑆b = W𝜙 (𝑆𝑡, 𝑧 𝑠, 𝑍 𝑎 ), 𝑆b𝑡+ℎ = 𝑆𝑡 + Δ𝑆. (4) We supervise the future representation with a cosine distance loss and the state change with a SmoothL1 loss: Lfuture = 𝑑cos ( 𝑆b𝑡+ℎ, 𝑆𝑡+ℎ ),

b 𝑆𝑡+ℎ − 𝑆𝑡 ), Ldelta = SmoothL1(Δ𝑆,

(5)

where 𝑑cos denotes mean token-wise cosine distance. To encourage action dependence, we introduce a counterfactual ranking loss. Keeping the current observation fixed, we e𝑡 to obtain: replace the demonstrated actions with a mismatched sequence 𝐴 − e𝑡, 𝑠𝑡 )). 𝑆b𝑡+ℎ = 𝑆𝑡 + W𝜙 (𝑆𝑡, 𝑧 𝑠, E 𝑎 ( 𝐴

(6)

The loss favors demonstrated actions over mismatched actions when predicting the same observed future: h i − Lrank = 𝑟 𝑚 + 𝑑cos ( 𝑆b𝑡+ℎ, 𝑆𝑡+ℎ ) − 𝑑cos ( 𝑆b𝑡+ℎ , 𝑆𝑡+ℎ ), +

(7)

where [𝑥] + = max(0, 𝑥), 𝑚 = 0.1, and 𝑟 ∈ {0, 1} masks unchanged negative sequences. We jointly optimize the action encoder, state encoder, and world model using the following objective: Lstage1 = Lfuture + 0.5 Ldelta + 0.1 Lrank .

(8)

Latent Action Planning. We integrate the frozen latent world model into pretrained 𝜋0.5 and train its PaliGemma VLM [3] to generate latent action plans in the action representation space learned in Stage 1. Specifically, we append learnable latent action queries 𝑄 to the VLM input sequence and transform the output hidden states 𝑈𝑄 into latent action b𝑎 = Π𝑎 (LN(𝑈𝑄 )), where Π𝑎 is a learned linear projection. These tokens condition the frozen world model tokens via 𝑍 to predict future visual representations: b𝑎 ). 𝑆b𝑡+ℎ = 𝑆𝑡 + W𝜙 (𝑆𝑡, 𝑧 𝑠, 𝑍 (9)

b𝑎 with the target representations 𝑍 𝑎 produced by the frozen action We supervise latent action planning by aligning 𝑍 encoder: b𝑎, 𝑍 𝑎 ) + 0.5 SmoothL1( 𝑍 b𝑎, 𝑍 𝑎 ). Lalign = 𝑑cos ( 𝑍 (10) To supervise the predicted visual consequences, we reuse the future representation and residual losses in Eq. 5, evaluated b𝑎 as the action condition: with 𝑍 Lworld = Lfuture + 0.5 Ldelta . (11) Future-Conditioned Action Generation. A lightweight resampler pools and projects the predicted future representation

into conditioning tokens 𝐹𝑡 = R ( 𝑆b𝑡+ℎ ). We prepend these tokens to the noisy action tokens in the action expert, enabling it to attend to both the original VLM context and the predicted future. We exclude latent-action query tokens from the context passed to the expert, so that the planning branch guides action generation only through its predicted visual consequences. In Stage 2, we jointly optimize the VLM planner, future-conditioning resampler, and action expert while keeping the world model frozen:
Lstage2 = Lflow + 𝜆 WAM Lworld + 𝜆 align Lalign, (12) where Lflow is the flow-matching objective used in 𝜋0.5, 𝜆WAM scales the auxiliary supervision, and 𝜆align controls the relative weight of latent-action alignment.

Experiments

4.1

Implementation Details

We initialize the VLM and action expert from pretrained 𝜋0.5 . For world modeling, we use a frozen copy of its SigLIP encoder and visual projector to extract 2048-dimensional visual features, which are spatially pooled into a 4 × 4 grid, yielding 16 tokens per camera. The latent world model processes these representations using a 12-layer Transformer with a hidden dimension of 1024, 16 attention heads, and an MLP dimension of 4096. The resampler then pools the predicted future representations to a 2 × 2 grid per camera and projects them into 12 conditioning tokens for the action expert, which retains the original flow-matching formulation of 𝜋0.5 . The world model, action encoder, and state encoder together comprise approximately 257M trainable parameters in Stage 1, while the full WAVE-0 contains approximately 4.3B parameters. We train with AdamW using a default peak learning rate of 10−4, weight decay of 0.01, and a cosine learning rate schedule. Benchmark-specific training and inference configurations are provided in Appendix A.1. Table 1 Success rates (%) on LIBERO and RoboTwin 2.0. Bold and underlined values indicate the best and second-best results, respectively. Δ denotes improvement over 𝜋0.5 . (a) Results on LIBERO.

(b) Results on RoboTwin 2.0.

Method

Spatial

Object

Goal

Long

Avg.

Method

Clean

Randomized

Avg.

OpenVLA GR00T N1 𝜋0 Motus LingBot-VA Fast-WAM ImageWAM VLA-JEPA JEPA-WAM LaWAM 𝜋0.5

84.7 94.4 96.8 96.8 98.5 98.2 97.2 96.2 95.6

88.4 97.6 98.8 99.8 99.6

79.2 93.0 95.8 96.6 97.2 97.0

53.7 90.6 85.2 97.6

76.5 93.9 94.1 97.7 98.5 97.6 98.4 97.2 96.7 98.6 96.9

𝜋0 ABot-M0 Motus GigaWorld-Policy LingBot-VA Fast-WAM AHA-WAM LaWAM ImageWAM 𝜋0.5 𝜋0.5 + WM

65.92 81.20 88.66 86.36 92.90 91.88

58.40 80.40 87.02 85.04 91.50 91.78 92.20 89.80

62.16 80.80 87.84 85.70 92.20 91.83 92.80 91.22

98.7

Δ Improvement

WAVE-0 (Ours)

Δ Improvement

99.4

98.8 98.6 -0.2

100.0

99.2 99.6 99.4 99.6 98.2 100.0

+1.8

98.8

97.2 97.2 98.4 98.0 98.6 +0.6

98.5

95.2 98.4 95.8 94.6 97.0 92.4 97.6 +5.2

+1.8

WAVE-0 (Ours)

93.40

92.64 93.20 81.12 89.48 91.46 +10.34

93.56

93.38

79.64 89.54 91.48 +11.84

80.38 89.51 91.47 +11.09

4.2

Evaluation on LIBERO

We evaluate on the four LIBERO suites: Spatial, Object, Goal, and Long, covering 40 tasks. Our training data comprise 1,693 trajectories and 273,465 frames across these suites. As shown in Table 1a, WAVE-0 achieves an average success rate of 98.7%, the highest among the compared methods, improving over 𝜋0.5 by 1.8 percentage points. The largest gain occurs on the Long suite, where success increases from 92.4% to 97.6%. This suggests that anticipating action consequences is particularly beneficial for sequential manipulation, where the outcome of each action affects subsequent steps. WAVE-0 also achieves 100.0% on Object and 98.6% on Goal, supporting the effectiveness of latent future conditioning across diverse manipulation tasks.

4.3

Evaluation on RoboTwin 2.0

RoboTwin 2.0 is a bimanual manipulation benchmark with 50 tasks. Following prior work [4, 21, 39], we train a single policy on all tasks using 2,500 demonstrations collected in clean scenes and 25,000 demonstrations collected under heavy domain randomization. As shown in Table 1b, WAVE-0 achieves an average success rate of 91.47%, improving over 𝜋0.5 by 11.09 percentage points, with consistent gains in both clean (81.12% to 91.46%) and randomized (79.64% to 91.48%) scenes. Compared with LaWAM, which also models dynamics in latent space, WAVE-0 achieves a higher average success rate (91.47% vs. 91.22%) and remains more robust under randomization (91.48% vs. 89.80%). Per-task results in Appendix Table 13 further show large gains over 𝜋0.5 on long-horizon tasks with multiple dependent subgoals, such as Stack Blocks Three (+23.0) and Stack Bowls Three (+33.0), suggesting that anticipating the consequences of latent action plans benefits sequential manipulation. Table 2 Success rates (%) on LIBERO-Plus and LIBERO-Pro. Bold and underlined values indicate the best and second-best results, respectively. Δ denotes improvement over 𝜋0.5 . LIBERO-Plus

Method

OpenVLA Fast-WAM ImageWAM VLA-JEPA JEPA-WAM LaWAM 𝜋0.5 WAVE-0 (Ours)

Δ Improvement

4.4

LIBERO-Pro

Camera

Robot

Language

Light

Background

Noise

Layout

Avg.

Avg.

0.8 16.4

3.5 44.5 50.3 67.1 59.2 71.6 75.3

23.0 68.9

8.1 78.2 98.1 95.6 93.3 93.5 96.7

34.8 53.7 85.5 93.6 94.6 94.1 96.8

15.2 37.7

28.5 60.7 80.5 85.1 76.1 83.3 86.2

15.6 51.5 83.1 79.5 79.2 76.6 84.5

52.0 40.2 48.7 48.3 41.9 52.7 53.0

80.8

63.3 79.2 37.2 69.4 75.9 +6.5

89.3

+14.0

91.4

85.4 68.2 87.1 82.6 86.1 +3.5

98.4

98.1

+1.7

+1.3

93.8

66.3 83.6 69.4 84.3 80.6 -3.7

87.7

88.0

61.4

+1.5

+3.5

+8.4

Out-of-Distribution Generalization

We evaluate generalization on LIBERO-Plus, LIBERO-Pro, and LIBERO-Para, directly using the model trained on LIBERO without additional fine-tuning. LIBERO-Plus evaluates robustness across seven perturbation categories, including camera viewpoints, robot initial states, language instructions, lighting, backgrounds, sensor noise, and object layouts. As shown in Table 2, WAVE-0 achieves an overall success rate of 88.0%, outperforming all compared methods and exceeding 𝜋0.5 by 3.5 percentage points. It improves performance in six of the seven categories, with the largest gains under robot initial-state perturbations (+14.0) and camera viewpoint changes (+6.5). On LIBERO-Pro, which measures generalization under changes to objects, spatial configurations, instructions, and environments, WAVE-0 achieves 61.4% success, the highest among the compared methods and an 8.4-point improvement over 𝜋0.5 . We further assess robustness to instruction paraphrasing on LIBERO-Para, where WAVE-0 improves success from 71.4% to 75.0%. Together, these results indicate that latent future conditioning improves generalization under visual, spatial, and linguistic distribution shifts.

t0

t1

t2

t3

Keyboard Pushback

t0

t1

t2

t3

Book Organization

t0

t1

t2

t3

WAVE-0

LaWAM

Image

USB Storage

(a) Real-world robot rollouts

(b) Attention visualization

Figure 3 Real-world rollouts and attention visualization. (a) Key frames from WAVE-0 rollouts on the three real-world tasks. (b) Attention maps on two RoboTwin 2.0 tasks. Table 3 Real-world success rates (%). Each task is evaluated over 20 trials.

4.5

Table 4 ciency.

Comparison of training sample effi-

Method

Book USB Keyboard Avg.

Training stage

LaWAM WAVE-0

ImageWAM LaWAM 𝜋0.5

50.0 40.0 40.0

307.20M 12.80M 345.60M

25.0 35.0 45.0

45.0 55.0 30.0

40.0 43.3 38.3

WAVE-0

85.0

65.0

70.0

73.3

Shared pretraining Policy per task Total for three tasks

10.24M 7.68M 33.28M

Δ Improvement

+45.0

+20.0

+40.0

+35.0

Amortized per task 115.20M 11.09M

Evaluation on Real-World Tasks

We evaluate WAVE-0 on three real-world tasks with a dual-arm AgileX Piper platform, namely Book Organization, USB Storage, and Keyboard Pushback, which require rearranging objects in clutter, precise insertion, and long-horizon bimanual coordination, respectively. For each task, we collect 200 demonstrations, train a separate model for each method on the same data, and evaluate it over 20 trials with diverse initial configurations (Figure 3(a)). As shown in Table 3, WAVE-0 achieves the best performance on all three tasks, reaching an average success rate of 73.3% compared with 43.3% for the strongest baseline LaWAM and 40.0% for ImageWAM. Relative to 𝜋0.5, WAVE-0 nearly doubles the average success rate from 38.3% to 73.3%.

4.6

Analysis

Training Efficiency. WAVE-0 learns latent dynamics from action-labeled target demonstrations without large-scale video

pretraining. In contrast, LaWAM performs 100k steps of world model pretraining and 200k steps of policy-integration pretraining with a global batch size of 1,024, processing 307.2M examples before benchmark-specific training. On RoboTwin 2.0, the two-stage training of WAVE-0 requires approximately 670 H100 GPU hours and processes 76.8M examples, compared with 1,280 H100 GPU hours and 102.4M examples for LaWAM’s benchmark-specific training alone. Across three real-world tasks, WAVE-0 processes 33.28M examples, compared with 345.60M for LaWAM, including shared pretraining and task-specific policy training. Amortized per task, these budgets are 11.09M and 115.20M, respectively, with WAVE-0 achieving higher success rates, as shown in Tables 4 and 3. These results support the efficiency of action-grounded latent world modeling without additional large-scale video pretraining. Attention Visualization. Figure 3(b) compares attention from action queries to current main-view image patches at the

final denoising step. In the illustrated examples, WAVE-0 exhibits more localized attention around the manipulated object and target bottle, whereas LaWAM shows more dispersed responses over the robot arm, image boundaries, and background regions.

4.7

Ablation Studies

4.7.1

Effects of World Model Integration Strategy

We investigate how the learned world model should be integrated into the policy by comparing 𝜋0.5, 𝜋0.5 + WM, and WAVE-0 on RoboTwin 2.0. As illustrated in Figure 1, 𝜋0.5 + WM uses the world model to predict future representations from generated actions and provides an auxiliary training loss against the observed future. In contrast, WAVE-0 explicitly conditions action generation on predicted futures during both training and inference. Both variants use the same frozen world model trained in Stage 1. As shown in Table 1b, auxiliary supervision improves average success from 80.38% to 89.51%, supporting the value of the learned latent dynamics for policy learning. WAVE-0 further increases success to 91.47%, outperforming 𝜋0.5 + WM by 1.98 and 1.94 percentage points in clean and randomized settings, respectively. These results indicate that while world model supervision already yields substantial gains, explicitly conditioning action generation on predicted futures provides consistent additional benefits. More broadly, they support the central premise of WAM that anticipating the consequences of actions improves action generation, and show that this benefit can be realized in a compact latent space without video generation. Effects of Training Objectives

0.1538

0.15

0.10

(b) Margin satisfaction 0.1648

0.1218

0.0717

Without rank With rank

0.05 0.0016

0.0018

0.0019

0.0020

5k

10k

15k

20k

0.00

Margin satisfaction rate (%)

(a) Action sensitivity gap

dwrong − dcorrect

100

50

44.75

Without rank With rank

25 0.00

0.00

0.00

0.00

5k

10k

15k

20k

Stage 1 training steps

(c) Stage 1: ranking supervision

(d) Stage 2: training objectives

w/o rank With rank

90

w/o world, align w/o align Full stage2

65

90

88.0 61.4

85.4 85

60

80

58.4

55

LIBERO-Plus

89.50

87.30 75.10

75

Stage 1 training steps

Success rate (%)

Counterfactual ranking in Stage 1. We remove Lrank while retaining Lfuture and Ldelta, and evaluate both variants on the same 2,048 samples from 256 episodes. Holding observations and robot states fixed, we measure the cosine prediction errors under demonstrated and mismatched actions against the same ground-truth future, denoted by 𝑑correct and 𝑑wrong . We report the mean gap 𝑔 = 𝑑wrong − 𝑑correct over valid samples and the percentage satisfying 𝑔 ≥ 0.1, termed the action sensitivity gap and margin satisfaction rate, respectively. As shown in Figure 4(a,b), ranking supervision increases the gap to 0.1648 and margin satisfaction to 89.5% at 20k steps, compared with 0.0020 and 0% without it. It also improves success by 2.6 and 3.0 percentage points on LIBERO-Plus and LIBERO-Pro, respectively, supporting the value of action-dependent dynamics for generalization, as shown in Figure 4(c).

Success rate (%)

4.7.2

65 88.0 61.4

85

84.6

85.3 58.0

80

LIBERO-Pro

59.7

60

55

LIBERO-Plus

LIBERO-Pro

Figure 4 Effects of training objectives.

Auxiliary objectives in Stage 2. Starting from Lflow

alone, adding Lworld improves success by 0.7 and 1.7 percentage points on LIBERO-Plus and LIBERO-Pro, respectively. Adding Lalign yields further gains of 2.7 and 1.7 points, reaching 88.0% and 61.4%, as shown in Figure 4(d). These results support the complementary benefits of supervising latent plans through predicted visual consequences and alignment with learned action representations.

Conclusion

We presented WAVE-0, a framework that bridges VLA policies and world action models through a lightweight latent world model. Instead of generating future frames or using predicted futures only as auxiliary training targets, WAVE-0 translates VLM-generated latent action plans into predicted future visual representations that explicitly condition the action expert during both training and inference. The world model is grounded in ground-truth robot actions and trained with counterfactual ranking supervision, which encourages action-dependent dynamics and improves policy generalization. Built on 𝜋0.5, WAVE-0 substantially improves performance on simulation and real-world benchmarks without large-scale world model pretraining, suggesting that grounding latent dynamics in executable actions offers an efficient path toward world-model-augmented robot policies.

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Appendix

A.1

Training and Evaluation Details on Simulated Benchmarks

LIBERO. All models are trained on 8 NVIDIA RTX PRO 6000 Blackwell GPUs with 96 GB memory per GPU, using Accelerate DDP, bf16 mixed precision, and the AdamW optimizer. We use a global batch size of 512, a peak learning rate of 1 × 10−4, weight decay of 1 × 10−2, and gradient clipping of 1.0. The learning rate is linearly warmed up for 1,000 steps followed by cosine decay. Training consists of two stages: the latent world model is pretrained for 20k steps, followed by 10k steps of action-policy training with the pretrained world model frozen. Stage 1 takes approximately 10 hours, while Stage 2 takes approximately 13 hours. For LIBERO, we use two camera views, a 7-dimensional action space, and an 8-dimensional proprioceptive state. The policy predicts 32-step action chunks and replans every 10 steps. Table 5 Training details of WAVE-0 on LIBERO. Configuration

Number of GPUs Precision Optimizer Global batch size Peak learning rate Final learning rate Weight decay Warmup steps Gradient clipping Training steps Action chunk size 𝐻 World model horizon ℎ Latent action queries World model

Stage 1: World Model

Stage 2: Action Policy

8 bf16 AdamW 512 1 × 10−4 2.5 × 10−6 1 × 10−2 1,000 1.0 20,000 32 9 – Trainable

8 bf16 AdamW 512 1 × 10−4 1 × 10−6 1 × 10−2 1,000 1.0 10,000 32 9 10 Frozen

12

RoboTwin 2.0. We train WAVE-0 on 8 NVIDIA H100 GPUs using Accelerate DDP and bf16 mixed precision, with

a global batch size of 512. Stage 1 takes approximately 6 hours for 50k steps, while Stage 2 takes approximately 78 hours for 100k steps, with the world model frozen. Observations include three camera views and a 14-dimensional proprioceptive state, with a 14-dimensional action space. Actions and proprioceptive states are normalized using dataset quantiles. The policy predicts and executes 32-step action chunks. In Stage 2, 𝜆 WAM warms up to 1.0 over 1,000 steps. We keep 𝜆align = 1.0 for the first 5k steps, decay it to 0.1 using a cosine schedule over the next 15k steps, and hold it constant thereafter. We evaluate all 50 tasks using 100 episodes per task under each of the clean and randomized settings. Success rates are averaged over tasks, and the overall score is the mean across both settings. Table 6 summarizes the training configuration. Table 6 Training details of WAVE-0 on RoboTwin 2.0. Configuration

Number of GPUs Precision Optimizer Global batch size Peak learning rate Final learning rate Weight decay Warmup steps Gradient clipping Training steps Action chunk size 𝐻 World model horizon ℎ Latent action queries World model

A.2

Stage 1: World Model

Stage 2: Action Policy

8 bf16 AdamW 512 1 × 10−4 2.5 × 10−6 1 × 10−2 1,000 1.0 50,000 32 31 – Trainable

8 bf16 AdamW 512 1 × 10−4 1 × 10−6 1 × 10−2 1,000 1.0 100,000 32 31 32 Frozen

Experimental Details on Real-World Tasks

Real-robot experiments. We evaluate 𝜋0.5, WAVE-0, LaWAM, and ImageWAM on a dual-arm Piper robot across

three real-world manipulation tasks: Book Organization, USB Storage, and Keyboard Pushback. Book Organization requires placing a book into the designated book organizer, USB Storage requires transferring a USB drive from the tabletop into a designated storage container, and Keyboard Pushback requires pushing the keyboard back into the drawer. Figure 5 shows representative rollouts of WAVE-0. The complete real-robot dataset contains 600 demonstrations, with 200 demonstrations per task, comprising 310,099 frames recorded at a nominal frequency of 15 Hz. Each observation includes RGB images from one fixed head camera and two wrist cameras, together with a 14-dimensional proprioceptive state. Actions are represented as 14-dimensional absolute joint commands. Each task-specific policy is trained on its corresponding 200 demonstrations. Training is performed on eight NVIDIA A800 GPUs with 80 GB of memory per GPU, using distributed data parallelism, BF16 mixed precision, and the AdamW optimizer. During closed-loop evaluation, 𝜋0.5 and WAVE-0 predict 32-step action chunks, whereas LaWAM and ImageWAM output 18-step and 16-step action chunks, respectively. 𝜋0.5 and WAVE-0 execute 10 actions per policy inference, while LaWAM and ImageWAM execute 8.

13

Book Organization

t0

t1

t2

t3

t4

USB Storage

t0

t1

t2

t3

t4

Keyboard Pushback

t0

t1

t2

t3

t4

Figure 5 Representative rollouts of WAVE-0 on three real-world manipulation tasks.

𝜋0.5 . For each real-robot task, we independently fine-tune 𝜋0.5 on the corresponding 200 demonstrations for 30k training steps, using a global batch size of 256. We maintain an exponential moving average of the policy parameters with a decay rate of 0.99 and use the resulting EMA checkpoints for real-robot evaluation. The policy predicts 32-step action chunks and executes 10 actions before replanning. The optimization configuration is summarized in Table 7. Table 7 Training details of 𝜋0.5 in the real-world experiments. Configuration

𝜋0.5

Number of GPUs Precision Optimizer Global batch size Peak learning rate Final learning rate Weight decay Warmup steps Gradient clipping Training steps Action chunk size 𝐻

8 bf16 AdamW 256 2.5 × 10−5 2.5 × 10−6 1 × 10−10 1,500 1.0 30,000 32

WAVE-0. WAVE-0 is trained in two stages. In Stage 1, the latent world model is pretrained for 40k steps using all 600 real-robot demonstrations collected from the three manipulation tasks. In Stage 2, the pretrained world model is frozen, and a task-specific action policy is independently trained for 30k steps using the corresponding 200 demonstrations from each task. Both stages use linear learning-rate warmup followed by cosine decay. The world model predicts visual representations 32 steps into the future, while the action policy generates 32-step action chunks using 32 latent action queries. The detailed training configuration is summarized in Table 8. LaWAM. For each real-robot task, LaWAM is independently trained on the corresponding 200 demonstrations for 100k optimization steps. Training is performed on eight GPUs with a per-GPU batch size of 16, resulting in a global batch size of 128. The learning rate is linearly warmed up for 500 steps and subsequently decayed using a cosine schedule. LaWAM uses three RGB camera views as input and does not condition its flow-matching action head on the robot state.

14

Table 8 Training details of WAVE-0 in the real-world experiments. Configuration

Number of GPUs Precision Optimizer Global batch size Peak learning rate Final learning rate Weight decay Warmup steps Gradient clipping Training steps Action chunk size 𝐻 World model horizon ℎ Latent action queries World model

Stage 1: World Model

Stage 2: Action Policy

8 bf16 AdamW 256 1 × 10−4 2.5 × 10−6 1 × 10−2 2,000 1.0 40,000 32 32 – Trainable

8 bf16 AdamW 256 5 × 10−5 1 × 10−6 1 × 10−2 1,500 1.0 30,000 32 32 32 Frozen

Its internal flow horizon is 50, from which the first 18 valid actions are returned during inference. The main training parameters are summarized in Table 9. ImageWAM. For each real-robot task, ImageWAM is independently trained on the corresponding 200 demonstrations for 60k optimization steps. Training is performed on eight GPUs with a per-GPU batch size of 16, resulting in a global batch size of 128. We train the action prediction module using BF16 mixed precision and the AdamW optimizer. The learning rate is linearly warmed up for 3,000 steps, corresponding to 5% of the total training budget, and then decayed using a cosine schedule. ImageWAM jointly learns visual dynamics and action prediction from the three camera views and produces a 16-step absolute joint-action chunk during inference. The main training parameters are summarized in Table 10. Table 9 Training details of LaWAM in the real-world experiments. Configuration Number of GPUs Precision Optimizer Per-GPU batch size Global batch size Peak learning rate Final learning rate Weight decay Warmup steps Gradient clipping Training steps Internal flow horizon Output action horizon 𝐻

Table 10 Training details of ImageWAM in the real-world experiments.

LaWAM 8 bf16 AdamW 16 128 1 × 10−4 5 × 10−7 1 × 10−8 500 1.0 100,000 50 18

Configuration ImageWAM Number of GPUs 8 Precision bf16 Optimizer AdamW Per-GPU batch size 16 Global batch size 128 Peak learning rate 1 × 10−4 Final learning rate 1 × 10−6 Weight decay 1 × 10−2 Warmup steps 3,000 Gradient clipping 1.0 Training steps 60,000 Action chunk size 𝐻 16

Inference efficiency. Our lightweight latent world model adds only modest inference overhead to 𝜋0.5 . As shown

in Table 11, WAVE-0 increases the mean server-side latency from 287.1 ms to 305.9 ms, an additional 18.8 ms, while enabling explicit future conditioning during action generation. Compared with ImageWAM, an efficient visual generation-based WAM requiring 582.6 ms per request, WAVE-0 reduces latency by 47.5%. LaWAM achieves a lower latency of 223.9 ms with a smaller model of 2.3B parameters, compared with 4.3B for WAVE-0. It also returns 18 actions per inference request, whereas WAVE-0 predicts 32. These differences in model size and inference configuration should be considered when interpreting the latency comparison. 15

Table 11 Mean server-side inference latency in the real-world experiments. Model

Checkpoint

A.3

Mean server latency

30k 100k 60k 30k

𝜋0.5 LaWAM ImageWAM WAVE-0

287.1 ms 223.9 ms

582.6 ms 305.9 ms

LIBERO-Pro Detailed Results Table 12 Results on LIBERO-Pro across different perturbation categories.

Method

Avg.

OpenVLA 𝜋0 𝜋0.5 Fast-WAM ImageWAM LaWAM VLA-JEPA JEPA-WAM

52.0 44.0 53.0 40.2 48.7 52.7 48.3 41.9

Obj. 97.0 95.0 97.0 87.0 95.6 97.8 96.6 85.4

WAVE-0 (Ours)

61.4

98.0

A.4

Spatial Sem. Task 97.0 0.0 97.0 0.0 97.0 0.01 58.0 32.2 95.2 49.6 93.2 52.6 93.0 51.4 69.0 51.6 54.6 97.4 48.0

Pos. 0.0 0.0 20.0 0.0 18.0 28.8 13.4 0.2

Env.

Obj.

89.0

98.0

60.0 46.0 36.2 56.6 43.4 22.6 35.0 64.2

94.0 98.0

93.2 91.0 91.8 90.2 92.8 83.0

Pos. 0.0 0.0 0.2 0.8 0.0 10.6 0.00 0.0

Object Sem. Task 98.0 0.0 90.0 0.0 96.0 0.0 98.6 9.2 99.6 6.6 99.6 10.0 99.8 10.0 99.0 10.0

Env. 0.0 29.0 0.7 35.4 40.6 61.0 49.8 14.0

54.2

99.8

70.4

13.2

RoboTwin Detailed Results

16

Obj. 96.0 94.0

Pos. 0.0 0.0

97.0

38.0

56.6 68.2 68.4 77.4 57.8 85.6

0.2 3.4 9.0 2.20 0.0 23.4

Goal Sem. 98.0 93.0 97.0 92.2 98.2

Task 0.0 0.0 0.0 8.6 10.0

98.4

28.4

98.2 72.6 97.8

12.0 11.2 21.4

Env. 98.0

39.0 46.0 7.6 31.4 25.6 35.4 46.6 47.0

Obj. 81.0 79.0 92.0

52.4 53.6 62.8 53.2 36.8 70.2

Pos. 0.0 0.0 0.1 0.0 0.0 1.2 0.2 0.0

Long Sem. Task 96.0 0.0 82.0 0.0 93.0 0.0 79.4 9.6 96.2 10.0 96.6 23.0 91.0 9.2 85.4 9.4

11.4

97.2

27.6

Env. 85.0

27.0 46.0 45.8 50.2 51.2 59.6 61.6 63.4

Table 13 Per-task success rates (%) on RoboTwin 2.0. Task

WAVE-0 (Ours)

Clean Adjust Bottle 100 Beat Block Hammer 100 Blocks Ranking RGB 100 Blocks Ranking Size 90 Click Alarmclock 100 Click Bell 100 Dump Bin Bigbin 95 Grab Roller 100 Handover Block 97 Handover Mic 97 Hanging Mug 47 Lift Pot 100 Move Can Pot 91 Move Pillbottle Pad 98 Move Playingcard Away 100 Move Stapler Pad 55 Open Laptop 97 Open Microwave 58 Pick Diverse Bottles 78 Pick Dual Bottles 94 Place A2B Left 91 Place A2B Right 99 Place Bread Basket 87 Place Bread Skillet 90 Place Burger Fries 98 Place Can Basket 84 Place Cans Plasticbox 97 Place Container Plate 97 Place Dual Shoes 94 Place Empty Cup 100 Place Fan 91 Place Mouse Pad 90 Place Object Basket 91 Place Object Scale 95 Place Object Stand 93 Place Phone Stand 97 Place Shoe 99 Press Stapler 93 Put Bottles Dustbin 90 Put Object Cabinet 86 Rotate QRcode 93 Scan Object 95 Shake Bottle 100 Shake Bottle Horizontally 100 Stack Blocks Three 97 Stack Blocks Two 100 Stack Bowls Three 82 Stack Bowls Two 93 Stamp Seal 84 Turn Switch 70 Average 91.46

Rand. 100 99 99 87 99 100 98 100 91 99 49 100 94 97 99 52 99 74 81 96 94 95 91 85 94 76 99 99 97 100 92 85 89 95 95 97 100 96 85 83 95 95 99 100 94 100 81 94 79 77 91.48

Motus

𝜋0.5

Fast-WAM

LingBot-VA

LaWAM

Clean Rand. Clean Rand. Clean Rand. Clean Rand. Clean Rand. 100 99 89 93 100 100 90 94 100 100 92 94 95 88 99 97 96 98 90 93 92 90 99 97 100 100 99 98 97 100 78 74 75 63 94 98 94 96 93 89 100 99 100 100 100 100 99 100 100 100 100 98 100 100 100 100 100 100 100 100 86 91 95 91 97 96 89 96 97 95 100 100 100 100 100 100 100 100 100 100 59 45 86 73 95 81 99 78 96 87 90 88 78 63 99 100 94 96 93 98 40 49 38 38 58 62 40 28 51 43 93 88 96 99 100 100 100 99 100 99 72 72 34 74 90 88 94 97 98 93 74 80 93 96 100 99 99 99 97 90 97 93 100 96 100 100 100 99 100 100 42 27 83 85 77 64 91 79 94 87 99 98 95 91 98 100 92 94 100 100 28 14 95 91 62 45 82 86 41 43 82 78 90 91 80 85 89 82 91 88 97 94 96 90 100 96 100 99 100 95 93 90 88 79 95 93 97 93 98 91 97 92 91 87 93 99 97 95 89 94 76 80 91 94 91 93 97 95 92 85 80 73 86 83 90 93 95 90 90 83 90 90 98 98 96 99 97 95 93 96 56 58 81 76 71 69 81 84 92 65 79 76 98 94 99 96 100 99 100 95 93 96 98 99 96 100 99 97 100 100 87 80 93 87 94 88 94 89 98 94 98 96 99 98 100 100 100 100 99 100 69 59 91 87 96 96 99 93 92 93 71 73 66 68 83 89 93 96 91 84 77 70 81 87 89 88 91 88 92 90 81 78 88 85 90 97 96 95 95 88 81 83 98 97 90 94 99 96 92 93 92 90 87 86 97 99 97 97 93 94 97 98 99 97 96 99 98 98 100 100 98 99 93 98 90 97 85 82 98 97 72 61 81 79 95 90 87 91 94 92 77 74 88 71 94 89 85 87 90 82 80 85 89 73 93 89 96 91 94 89 91 88 67 66 89 92 96 91 96 90 98 100 100 97 100 100 100 97 100 100 98 100 100 98 100 100 100 99 100 100 77 68 91 95 95 97 99 98 90 75 93 94 100 98 100 100 100 98 100 97 48 49 79 87 80 81 86 83 90 80 84 81 98 98 92 98 94 98 100 99 35 56 93 92 90 94 96 97 89 88 67 74 84 78 61 59 44 45 47 56 81.12 79.64 88.66 87.02 91.88 91.78 92.90 91.50 92.64 89.80

17