DC-WAM: Dynamic-Centric Visual Supervision and Reasoning for World-Action Models
1. Paper overview
In one sentence: DC-WAM concentrates video supervision and attention on motion to improve manipulation robustness, while using a single visual-cache prefill for action-only denoising instead of repeatedly generating future video. e02e03e04e06e07e08e09e12e15
| At a glance | What to know |
|---|---|
| Research problem | Source description Uniform RGB reconstruction can reward texture, lighting and background fidelity more strongly than manipulation dynamics. The paper asks whether an existing RGB future-prediction branch can provide better control supervision without adding a predicted modality or requiring a tracker during execution. e02 |
| Core mechanism | |
| A key reported result | LIBERO-Plus out-of-distribution manipulation: 60.9% success; 37.2-point drop Average success rate (%) and ID–OOD drop (percentage points). Clean-only training; seven perturbation dimensions, each with L1–L5 severity; identical evaluation seeds and episode horizons across methods. FastWAM-AC: 53.8%, 42.9-point drop; FastWAM: 51.5%, 46.1-point drop. The gain over the action-conditioned baseline is 7.1 points. Camera shifts remain weak: 23.9% versus 24.0%; improvements cover six of seven dimensions. e10e12 |
| Reading caution | Reader analysis Figure 2 omits stop-gradient on action inputs that Eq. (10) includes, labels routing strength alpha_tau rather than alpha, and calls the downsampled target VAE-dimensional where Eq. (8) specifies DiT resolution. Equations govern this explanation; the diagram is preserved unchanged. e04e05e06 |
Core contributions
Figure 2. One offline motion map supplies both spatial loss weights and relevance targets for visual attention. Original paper, p. 3 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Start along the bottom: training video passes through CoTracker3, Gaussian rasterization and downsampling. The VAE-resolution map weights the orange sparse loss, while the downsampled map supervises the purple relevance predictor. The blue box adds a separate dense signal by differencing adjacent visual flow targets. These are latent flow-matching velocities, not an added optical-flow output modality. At upper right, read attention rows as queries and columns as keys. The action row excludes future-video keys, while future-video queries can read actions. The equations on pages 4–6 define the detached inputs, target resolution and squared-error weighting more precisely than this schematic. e03e04e05e06e08e09e15
What it supports. The architectural contribution changes where video training places its emphasis while retaining separate video and action branches. Motion supervision is constructed offline, and the learned relevance predictor biases existing visual attention. This supports a training-mediated route from future prediction to action learning without requiring future observations as action inputs.
Where the evidence stops. Figure 2 shows sg only on V, but Eq. (10) detaches V and A. It labels routing strength alpha_tau rather than Eq. (12)'s alpha, and labels the downsampled target VAE-dimensional rather than Eq. (8)'s DiT grid. The crop preserves these discrepancies; the explanation follows the equations.
2. Motivation
2.1 The problem and the proposed response
Uniform RGB reconstruction can reward texture, lighting and background fidelity more strongly than manipulation dynamics. The paper asks whether an existing RGB future-prediction branch can provide better control supervision without adding a predicted modality or requiring a tracker during execution. e02
2.2 What this reading follows
A robot can predict a visually convincing future yet still choose the wrong action. DC-WAM asks the video branch to emphasize what changes during manipulation: moving grippers, displaced objects and interaction regions. Its training recipe combines differences between adjacent latent flow fields with motion-weighted reconstruction error, then learns attention biases from the same offline tracking signal. Read the architecture alongside the masks: actions cannot inspect future visual tokens, but visual losses can still shape the action branch during training. The tables show improved robustness from clean demonstrations, while the diagrams leave an unresolved question about how routing reaches the deployment cache. e02e03e04e06e07e08e09e12e15
3. Research context
We place the paper in the collection through its world–action interface. The catalog labels and the reading’s assessment are shown separately.
| Catalog dimension | Recorded classification |
|---|---|
| Major category | WAMs |
| Architecture | Dual-system |
| Prediction paradigm | Joint prediction |
| Quadrant | Q3 · Dual-system × Joint prediction |
3.1 Evidence-based assessment
Supports the recorded classification
Two explicit modality-specific branches coupled through MoT support Dual-system, while Eq. (1) and the joint objectives support Joint prediction. This is not an inverse-dynamics pipeline: actions are directly flow-matched, and deployment uses cached visual conditioning. Joint training does not make the architecture a single shared predictor. e03e07e08e09
This is the collection’s architectural analysis, not a new related-work survey. Benchmark comparisons and their protocols appear in Section 6.
4. Problem formulation
4.1 Inputs and outputs
| Inputs | Outputs |
|---|---|
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4.2 Equations and their role
5. Method in detail
5.1 Turn tracked motion into a supervision budget
Follow one training episode before thinking about the transformer. Candidate points are tracked across frames, and backward displacement determines whether each point exceeds the motion threshold. A moving point contributes a Gaussian neighborhood whose strength is proportional to its displacement. Summing those neighborhoods creates a map on the VAE grid; normalization uses the maximum over the entire episode within a camera view. Consequently, the target preserves both where movement occurs and which moments contain stronger movement. TrackFM uses this map to weight visual velocity errors, while DynaRoute learns a downsampled version. Reader interpretation: the map is a motion proxy for useful interaction, not a semantic guarantee of task relevance. The source's robustness argument explicitly depends on trajectories remaining stable when appearance changes. e04e05e09
Figure 4. Deployment reuses a visual cache after one routing and video-prefill pass. Original paper, p. 5 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. On the left, f0 denotes the observed frame, the later f labels denote future frames, and the a labels mark action tokens. White entries prohibit attention: action queries read the observation and actions but not future-video keys. Black arrows show routing biases entering video attention. On the right, the diagram retains the observation block and action blocks. Eqs. (15)–(17) describe the prefill inputs: clean observed latents, Gaussian noise in future visual slots, Gaussian action noise and an initial diffusion timestep of one. DynaRoute is evaluated once for this cache construction, after which only the action branch continues denoising. e03e06e07e09e18
What it supports. The source's action-only deployment still performs an initial video-branch computation. Its saving comes from avoiding repeated future-video denoising and reusing visual keys and values. This explains the intended inference procedure, but the paper provides no latency or throughput measurement to quantify the saving.
Where the evidence stops. The figure applies b0 to observed-frame attention, whereas the routing prose and targets emphasize future tokens. Observation queries also cannot read future keys in this mask. The exact supervision and propagation needed to create an action-readable routed cache are therefore unresolved in the supplied formulation.
5.2 Separate forward information from backward learning
The attention mask permits future-video queries to read action tokens but forbids action queries from reading future-video tokens. During training, therefore, predicting video can depend on the demonstrated action representation even though action prediction cannot exploit unseen future observations. A visual loss can still send gradients backward through that action-conditioned computation. This is the mechanism probed by the final row of Table 4: keeping the forward pass but blocking visual-objective gradients into actions reduces OOD success from 60.9% to 57.0%. Do not confuse that ablation with Eq. (10), where both inputs to the relevance predictor are detached. The latter describes DynaRoute's inputs; the former severs a separate training pathway. Reader interpretation: the ablation supports auxiliary visual supervision as a contributor to policy learning rather than demonstrating online planning with imagined futures. e03e06e08e15
5.3 Trace the remaining video computation at deployment
At deployment, the paper starts at diffusion timestep one with a clean observation and noisy future-video and action slots. DynaRoute predicts a bias for a single video-cache prefill, then the action branch denoises using cached visual keys and values. Thus the method does not repeatedly render a future trajectory to choose an action. The source's introductory claim that the video branch can be removed should be read together with this one-time computation. A remaining implementation question is visible in Figure 4: its deployment bias is drawn on observed-frame attention, whereas the earlier routing formulation emphasizes future tokens. Since the published mask prevents observed queries from reading future keys, a reproduction must establish which tokens actually receive supervised relevance and which cached tensors influence actions. The supplied PDF does not close that gap. e02e03e06e07e09e18
5.4 Training and inference
During training
Train action flow matching together with temporal-difference visual loss, motion-weighted visual flow error and relevance BCE plus soft Dice loss. Observation tokens stay clean while action and future-video samples are noised. Dice addresses sparse-target imbalance. e06e08e09
Matched baselines share Wan2.2, demonstrations, action space and evaluation protocol. Simulation training uses 2,000 clean LIBERO demonstrations; physical training uses 100 successful demonstrations per task. All models are trained on eight NVIDIA A100 GPUs. Optimizer, training duration and frozen-module choices are not specified. e10e11e18
During inference
At diffusion timestep 1, combine the clean observed latent with Gaussian noise in future-video slots and initialize noisy actions. Evaluate DynaRoute once during video-cache prefill, disable further video-branch execution, and reuse cached keys/values throughout action denoising. No online tracker, SAM model or ground-truth motion map is required. e07e11
The source describes action generation rather than inverse dynamics or online video-rollout search. It does not specify the action-execution/replanning cadence or report deployment latency. The introductory statement that the RGB branch can be removed is qualified by the explicit one-pass cache construction. e02e07e18
5.5 Implementation flow
- Couple two prediction branches
A Wan2.2 visual-action MoT uses separate video and action branches. Future visual queries can attend to actions; action queries cannot attend to future visual tokens. Video losses can therefore train action representations through action-conditioned visual computation without exposing future observations to action prediction. e03e04e15
- Construct motion supervision offline
Sample points uniformly or inside SAM foreground regions and track them with CoTracker3. Threshold backward frame-to-frame displacement, rasterize motion-weighted Gaussian responses on the VAE grid, and normalize across each episode and camera view. Downsample the map to the DiT grid for routing supervision. e04e05
- Predict relevance and bias visual attention
At each diffusion timestep, DynaRoute consumes visual and action tokens with stop-gradient, plus fused language/proprioception and timestep conditioning. Sigmoid relevance becomes a centered logarithmic key-side bias, broadcast across visual queries and heads and shared across MoT layers. e06
6. Experiments & results
DC-WAM trains a robot action policy with future-video supervision concentrated on temporal changes and tracked interaction regions. Its two-branch Wan2.2-based model adds DynaRoute attention biases, then deploys with one visual-cache prefill followed by action-only denoising. The clearest benefit is improved success under distribution shift; the supplied paper leaves important routing and reproduction details unresolved.
6.1 Read the original evidence
Table 1. The strongest aggregate improvement is under distribution shift, with camera perturbations remaining an exception. Original paper, p. 7 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Read the first average as clean LIBERO success and the lower average as LIBERO-Plus success; every success entry is a percentage. The final row subtracts OOD success from ID success and is measured in percentage points, with lower better. Page 6 specifies 2,000 clean training demonstrations, four standard LIBERO suites with 50 rollouts per task, seven OOD perturbation dimensions and five severity levels. The methods share evaluation seeds and horizons. Compare first with FastWAM-AC because it preserves the action-conditioned visual interaction, then inspect individual perturbation rows rather than treating the average as uniform robustness. e10e12
What it supports. DC-WAM reaches 98.1% clean success and 60.9% OOD success, versus 96.7% and 53.8% for FastWAM-AC. The corresponding ID–OOD drop shrinks from 42.9 to 37.2 points. Lighting rises from 81.4% to 91.7%, but camera success is 23.9% versus 24.0%, so robustness is improved rather than solved.
Where the evidence stops. No uncertainty or per-severity breakdown accompanies this table. Small differences, particularly the camera comparison, should not be treated as statistically established. The aggregate OOD result also includes nonappearance shifts such as language and robot initialization.
Table 2. Physical manipulation improves across the reported conditions, with the largest gain on plate stacking under lighting shifts. Original paper, p. 7 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Each task forms a three-row block: clean, lighting and background conditions. All success rates are percentages. Parenthesized downward arrows report the absolute drop from that method's own clean result; the final delta column instead compares DC-WAM with FastWAM-AC in the same condition. Page 6 and Figure 5 establish the physical setup: an Agilex Piper bimanual robot, 100 successful clean demonstrations per task and 100 evaluation trials per task-condition for each method. The spotlight changes illumination, and colored-paper patches introduce background distractors. Policies are evaluated without adaptation, so these rows test transfer from clean demonstrations to unseen appearance changes. e11e13e18
What it supports. For Pile-Plates under lighting changes, success rises from 41% to 71%, a 30-point gain, while the clean-to-lighting drop falls from 39 to 18 points. Every displayed task-condition improves. Nevertheless, DC-WAM reaches only 48% on lit bowl stacking and 45% on potato collection with background distractors.
Where the evidence stops. These are executed-task outcomes on one robot platform, not video-quality scores. The paper gives trial counts but no confidence intervals, detailed success rubric or evaluation randomization procedure; the table cannot establish generalization to other embodiments or arbitrary visual perturbations.
6.2 Results and evaluation conditions
| Task & protocol | Reported result | Comparison & interpretation |
|---|---|---|
| LIBERO in-distribution manipulation Spatial, Object, Goal and Long suites; 50 rollouts per task; 2,000 clean training demonstrations. | 98.1 Average success rate (%) | FastWAM-AC 96.7; FastWAM 97.6. Reported gains are 1.4 and 0.5 percentage points; uncertainty is not supplied. e10e12 |
| LIBERO-Plus out-of-distribution manipulation Clean-only training; seven perturbation dimensions, each with L1–L5 severity; identical evaluation seeds and episode horizons across methods. | 60.9% success; 37.2-point drop Average success rate (%) and ID–OOD drop (percentage points) | FastWAM-AC: 53.8%, 42.9-point drop; FastWAM: 51.5%, 46.1-point drop. The gain over the action-conditioned baseline is 7.1 points. Camera shifts remain weak: 23.9% versus 24.0%; improvements cover six of seven dimensions. e10e12 |
| Real-world Stack-Bowl Agilex Piper; 100 clean demonstrations; 100 trials per task-condition and method; no adaptation. | 84 / 48 / 61 Success rate (%), clean / lighting / background | FastWAM-AC: 76 / 34 / 52. Gains are 8 / 14 / 9 percentage points; substantial failures remain under lighting shifts. e11e13 |
| Real-world Pile-Plates Agilex Piper; 100 clean demonstrations; 100 trials per task-condition and method; external spotlight and colored-paper distractors. | 89 / 71 / 69 Success rate (%), clean / lighting / background | FastWAM-AC: 80 / 41 / 46. The lighting gain is 30 percentage points; the clean-to-lighting drop falls from 39 to 18 points. e11e13 |
| Real-world Collect-Potato Open basket, place potato inside, close basket; same clean-training and 100-trial-per-condition protocol. | 70 / 66 / 45 Success rate (%), clean / lighting / background | FastWAM-AC: 62 / 53 / 30. Gains are 8 / 13 / 15 points; background robustness remains limited in absolute terms. e11e13 |
| Dense and sparse supervision ablation LIBERO / LIBERO-Plus; DynaRoute enabled for the added-supervision variants. | Combined: 98.1 / 60.9 Success rate (%) | Dense with routing: 97.1 / 56.6; sparse with routing: 97.4 / 58.7; FastWAM-AC: 96.7 / 53.8. Combining signals performs best. Comparisons against FastWAM-AC also add routing, so they do not isolate either visual loss alone. e14 |
| Routing and visual-to-action gradient ablation Same dynamic supervision; LIBERO / LIBERO-Plus. | DynaRoute: 98.1 / 60.9 Success rate (%) | No routing 97.7 / 59.1; shuffled relevance 96.8 / 57.8; action-query routing 95.8 / 49.2; visual-to-action stop-gradient 97.0 / 57.0. Aligned visual routing improves OOD success by 1.8 points over no routing. Blocking the visual-loss gradient into actions costs 3.9 OOD points despite unchanged forward computation. e15 |
6.3 Ablations and diagnostic examples
Read component removals and qualitative examples within their stated evaluation conditions.
Table 3. Dense temporal changes and sparse motion weighting work best together in the reported routing-enabled variants. Original paper, p. 7 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. The two columns distinguish clean LIBERO from OOD LIBERO-Plus success. Dense means temporal-difference supervision over the VAE grid; sparse means TrackFM weighting near tracked motion. The two middle rows both enable DynaRoute, while DC-WAM combines their visual supervision. Compare those three rows to assess whether the two signals are complementary under routing. The first row is a broader reference: FastWAM-AC lacks both dynamic supervision and DynaRoute. This distinction matters because the printed plus signs do not make each change a single-factor loss ablation. Page 6 describes the setup, and page 7's caption defines which components each row includes. e08e09e10e14
What it supports. Combined supervision reaches 60.9% OOD success, compared with 56.6% for dense supervision with routing and 58.7% for sparse supervision with routing. It also has the highest clean score at 98.1%. The pattern supports complementarity in this configuration, with the sparse-only variant stronger than the dense-only variant.
Where the evidence stops. The improvements over FastWAM-AC include adding routing. This table is not a full factorial decomposition of both losses and routing, and it supplies no uncertainty estimates for the differences among variants.
Table 4. Spatial alignment, attention location and the visual-loss gradient path each affect the reported action success. Original paper, p. 7 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Here the dynamic supervision is held constant while routing changes. No routing removes the bias; shuffled relevance disrupts its spatial correspondence; action-query routing applies the cues to a different attention pathway. DynaRoute is the aligned visual-attention version. Read the separated final row carefully: the paper says this stop-gradient variant blocks gradients from visual objectives into the action branch while retaining the forward computation. That intervention is distinct from the detached visual and action inputs of the relevance predictor in Eq. (10), which are part of the normal method. The left and right columns report clean and OOD success percentages, respectively. e03e06e07e15e18
What it supports. DynaRoute reaches 60.9% OOD success versus 59.1% without routing and 57.8% with shuffled relevance. Direct action-query routing falls to 49.2%. Blocking the visual-to-action training gradient yields 57.0%, a 3.9-point loss, supporting the claim that video supervision helps train action representations through their coupling.
Where the evidence stops. These results support the reported mechanisms within one experimental setup. They do not resolve the observed-token cache ambiguity or quantify statistical reliability. The paper also leaves the exact shuffling procedure and routing-network implementation unspecified.
7. Analysis & limitations
7.1 What the evidence leaves open
Figure 2 omits stop-gradient on action inputs that Eq. (10) includes, labels routing strength alpha_tau rather than alpha, and calls the downsampled target VAE-dimensional where Eq. (8) specifies DiT resolution. Equations govern this explanation; the diagram is preserved unchanged. e04e05e06
The routing text specifies future-token relevance, but Figure 4 depicts a bias on observed-frame f0 attention. How that bias is supervised and transferred into the action-readable cache remains unresolved, especially because the mask excludes future keys from action queries. e03e06e07
Motion-map robustness assumes tracking remains stable. Figure 3 gives qualitative attention examples without a quantitative attention-stability metric; Figure 1 shows nonmonotonic PSNR versus success, not proof that visual fidelity is universally irrelevant. e05e16e17
Tables provide no confidence intervals or repeated-training-seed dispersion. Tests cover one physical platform and three tasks; larger datasets, other platforms and architectures beyond MoT are future work. No latency or throughput table establishes the efficiency magnitude. e11e12e13e15e18
7.2 Questions for discussion
- How is observed-frame relevance supervised for the routed cache when the equations describe future-token targets?
- Does motion-derived supervision retain its advantage when camera motion or tracking errors dominate inter-frame displacement?
8. Reproducibility audit
8.1 Requirements and known gaps
Required ingredients include Wan2.2, the visual-action mask, WanVAE/umT5 encoding, offline CoTracker3 tracks and optional SAM point sampling. Gaussian rasterization specifies lambda=0.25 and sigma_p=1.25; preserve episode/view normalization and VAE-to-DiT downsampling. e03e04e05
Missing specifications include motion threshold, point count, chosen sampling mode, routing-network architecture, alpha and Dice weight, concrete horizons, optimizer schedule, trainable/frozen modules, denoising steps and physical success rubric. The promised appendix is absent, preventing an exact reproduction recipe. e04e06e07e09e10e11e18
Proposed checks: reproduce aligned versus shuffled/no-routing comparisons with fixed losses and seeds, and trace whether perturbing future-only versus observed-token bias changes the action-readable cache under the published mask. These checks were not run. e03e06e07e15
8.2 Proposed reproduction checks
The following checks are proposals motivated by the paper. They have not been run as part of this reading.
Check 1: Does spatial alignment add robustness beyond the visual losses?
Reader-proposed experiment, not run: train aligned DynaRoute, no-routing and spatially shuffled-relevance variants on the same 2,000 clean demonstrations, with identical initial checkpoints, dynamic losses, training budget and evaluation seeds. Shuffle token positions within a frame while preserving the relevance-value distribution, documenting this as a proposed control because the paper does not specify its permutation. Evaluate clean LIBERO and every LIBERO-Plus dimension/severity, using repeated training seeds and uncertainty intervals. The prediction motivated by Table 4 is that aligned relevance outperforms both controls, especially under appearance shifts, without requiring better future PSNR. If no-routing or distribution-matched shuffled relevance performs equivalently, the claim that spatial routing supplies the extra robustness is weakened. e05e06e10e12e15e16e18
Check 2: Can the published bias change the action-readable cache?
Reader-proposed implementation check, not run: fix an observation, instruction, proprioception and all noise tensors. At timestep one, perform separate prefills with zero bias, a bias altered only on future-token keys, and a bias altered only on observed-token keys. Preserve the published attention mask and compare each layer's action-readable visual keys/values and the final denoised action chunk. Also record which token positions receive the routing target. Under the displayed mask, a future-only perturbation has no evident route into observation keys; an observed-token effect would identify the additional routing scope suggested by Figure 4. If only future tokens are supervised and their perturbation never changes action-readable tensors, the stated deployment-routing mechanism needs clarification. This checks graph connectivity, not task success or a full reproduction. e03e06e07e09e18
8.3 Reading coverage
Visual audit: All nine original PDF pages were rendered at 200 DPI and visually inspected after reading all four text chunks. Page 1 verifies the title, seven authors, three affiliations and v1 date, and contains Figure 1's PSNR diagnostic. Pages 2–6 supply the full method, equations, masks, tracker settings, eight-A100 training statement, dataset counts, evaluation protocol and real-world Figure 5. Page 4's Figure 3 attention examples were also inspected. Page 7 supplies all four numerical tables, ablation explanations and conclusion. Pages 8–9 are references and confirm that the appendix promised on page 5 is absent. All six final crops were actually viewed, including the 300/400-DPI narrow tables and inference diagram. Figure 2's stop-gradient/alpha/grid-label discrepancies and Figure 4's observed-token bias ambiguity are disclosed in the corresponding cautions. Original table headers, rows, legends and parenthetical drop annotations are intact; caption definitions are explained in the guides. No external supplement, code or later revision was inspected, and no experiment was run. The text extraction's malformed symbols on pages 3 and 5 were checked against these page images.
PDF pages inspected for this edition: 1, 2, 3, 4, 5, 6, 7, 8, 9. Appendix coverage: not present.
Original figures and tables remain the work of the source’s authors. Extractions preserve their scientific content; any HTML wrapper layout is disclosed with each figure. The surrounding reading notes are our own.
Text reading scope & known omissions
- PDF p. 1: title, byline, affiliations, arXiv version, Abstract
- PDF pp. 1–2: Introduction and Related Work
- PDF pp. 2–3: Method, Overview and Architecture
- PDF pp. 3–4: Tracker-Derived Dynamic Map Construction
- PDF pp. 4–5: Dynamics-Aware Attention Bias and action-only inference
- PDF pp. 5–6: Training Objective, Eqs. (18)–(26)
- PDF pp. 6–7: Experiments, Experimental Setup, Main Results, Ablation Studies, Analysis and Conclusion
- PDF pp. 8–9: References
Outside the original text pass
- Text extraction does not reconstruct figure images; inspect the retained PDF for figures and equation/table layout.
- Separate supplemental material availability has not been fully verified.
- Some PDF font mappings yielded unpaired Unicode surrogates; replacement characters are recorded by page in extractionNotes and require PDF visual verification.
- Identity: the inspected title page shows arXiv:2607.25918v1, 28 July 2026. The title and all seven authors match the catalog after normalizing name order. The catalog affiliation lists only Tsinghua University; the PDF additionally credits Dense-AI and University of Michigan.
- The manifest records an earlier same-v1 HTML artifact, SHA-256 d953e56de116169f837cf4a3763594733de0357ff87a9fc98f9ed57714acb0ba. That artifact was not reread or used as evidence here. This report uses the supplied PDF hash, with no later edition substituted.
- All four supplied chunks were individually read, covering all nine PDF pages. The extraction does not reconstruct figures; all nine rendered pages and all six final original crops were visually inspected. Malformed font mappings on pages 3 and 5 were checked against the PDF images; replacement characters were not treated as mathematical notation.
- Page 5 refers to additional DynaRoute details and analyses in an Appendix, but no appendix is present in the supplied PDF, which ends with references on pages 8–9. Separate supplemental material availability has not been fully verified; no supplement was supplied.
- Code, external resources and the earlier HTML were not inspected. No experiment was reproduced. The manifest's acquisition timestamp is preserved exactly; its provenance notes that the earlier PDF HTTP request time was not independently retained.
The visual audit above records the subsequent illustrated pass.
8.4 Traceable evidence
e01PDF p. 1, title/byline/affiliations and arXiv margin identifier
The exact DC-WAM title appears with Haoyuan Ji, Lingxiang Fan, Shang Su, Yinqiao Lu, Mengkai Shi, Jun Gao and Shuo Feng; affiliations are Tsinghua University, Dense-AI and University of Michigan. The identifier is 2607.25918v1, dated 28 Jul 2026.
Go to primary source ↓e02PDF pp. 1–2, Abstract and Introduction
The paper motivates replacing appearance-dominated RGB supervision with interaction dynamics, while retaining the RGB branch and avoiding additional deployment inputs. The introduction says the visual branch can be removed following Fast-WAM-style inference.
Go to primary source ↓e03PDF p. 2, Method Overview Eq. (1) and Architecture; p. 3, architecture continuation below Figure 2
Inputs are current RGB, language and proprioception; outputs are an action chunk and future visual evolution. Wan2.2 supports two visual-action MoT branches. Future video attends to actions, while action queries are masked from future visual tokens.
Go to primary source ↓e04PDF p. 3, Figure 2 and Tracker-Derived Dynamic Map Construction, Eqs. (2)–(5)
The figure shows WanVAE, umT5, CoTracker3, dense/sparse supervision and routing. Points are sampled uniformly or using SAM foregrounds; backward motion exceeding delta_mot selects dynamic points. Gaussian rasterization uses lambda=0.25 and sigma_p=1.25. The figure writes sg(V_j) but not sg(A_j), alpha_tau, and a VAE-dimensional label on the downsampled routing target.
Go to primary source ↓e05PDF p. 4, Eqs. (6)–(8) and accompanying dynamic-map discussion
Motion-weighted Gaussian responses are summed and normalized by the episode-wide maximum within each camera view. The VAE map is downsampled to the DiT grid. Reduced sensitivity to persistent appearance changes is conditional on stable point trajectories.
Go to primary source ↓e06PDF p. 4, Dynamics-Aware Attention Bias, Eqs. (9)–(12); p. 5, Eqs. (13)–(14)
Clean observation tokens accompany noisy future visual and action tokens. Eq. (10) applies stop-gradient to both visual and action inputs of G_psi. Sigmoid relevance produces a log bias with alpha, centered over visual tokens and shared across layers, heads and visual queries. The prose introduces relevance and bias for future visual tokens.
Go to primary source ↓e07PDF p. 5, Action-only inference with routed video cache, Eqs. (15)–(17), Figure 4 and caption
At tau_init=1, clean observations and Gaussian future/action slots feed a single routing and video-cache prefill; subsequent denoising reuses the cache without rerunning the video branch. Figure 4 labels an observed-frame bias b0 and preserves the action-to-future attention mask, leaving observation-target supervision unclear relative to the future-token routing prose.
Go to primary source ↓e08PDF p. 5, Training Objective and Flow matching, Eqs. (18)–(23)
The total objective sums action FM, visual temporal differences, tracker-weighted visual FM and routing loss. Linear interpolation has target epsilon minus clean sample. Eq. (22) matches adjacent predicted and target visual velocity differences; Eq. (23) defines squared local flow error.
Go to primary source ↓e09PDF p. 6, Eqs. (24)–(26)
TrackFM divides the motion-weighted visual-error sum by total map weight plus epsilon. Routing combines BCE and lambda_Dice-weighted soft Dice against the downsampled dynamic map; the Dice term addresses sparse dynamic regions.
Go to primary source ↓e10PDF p. 6, Experimental Setup, Baselines and LIBERO and LIBERO-Plus
All models train on eight NVIDIA A100 GPUs. FastWAM and FastWAM-AC share backbone, demonstrations, action space and evaluation protocol with DC-WAM. The four LIBERO suites use 50 rollouts per task. Training uses 2,000 clean demonstrations; LIBERO-Plus has seven perturbation dimensions and five difficulty levels, with matched seeds/horizons.
Go to primary source ↓e11PDF p. 6, Real-world Evaluation and Figure 5
Agilex Piper bimanual tasks are bowl stacking, plate stacking on a shelf and basket/potato manipulation. Each task has 100 successful demonstrations; each method receives 100 trials per task-condition. Conditions use an external spotlight or colored-paper background patches. No external tracker, segmentation model or ground-truth dynamic map is used at execution.
Go to primary source ↓e12PDF p. 7, Table 1, all rows and caption
FastWAM/FastWAM-AC/DC-WAM have LIBERO averages 97.6/96.7/98.1 and LIBERO-Plus averages 51.5/53.8/60.9. ID–OOD drops are 46.1/42.9/37.2 points. DC-WAM's Camera/Robot/Language/Light/Background/Noise/Layout values are 23.9/51.7/83.4/91.7/61.3/54.2/69.8; FastWAM-AC values are 24.0/43.9/70.7/81.4/50.5/50.8/63.2. No uncertainty is shown.
Go to primary source ↓e13PDF p. 7, Table 2, all task-condition rows and caption
Clean/light/background success for FastWAM-AC versus DC-WAM is 76/34/52 versus 84/48/61 for Stack-Bowl, 80/41/46 versus 89/71/69 for Pile-Plates, and 62/53/30 versus 70/66/45 for Collect-Potato. Parentheses show absolute drops from each method's clean success. Training is clean-only and evaluation uses no adaptation.
Go to primary source ↓e14PDF p. 6, Dense and sparse dynamics supervision; p. 7, Table 3 and caption
LIBERO/LIBERO-Plus success is 96.7/53.8 for FastWAM-AC, 97.1/56.6 for dense with routing, 97.4/58.7 for sparse with routing and 98.1/60.9 for DC-WAM. Dense means temporal differences; sparse means TrackFM. FastWAM-AC removes both dynamic supervision and routing.
Go to primary source ↓e15PDF p. 7, Table 4 and Dynamics-aware routing and gradient path
Under the same dynamic supervision, LIBERO/LIBERO-Plus results are no routing 97.7/59.1, shuffled 96.8/57.8, action-query routing 95.8/49.2, DynaRoute 98.1/60.9 and DynaRoute with stop-gradient 97.0/57.0. The last variant blocks visual-objective gradients into actions while preserving forward computation; this differs from DynaRoute's detached inputs in Eq. (10).
Go to primary source ↓e16PDF p. 1, Figure 1 and caption; p. 7, Does higher PSNR imply better control?
The scatter plot compares future PSNR in dB with LIBERO-Plus success. Dense with routing has the lowest plotted PSNR but exceeds FastWAM-AC success; DC-WAM has the highest plotted success without the highest PSNR. Exact PSNR point values are not tabulated.
Go to primary source ↓e17PDF p. 4, Figure 3 and caption; p. 7, How does DC-WAM reshape visual attention?
Clean/L1/L2/L3 example images and attention overlays compare FastWAM-AC with DC-WAM. The authors interpret DC-WAM as retaining more concentrated interaction-relevant attention. No numerical colorbar, attention-stability statistic or sampling protocol is given for these examples.
Go to primary source ↓e18PDF p. 5, paragraph after Eq. (14); pp. 3–6, method/setup; p. 7, Tables 1–4 and Conclusion; pp. 8–9, References and document end
DynaRoute implementation details are deferred to an Appendix that is absent from this nine-page artifact. The supplied method/setup omit optimizer/schedule, detailed routing-network configuration, concrete horizons and denoising/execution cadence. Results provide no latency table or uncertainty estimates. The conclusion proposes larger datasets, diverse robots and non-MoT architectures; the document ends with references.
Go to primary source ↓8.5 Primary sources
DC-WAM: Dynamic-Centric Visual Supervision and Reasoning for World-Action Models ↗
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