{\Delta}WAM: Distilling Action Tangent Fields into World Action Models

• Future-video prediction provides dense supervision, but persistent backgrounds, camera views, and untouched objects can dominate loss without teaching action consequences.Source: §1 · p. 2
• Motion-centric targets reduce static-appearance supervision but can mistake lighting or distractor motion for action dependence and discard contact-relevant appearance cues.Source: §1 · p. 2
• The Residual-VAE target subtracts a current-frame-derived reference from the future latent, preserving exact recovery while making scene departure explicit.Source: §1 · p. 2
• Action Tangent Fields estimate locally action-responsive residual directions from perturbed actions and upweight those directions while retaining the demonstrated future as target.Source: §1 · p. 2
• The method mid-trains Wan on robot video, then post-trains a Fast-WAM-style policy with cached ATFs, keeping the ACWM out of policy training and inference.Source: §1 · p. 2
• ∆WAM reaches 87.8% vs 51.5% aggregate success on LIBERO-Plus and 79.3% vs 72.7% on RoboTwin 2.0-Plus, using one VideoDiT evaluation at inference.Source: §1 · p. 2

2.1 WORLD ACTION MODELS

• GE-Act 2.0 scales predict-then-act with heterogeneous interaction data (Liao et al., 2025), while LingBot-VA and Cosmos Policy jointly model world and action outputs (Li et al., 2026c; Kim et al., 2026).Source: §2.1 · pp. 2–3
• Fast-WAM and Light-WAM omit explicit generation at deployment, while Efficient-WAM and Faster-WAM reduce generation or video–action interaction costs (Yuan et al., 2026; Li et al., 2026d; Li et al., 2026b; Zhao et al., 2026).Source: §2.1 · p. 3
• Full video latents preserve detail but emphasize static appearance; flow, residual, and motion-centric targets emphasize change but may discard useful cues, whereas ATFs selectively emphasize locally action-responsive directions.Source: §2.1 · p. 3

2.2 ACTION-CONDITIONED WORLD MODELS

• Action-conditioned world models broaden control interfaces through action tokens, pixel-space flow, or rendered action observations (Li et al., 2026a; Zou et al., 2026).Source: §2.2 · p. 3
• Unlike rollout-oriented simulation methods, ∆WAM perturbs demonstrated actions, transfers local action–world geometry from an ACWM, and keeps real demonstrations as prediction targets.Source: §2.2 · p. 3

3 METHOD

• ∆WAM trains a VideoDiT–ActionDiT policy on real action–future pairs, transferring locally action-responsive directions from an embodiment-specific ACWM into world-error weighting.Source: §3 · p. 3

3.1 RESIDUAL VIDEO MID-TRAINING

• The first-frame anchor plus the future residual exactly recovers the absolute VAE latent, while centering prediction on scene changes such as robot motion, object displacement, and contact.This preserves the VAE representation, not necessarily the original RGB pixels.Source: §3.1 · pp. 3–4

3.2 ACTION TANGENT FIELDS FROM LOCAL DYNAMICS

• An embodiment-specific ACWM probes matched-condition nearby actions; normalized finite differences span sampled action-responsive residual directions, which are cached instead of estimating the full Jacobian.The cached basis means the ACWM is not needed during policy training or inference.Source: §3.2 · p. 5

3.3 ATF-GUIDED WORLD-ACTION POST-TRAINING

• Post-training retains the real demonstrated residual target and adds weight to errors projected onto sampled action-responsive directions, while ordinary residual loss covers every latent element.The added projection term is zero when no sampled directions are available.Source: §3.3 · p. 6

3.4 SINGLE-PASS WORLD CONDITIONING AT INFERENCE

• At inference, one VideoDiT pass produces world tokens that are reused while ActionDiT integrates the action chunk through four descending Euler steps.The image encoding and VideoDiT features remain fixed across those steps.Source: §3.4 · p. 6

4.1 LIBERO-PLUS

• 87.8% aggregate success on LIBERO-Plus is 2.1 points above the strongest baseline, π0.5; original-setting success is 98.2%, near the best reported 98.6%.The aggregate is pooled across perturbation instances.Source: Table 1 · p. 7, §4.1 · p. 7
• LIBERO-Plus leads under robot-initialization shifts (96.2%, 6.5 points above the best competitor) and language shifts (91.2%), but camera success (60.9%) trails the best by 14.9 points.Lighting reaches 86.8% and layout 58.4%; background performance is 94.1%, although π0.5 and X-VLA remain ahead.Source: §4.1 · p. 7

4.2 ROBOTWIN AND ROBOTWIN 2.0-PLUS

• 92.8% on Clean and 92.1% on Randomized yield the best RoboTwin average, 92.4%; this is within 0.1 points of pretrained LingBot-VA on Clean and 0.6 points ahead on Randomized.The Clean–Randomized gap is 0.7 points.Source: §4.2 · p. 7, Table 2 · p. 8
• 79.3% aggregate success on RoboTwin 2.0-Plus is 5.1 points above LingBot-VA; the method leads on language (88.8%), lighting (91.4%), and layout (91.3%), but camera success is 19.1%.It also scores 92.2% in the original setting; background and observation-noise results trail the best by 0.1 and 2.1 points.Source: Table 2 · p. 8, §4.2 · p. 8

4.3 REAL-WORLD EXPERIMENTS ACROSS EMBODIMENTS

• On NERO, ∆WAM averages 0.79 on test-tube insertion versus 0.58 for π0.5 and 0.54 on bowl stacking versus 0.33 for both baselines; on Tianji it leads every task average.Its largest Tianji margin is on bimanual cooking, where baselines score at most 0.02; Table 3 averages three trials per task and condition.Source: §4.3 · p. 8, Table 3 · p. 9

4.4 ABLATION STUDY

• 87.8% average success is reached with one or two VideoDiT denoising steps, versus 88.1% with four, so the method uses one step.Inference time rises from 0.43 s at one step to 1.57 s at four; the three extra steps buy 0.3 points at 1.14 s additional latency.Source: Figure 4 · p. 9, §4.4 · p. 9
• Success rises from 79.0% at K = 0 to 85.1% at K = 4 and 87.8% at K = 8, motivating the use of eight local action perturbations.K = 0 retains the real action and residual targets but omits the ATF loss.Source: Figure 4 · p. 9, §4.4 · p. 9

5 CONCLUSION

• Robustness gains hold on LIBERO-Plus, RoboTwin, and RoboTwin 2.0-Plus, though large camera and layout changes remain challenging.Source: §5 · p. 9
• Residual-VAE prediction makes temporal change explicit while retaining the full future latent.Source: §5 · p. 9
• The ATF loss upweights errors along directions responsive to nearby actions while keeping the real future as the target; one VideoDiT pass suffices at inference.Source: §5 · p. 9