Privileged Foresight Distillation: Zero-Cost Future Correction for World Action Models
1. Paper overview
In one sentence: PFD distills the action-velocity change induced by privileged future observations into a current-only policy, improving manipulation success while retaining a small, measurable adapter cost. e01e02e04e05e10e12e14e16
| At a glance | What to know |
|---|---|
| Research problem | Author claim If future-video prediction can be removed at deployment, does its training contribution reduce to visual regularization? The authors argue that real future observations reveal an action-specific denoising correction that ordinary current-only training only partly captures. PFD tests whether this correction can be transferred without generating future video at inference. e02 |
| Core mechanism | |
| A key reported result | LIBERO four-suite manipulation: PFD: Spatial 98.6, Object 99.2, Goal 99.2, Long 95.4; average 98.10 ±0.06. Success rate (%). One model per suite; 500 demonstrations across 10 tasks per suite; 500 evaluation trials per suite. Reproduced Fast-WAM: 97.0/99.4/96.6/94.8; 96.95 ±0.08 average. Released Fast-WAM reports 97.60. The controlled reference gives +1.15 percentage points overall, strongest on Goal (+2.6); Object decreases 0.2 points. The meanings of ± and the repeat count are unspecified. Published embodied-pretraining baselines provide context, not a unified retraining comparison. e08e10 |
| Reading caution | Source description The authors test one backbone family, an output MLP and a full-horizon teacher mask. They provide no formal conditions guaranteeing that a small adapter can approximate the residual. e15 |
Core contributions
Figure 1. One backbone supplies both predictions; only the student and adapter remain at deployment. Original paper, p. 3 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Start with the bottom action-query row in each matrix: dark cells indicate visible tokens. The student sees the current video token and action tokens; the teacher additionally sees future video tokens. Then follow the blue student path into the green adapter and compare it with the deployment panel. Use the caption and Eqs. (4)–(5) to read the correction: the adapter consumes live base velocity and action time, and its target is the detached teacher-minus-student difference. The drawing calls the adapter gθ and time t; the equations use gφ and τ_a. The final quantity is a velocity used for action sampling. e03e04e05e06e07e16
What it supports. The mask comparison makes privileged access explicit without adding a separately parameterized teacher. At inference, the crossed-out branch and absent future tokens are the central savings. The residual is learned during training; deployment does not recover the actual future or run the privileged forward.
Where the evidence stops. The drawing marks the student stop-gradient, routes a residual arrow into the adapter, and displays L1/cross-entropy losses. Its caption and Eqs. (4)–(10), pp. 4–5, instead specify live student input, detached target and squared flow losses. Those equations guide this reading; the graphical inconsistencies remain unresolved.
2. Motivation
2.1 The problem and the proposed response
If future-video prediction can be removed at deployment, does its training contribution reduce to visual regularization? The authors argue that real future observations reveal an action-specific denoising correction that ordinary current-only training only partly captures. PFD tests whether this correction can be transferred without generating future video at inference. e02
2.2 What this reading follows
A policy can learn from future observations without producing a future video when it acts. PFD makes that idea concrete by running the same backbone under two attention masks during training: one exposes only the current frame to action queries, while the other exposes the demonstrated future as well. Their action-velocity difference becomes a detached training target for a small adapter. The useful question is whether this extra target transfers action-relevant information beyond ordinary fine-tuning. The experiments support that account within the tested settings, while the original architecture drawing, uncertainty reporting and depth–width controls require careful interpretation. This edition reads the supplied v2 PDF. e01e02e04e05e10e12e14e16
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 | Not assigned |
| Architecture | Not assigned |
| Prediction paradigm | Not assigned |
| Quadrant | Not assigned |
This table preserves the labels recorded at reading time. The current major category is WAMs. View the current classification.
3.1 Evidence-based assessment
Insufficient evidence to decide
The supplied catalog has no assigned class. Architecture evidence shows one shared Mixture-of-Transformers parameter set with video/action experts and two training masks, rather than a separately parameterized teacher pipeline. Training combines video/action flow objectives with privileged residual distillation; deployment is current-only action denoising, not future generation followed by inverse dynamics. This supports an integrated-backbone reading but leaves the unassigned catalog quadrant unchanged. e03e04e06e07
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 Define foresight by changing what action queries can see
Begin with the action velocity predicted from a demonstrated sequence corrupted for flow matching. PFD evaluates that noisy example twice with the same parameters, timesteps and noise realization. The student action queries attend to the current frame and action tokens; the teacher adds access to future-video tokens from the demonstration. Subtracting their predictions therefore measures the effect of this changed attention support at the current model state. It does not supply a model-independent optimal action, and the future tokens enter through the same corrupted-input construction rather than an independently generated rollout. The difference is detached before becoming a target. My interpretation is that this pairing is the strongest design choice for attribution: it removes separate-teacher capacity and noise differences, while still leaving the residual dependent on the backbone's learned behavior. e04e05
5.2 Understand why two numerically equal losses train differently
The adapter receives the live base velocity and predicts a correction, which is added back to that velocity. Residual matching compares the correction with a fully detached teacher-minus-student target. Teacher consistency instead compares the corrected output with a detached teacher prediction. Substituting the corrected output shows equal squared-error values, but automatic differentiation encounters different graphs: residual matching reaches the backbone through the adapter input, while teacher consistency also has the direct base-velocity path. This explains why replacing one term with the other is an implementation change even if logged loss values look identical. Zero initialization begins with no correction; partial fine-tuning subsequently permits both the head and selected backbone blocks to adapt. Follow Eqs. (4)–(10) and the page-5 routing discussion for this mechanism, because Figure 1's student stop-gradient and loss formulas disagree with them. e05e06e09e16
5.3 Separate a useful correction from a universal explanation
The experimental sequence asks whether the correction improves action success, then whether simpler interventions produce the same pattern. LIBERO's reproduced baseline rises from 96.95 to 98.10 under default PFD, while adapter-only training reaches 96.60. Direct fine-tuning and shuffled futures also miss the gain, supporting the importance of aligned privileged supervision in this setup. However, direct fine-tuning changes the objective and removes the adapter, and the wider-adapter probe also reduces video depth. My assessment is that these controls motivate the foresight account without proving that every alternative regularizer or width setting would fail. Finally, deployment removes the teacher but keeps the adapter at every denoising step. The measured 5.15% cached-context overhead is the concrete tradeoff accompanying the success improvement; projected future-generation costs provide context rather than a matched timing study. e10e12e14
5.4 Training and inference
During training
Main runs update the last 12 of 30 blocks in each expert plus the adapter; other backbone blocks remain frozen. The adapter is a three-layer SiLU MLP of width 512, using a linear velocity projection and sinusoidal action-time embedding. Loss weights are video=1, ground truth=1, residual=0.5, teacher=0.1. e09
Training uses Wan2.2-5B without embodied pretraining, 8 H100 GPUs, 30 LIBERO epochs or 15 RoboTwin epochs, AdamW with cosine decay, weight decay 0.01 and gradient clipping 1.0. Learning rates are 6×10⁻⁵ and 10⁻⁴ respectively. The additional teacher forward increases training work; numerical batch size and detailed inherited schedules are not restated. e08e09
During inference
Use 10 flow-matching denoising steps with classifier-free guidance scale 1.0. At every step, add the adapter prediction to the student velocity and update the action sample. Neither the teacher mask nor future frames are instantiated. The paper specifies chunk prediction, but does not detail the executed prefix or observation-refresh loop. e07e14
5.5 Implementation flow
- Construct the paired predictions
The Mixture-of-Transformers backbone contains video and action experts coupled by attention. Student action queries see current-frame video tokens and action tokens. Teacher queries additionally see future-video tokens derived from the demonstrated trajectory. Both forwards share parameters, timesteps and the same corrupted inputs; the teacher is neither an EMA network nor a separately frozen copy. e03e04
- Learn the mask-induced difference
Detach the teacher prediction and the teacher-minus-student residual target. Apply the token-wise adapter to the live student velocity and action timestep. Its zero-initialized output projection initially leaves the student unchanged. The target evolves as the shared backbone changes; it is not an oracle correction independent of the model. e05
- Route supervision through the corrected output
Combine video flow matching, corrected-action ground truth, residual matching and weak teacher consistency. Residual matching reaches trainable backbone blocks through the adapter input; teacher consistency also has a direct path through the base velocity. Equal forward loss values therefore do not imply equivalent optimization. e06
6. Experiments & results
Privileged Foresight Distillation (PFD) compares two attention masks on the same world-action backbone, then learns the future-enabled change in action velocity through an output adapter. Deployment uses only the current frame and corrected action denoising. The reported LIBERO mean improves by 1.15 percentage points over reproduced Fast-WAM, with a measured 5.15% cached-context latency overhead; the title's zero-cost wording does not mean zero additional computation.
6.1 Read the original evidence
Table 1. PFD improves three LIBERO suites, with its largest gain on Goal. Original paper, p. 6 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Read the two Fast-WAM rows separately before comparing PFD. The released row is transcribed from prior work; the reproduced row is the paper's unified-pipeline reference. Each suite uses a model trained on 500 demonstrations across 10 tasks and evaluated over 500 trials. Compare the partial-fine-tune PFD row against reproduced Fast-WAM column by column, then use Average for the four-suite mean. The Emb. PT. check marks identify embodied pretraining in the context baselines; dashes indicate its absence for Fast-WAM and PFD. Finally inspect the adapter-only row to see what happens when the backbone is frozen. e08e09e10e12
What it supports. The mean rises from 96.95 to 98.10, a 1.15-point improvement. Goal gains 2.6 points, Spatial 1.6 and Long 0.6, while Object loses 0.2. Adapter-only PFD averages 96.60, so the main result depends on updating backbone blocks alongside the residual head in this configuration.
Where the evidence stops. The PDF does not define the ±0.08/±0.06 statistics or repeat count. High success rates and 500-trial evaluation warrant caution about small differences. The broader published baselines have different pretraining histories and were not all retrained in the PFD pipeline.
Table 2. The reported gain extends to both RoboTwin scene conditions. Original paper, p. 6 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Use Clean and Randomized as separate conditions before reading their displayed average. The experiment uses 2,500 clean-scene and 25,000 randomized-scene demonstrations across more than 50 bimanual tasks, with 100 evaluation trials per task in each condition. PFD and the Fast-WAM row both lack an embodied-pretraining check mark. The indented 'from Wan2.2' rows distinguish backbone variants of the context methods. A dash in LingBot-VA's randomized column is missing evidence, not a zero score; its displayed 80.6 average should not be interpreted as an observed two-condition mean. Preserve the original table's missing entry. e08e11
What it supports. PFD reports 93.11% clean and 92.69% randomized success, compared with 91.88% and 91.78% for Fast-WAM. These are gains of 1.23 and 0.91 points. Its displayed 92.9% average also exceeds the 92.2% LingBot-VA embodied-pretraining row, extending the paper's empirical claim beyond LIBERO.
Where the evidence stops. Table 2 does not label Fast-WAM as released or reproduced, although Section 4.1 distinguishes those variants. The ± values are undefined. These benchmark results do not separately establish physical-robot deployment or robustness beyond the evaluated scene randomization.
Table 4. Current-only deployment retains a measured adapter overhead; the future-generating rows are projections. Original paper, p. 8 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. First separate the upper projected rows from the lower measured comparison using Section 4.4 beneath the original table. The authors apply previously reported joint/IDM slowdown factors to their cached-context baseline; those absolute values are not fresh measurements of all four methods. For the lower two rows, each LIBERO chunk contains 32 actions, sampled in 10 denoising steps on one H100. Timing uses 20 trials after five warmup runs. The prose gives greater precision than the table: 257.77 ms for Fast-WAM and 271.04 ms for PFD. These values concern producing a whole chunk, not independently timing each executed action. e07e09e14
What it supports. The measured increment is 13.27 ms per chunk, or 5.15%, consistent with adding a small adapter at each denoising step. PFD avoids generating future video, but the paper's title should not be read as a claim of literally zero latency or zero extra training cost.
Where the evidence stops. The 786.2/1098.1 ms joint/IDM rows are projections, despite sharing a latency column with measured rows. Prompt-mode timing uses its own baseline and must remain separate. Training wall time and full deployment feedback/control latency are not quantified here.
6.2 Results and evaluation conditions
| Task & protocol | Reported result | Comparison & interpretation |
|---|---|---|
| LIBERO four-suite manipulation One model per suite; 500 demonstrations across 10 tasks per suite; 500 evaluation trials per suite. | PFD: Spatial 98.6, Object 99.2, Goal 99.2, Long 95.4; average 98.10 ±0.06. Success rate (%) | Reproduced Fast-WAM: 97.0/99.4/96.6/94.8; 96.95 ±0.08 average. Released Fast-WAM reports 97.60. The controlled reference gives +1.15 percentage points overall, strongest on Goal (+2.6); Object decreases 0.2 points. The meanings of ± and the repeat count are unspecified. Published embodied-pretraining baselines provide context, not a unified retraining comparison. e08e10 |
| RoboTwin 2.0 bimanual manipulation Multi-task setup: 2,500 clean-scene and 25,000 randomized-scene demonstrations across more than 50 tasks; 100 trials per task per condition. | PFD: clean 93.11, randomized 92.69, average 92.9 ±0.12. Success rate (%) | Fast-WAM row: 91.88/91.78, average 91.8 ±0.22; LingBot-VA with embodied pretraining: 92.2 average. Reported gains are +1.23/+0.91 points by condition and +1.10 on the displayed average. Table 2 cites Fast-WAM without a released/reproduced label, unlike Table 1; preserve that provenance ambiguity. No physical-robot evaluation is separately reported. e08e11 |
| LIBERO foresight-transfer ablations Section 4.3 controls under the stated PFD training budget; four-suite evaluation. | Default 98.10; pure fine-tuning 96.70; shuffled future 96.62; width 1024 at depths (12,6): 97.36; depths (6,6): 97.40; adapter-only 96.60. Average success rate (%) | Reproduced Fast-WAM: 96.95. Aligned future information helps under these controls, and freezing the backbone loses the gain. Width and video depth change together in the 97.36 row; it is not a clean width ablation. Its displayed suite values average to 97.35; retain the reported 97.36 without inferring unseen precision. e12 |
| LIBERO action-chunk inference latency Single H100; 32-action chunks; 10 denoising steps; 20 timing trials after discarding 5 warmup runs. | Measured cached-context PFD 271.04 versus baseline 257.77: +13.27 ms, +5.15%. Milliseconds per chunk; relative overhead | Table 4 displays 271.0 versus 257.7. Its joint/IDM values, 786.2/1098.1 ms and 3.05×/4.26×, are projections from prior relative slowdowns. The adapter is inexpensive but not free. Prompt-mode PFD separately reports 282.29 ms and +7.80 ms (+2.84%) over its corresponding baseline; do not mix prompt and cached-context protocols. e14 |
6.3 Ablations and diagnostic examples
Read component removals and qualitative examples within their stated evaluation conditions.
Table 3. Breaking temporal correspondence removes the gain; changing width and depth together leaves an unresolved attribution. Original paper, p. 7 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Treat each row as a different intervention, rather than as another leaderboard entry. Pure fine-tuning unfreezes the same backbone subset but removes the teacher and adapter and uses action supervision. Shuffled-future PFD keeps the teacher mask, adapter, losses and schedule while substituting unrelated batch trajectories for future frames. The width-1024 row keeps action depth at 12 and reduces video depth to 6; the supplementary depth row reduces both experts to 6 with width 512. Default PFD uses depths (12,12) and width 512. The bottom adapter-only row freezes the entire backbone. These distinctions matter when assigning a cause to the numerical gaps. e09e12
What it supports. Default PFD averages 98.10, versus 96.70 for direct fine-tuning and 96.62 for shuffled futures. The 97.36 wider/shallow-video setting and 97.40 shallow-both-experts setting recover only part of the gain. Temporal alignment is useful under the tested protocol, and the default adapter cannot recover the improvement with a frozen backbone.
Where the evidence stops. These rows do not isolate width at fixed depth. The wider row's displayed suite entries average to 97.35, while its reported average is 97.36; unseen precision is unspecified. Table 3 supplies no uncertainty estimates, so small row differences lack a reported significance test.
Figure 2. The visual summarizes Table 3's ranking, with a deliberately narrow vertical range. Original paper, p. 8 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Read the printed values and dashed Fast-WAM reference before interpreting bar height. The axis begins at 96.0%, so the drawing emphasizes differences within an already high-success regime. Red bars mark pure fine-tuning and shuffled future; amber bars mark the shallow model and the wider adapter with reduced video depth. Blue arrows measure the remaining 0.70- and 0.74-point gaps to default PFD. Consult Table 3 on page 7 for full settings: the K=6 bar reduces both expert depths, whereas the width-1024 bar retains action depth 12. The compact chart labels emphasize video depth and do not display that whole distinction. e12e13
What it supports. Both amber settings exceed the 96.95 baseline but remain below 98.10. The red controls fall below baseline. This makes the pattern supporting the authors' foresight interpretation easy to see, but the chart is a visualization of the same ablation measurements, not an independent experiment.
Where the evidence stops. The 'Confound Rejected' labels express the authors' interpretation, not a universal causal guarantee. No error bars are provided, and the truncated axis magnifies apparent differences. The plotted 97.36 repeats Table 3's reported mean despite its displayed-row arithmetic discrepancy.
7. Analysis & limitations
7.1 What the evidence leaves open
The authors test one backbone family, an output MLP and a full-horizon teacher mask. They provide no formal conditions guaranteeing that a small adapter can approximate the residual. e15
Figure 1 conflicts with its caption and Eqs. (4)–(10): it marks the student as stop-gradiented, draws a residual-to-adapter arrow, and shows L1 residual matching and cross-entropy instead of the squared flow losses. This report follows the explicit equations and gradient-routing prose; the figure alone cannot specify implementation. e16
The controls support a bounded empirical account, not universal elimination of capacity or regularization explanations. Pure fine-tuning also removes the adapter and changes supervision; the depth–width probe changes two factors. No multi-seed uncertainty is defined for these ablations. e12
7.2 Questions for discussion
- Would the residual remain useful when the future is ambiguous from the current observation?
- How much of the improvement survives a fixed-depth width comparison and repeated training seeds?
8. Reproducibility audit
8.1 Requirements and known gaps
A reproduction needs the inherited Fast-WAM checkpoint/configuration, aligned demonstrations and paired noisy forwards with identical parameters. Exact batch size, frame horizon, action representation, preprocessing, software versions and weighting schedules are not fully specified here; the PDF's code link establishes only an author availability claim. e01e04e08e09
Proposed checks: audit gradient paths against Eqs. (4)–(10), then compare aligned and shuffled teachers under identical settings. Separately hold action depth fixed while crossing video depth and adapter width, reporting seed variation, trainable parameters and compute. These would test implementation fidelity and the unresolved width–depth confound. e06e09e12e16
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: Audit the residual graph, then test aligned versus shuffled futures
Reader-proposed; not run. On LIBERO Goal, first reuse one noisy batch to check that the two teacher-derived losses have equal forward values, that the teacher and residual target are detached, and that residual matching reaches the permitted backbone blocks through the live adapter input after the zero-initialized head has begun learning. Detaching that input should remove this particular gradient path. Then compare aligned and shuffled-future PFD with identical initialization, noisy samples, depths, width, loss weights and training budget across three proposed seeds, using the paper's 500-trial suite evaluation. Record residual error and success, not just total loss. A reproducible aligned-future advantage would support the central account; its disappearance under these controls would weaken it. e05e06e08e09e10e12e16
Check 2: Resolve the width–video-depth confound with a factorial comparison
Reader-proposed; not run. Hold action depth at 12 and cross video depth {6,12} with adapter width {512,1024}, keeping the aligned teacher, data, optimizer, epochs and evaluation fixed. Include reproduced Fast-WAM and use paired evaluation seeds across the four LIBERO suites. Report success variation across training seeds together with trainable parameter counts, GPU time and chunk latency; do not assume these settings have equal compute. A width benefit at fixed video depth would expose an effect Table 3 cannot isolate. A persistent depth benefit at both widths would strengthen the proposed role of video-side adaptation. The published (6,6) row cannot substitute for the missing (12,6), width-512 control. e08e09e12e14
8.3 Reading coverage
Visual audit: All ten PDF pages were rendered and visually inspected, including the title/byline/version on page 1, architecture and caption on page 3, equations and gradient routing on pages 3–5, complete training/evaluation configuration on pages 5–6, Tables 1–2 on page 6, Table 3 and control definitions on page 7, Figure 2 and measured/projected latency context on page 8, limitations on page 9, and references on pages 9–10. All four text chunks were read in full. Six original crops were inspected individually with all table headers, diagram legends and chart axes retained. Figure 1's conflicting gradient/loss markings and Figure 2's compressed depth labels are disclosed in their guides. No appendix is present; separate supplements, code and cited external works were not inspected.
PDF pages inspected for this edition: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. 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
- Title, authors, version and abstract (p. 1)
- 1 Introduction (pp. 1–2)
- 2 Related Work (p. 2)
- 3 Method, including 3.1–3.5 and Eqs. (1)–(10) (pp. 3–5)
- 4 Experiments, including 4.1–4.4 (pp. 5–9)
- 5 Conclusion and Limitations (p. 9)
- References (pp. 9–10)
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.
- Identity: the title and all three authors match the supplied catalog. The inspected PDF is arXiv:2604.25859v2 [cs.RO], stamped 2 May 2026, with a title-page and running-header date of May 5, 2026. The catalog records submission on 2026-04-28. Only the supplied v2 artifact was reviewed; the earlier edition and the reason for the two PDF dates were not verified.
- The supplied extraction does not reconstruct figure images; this limitation was addressed by visually inspecting all ten original PDF pages and all six final crops.
- Separate supplemental material availability has not been fully verified. No appendix is present in the supplied ten-page PDF.
- The linked code and inherited Fast-WAM implementation were not inspected; no experiments were reproduced and no external sources were opened.
The visual audit above records the subsequent illustrated pass.
8.4 Traceable evidence
e01PDF p. 1, title/byline, date, arXiv margin stamp and abstract code statement
Title matches the observed title. Authors are Pengcheng Fang (The University of Southampton), Hongli Chen (The University of Queensland), and Xiaohao Cai (The University of Southampton). Margin: arXiv:2604.25859v2 [cs.RO], 2 May 2026; title date: May 5, 2026. The abstract states that code is available.
Go to primary source ↓e02PDF pp. 1–2, Abstract and Section 1, regularizer/privileged-foresight distinction and contributions
The authors ask what future-video training contributes after removing test-time imagination and propose distilling a future-conditioned action correction.
Go to primary source ↓e03PDF p. 3, Figure 1, attention matrices, training/inference panels and caption
The action-query row sees current video plus actions in the student and all video plus actions in the teacher. The caption states a live student prediction, detached residual and current-only inference.
Go to primary source ↓e04PDF pp. 3–4, Sections 3.1–3.2, Eqs. (1)–(3) and conditioning note
Video and action experts use flow matching. Same-parameter student/teacher forwards reuse identical corrupted inputs and differ in video attention support; the teacher forward is detached. Observation conditioning and scheduler weights follow Fast-WAM but are omitted from the displayed forwards.
Go to primary source ↓e05PDF p. 4, Section 3.3, Eqs. (4)–(5) and adapter initialization paragraph
The detached teacher-minus-student target is predicted by an adapter consuming live base velocity and action timestep. Its zero-initialized output preserves the original student at initialization.
Go to primary source ↓e06PDF pp. 4–5, Section 3.4, Eqs. (6)–(10), Gradient routing and L_res versus L_teacher
Four weighted losses include video/action squared flow errors, detached-target residual matching and teacher consistency. The two teacher losses have equal numerical values but distinct direct and adapter-mediated gradient paths.
Go to primary source ↓e07PDF p. 5, Section 3.5 and Section 4.1 Inference
Every inference step adds the adapter output to the current-only student velocity. Ten denoising steps and guidance scale 1.0 are used, with no teacher mask or future-video generation.
Go to primary source ↓e08PDF p. 5, Section 4.1 Benchmarks and Baselines
LIBERO uses four suites, 500 demonstrations over 10 tasks and 500 trials per suite. RoboTwin uses 2,500 clean and 25,000 randomized demonstrations over more than 50 tasks, with 100 trials per task. Context baselines are copied from Fast-WAM; PFD/Fast-WAM use Wan2.2-5B without embodied pretraining.
Go to primary source ↓e09PDF pp. 5–6, Section 4.1 Training and Implementation
Training specifies 8 H100 GPUs, 30/15 epochs, AdamW, cosine decay, 0.01 weight decay, 1.0 clipping and learning rates 6×10⁻⁵/10⁻⁴. Default depths are (12,12) of 30 blocks each; adapter width is 512 with three SiLU MLP layers. Loss weights are 1/1/0.5/0.1.
Go to primary source ↓e10PDF p. 6, Table 1, Fast-WAM and PFD rows, and Section 4.2 LIBERO
Reproduced Fast-WAM averages 96.95 ±0.08 and PFD 98.10 ±0.06. PFD suite results are 98.6/99.2/99.2/95.4. Released Fast-WAM is 97.60, adapter-only PFD 96.60, and LingBot-VA 98.5. The ± statistic is not defined.
Go to primary source ↓e11PDF p. 6, Table 2, Fast-WAM, PFD and LingBot-VA rows, and Section 4.2 RoboTwin
PFD reports 93.11/92.69 and 92.9 ±0.12 average; Fast-WAM reports 91.88/91.78 and 91.8 ±0.22 average. LingBot-VA with embodied pretraining averages 92.2; its Wan2.2 row lacks a randomized result. Fast-WAM's row has no released/reproduced qualifier.
Go to primary source ↓e12PDF p. 7, Table 3, all rows, and Section 4.3 control descriptions
Default averages 98.10; pure fine-tune 96.70; shuffled future 96.62; width1024/depths(12,6) 97.36; depths(6,6) 97.40; adapter-only 96.60. Pure fine-tuning uses action supervision without teacher/adapter; shuffled futures come from unrelated batch trajectories. The wider row also reduces video depth; its displayed suite entries are 97.9/99.8/97.2/94.5.
Go to primary source ↓e13PDF p. 8, Figure 2, axes, labels, arrows and legend; PDF p. 7, Table 3 for complete depth settings
Figure 2 plots a 96.95 baseline, 98.10 default, 97.40 shallow model and 97.36 wider/shallow-video model, with 0.70/0.74 point gaps. The vertical axis starts at 96.0 and no uncertainty bars are shown. Table 3 identifies both expert depths where the figure labels emphasize video depth.
Go to primary source ↓e14PDF p. 8, Table 4 and Section 4.4, projection paragraph and timing protocol
Table values for joint/IDM are projected from previous slowdowns. Measured cached-context latency is 257.77 ms baseline and 271.04 ms PFD, +13.27 ms/+5.15%, on one H100 for 32-action chunks and ten denoising steps, over 20 trials after five warmups. Prompt-mode PFD is 282.29 ms, +7.80 ms/+2.84%.
Go to primary source ↓e15PDF p. 9, Section 5, Limitations paragraph
The study uses one output MLP, a full-horizon teacher mask and one backbone family. Richer adapters/masks and theoretical conditions for low-capacity residual approximation remain unexplored.
Go to primary source ↓e16PDF p. 3, Figure 1 training panel and caption; PDF pp. 4–5, Eqs. (4)–(10) and gradient-routing prose
The graphic places a stop-gradient marker at the student, an arrow from residual to adapter, and L1/cross-entropy loss formulas. Its caption and equations instead specify a live adapter input, a detached residual target, and squared velocity losses including video flow matching. These source inconsistencies are retained, not repaired.
Go to primary source ↓8.5 Primary sources
Privileged Foresight Distillation: Zero-Cost Future Correction for World Action Models ↗
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