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Sparsity Should Be ALLOTted by Output: Training-Free Allocation of Block-Sparse Attention for Video Diffusion Transformers

Tianze Xia, Xiaoling Zhou, Ruya Lan, Yiqiao Liao, Chengru Song, Shiming Xiang

arXiv:2610.29441v1cs.CV

TL;DR

Video Diffusion Transformers incur high costs from full 3D attention, while allocation heuristics and local metrics may not capture final-video effects. ALLOT calibrates layer-step cells against output error and jointly allocates density under measured latency. It outperforms or ties compared allocation methods across the reported settings at equal or shorter wall-clock time.

  • Problem

    Existing sparse-attention allocation relies on heuristics or local metrics rather than direct final-video effects, although allocation substantially affects fidelity.

    Source: §1 · p. 1

  • Method

    ALLOT estimates each layer-step cell's final-video error using cell probing and trajectory calibration, then jointly optimizes densities under measured latency.

    Source: §1 · p. 1, §4.1 · p. 3, §4.3 · p. 5

  • Results

    ALLOT outperforms every compared allocation method on XAttention and outperforms or ties the default on four other published pipelines, all at equal or shorter wall-clock time.

    Source: §1 · p. 2, §6 · p. 8

  • Takeaways & Limitations

    For fixed models and selection strategies, offline sensitivity measurements can be reused across prompts, budgets, step counts, guidance scales, and samplers.

    Source: §6 · p. 8

    ALLOT requires offline calibration, and changing selection strategies requires new cell probes.

    Source: §6 · p. 8

Abstract

from arXiv · show

Full 3D attention is costly in video Diffusion Transformers. Block-sparse attention reduces this cost by computing only selected attention blocks. However, existing methods either overlook the potential to optimize sparsity allocation or rely on heuristic rules or local metrics to guide it. In this work, we observe that sparsifying attention in different layers and at different denoising steps affects final-video fidelity to substantially different degrees. Yet the identities of the most sensitive layer-step pairs remain nearly unchanged across inputs. Building on these findings, we propose Allocating Layer-step Latency by Output Tests (ALLOT), a training-free sparsity allocation method. Treating each layer-step pair as a cell, ALLOT estimates each cell's contribution to final-video error through (i) cell probing and (ii) trajectory calibration, then jointly optimizes cell densities under a measured-latency budget. It preserves existing selection strategies and kernels, replacing only the allocation component. At equal or shorter wall-clock time, ALLOT outperforms every compared allocation strategy with XAttention, with an 11.8 dB PSNR gain on HunyuanVideo. Extensive experiments across four additional published pipelines on Wan2.1, Wan2.2, and HunyuanVideo show that ALLOT outperforms or ties the default in all nine settings.

1. Introduction

Full 3D attention makes video generation costly, while existing block-sparse methods leave allocation to heuristics or local metrics that may not reflect final-video fidelity. ALLOT measures layer-step sensitivity and allocates density under a latency budget, outperforming compared allocation strategies at equal or shorter wall-clock time.

1. Introduction

  • Full 3D attention cost grows quadratically with token count, motivating sparse attention for video Diffusion Transformers.Attention accounts for more than half of end-to-end time for a reported Wan2.1-14B generation.Source: §1 · p. 1
  • Existing allocation rules rely on heuristics or local metrics, which may transfer poorly across settings and can yield lower fidelity than a uniform baseline.Changing only allocation can substantially alter final-video fidelity.Source: §1 · p. 1
  • ALLOT treats each layer-step pair as a cell, estimates its final-video sensitivity using cell probing and trajectory calibration, then jointly allocates densities under measured latency.Sensitivity is the final-video degradation relative to the dense output; existing selection strategies and kernels remain unchanged.Source: §1 · pp. 1–2
  • Figure 1 contrasts dense output, baseline, and ALLOT output at equal wall-clock time, alongside paired PSNR gains and confidence intervals.The illustrated prompts are near the median gain; open markers denote ties.Source: Figure 1 · p. 2
  • ALLOT outperforms or ties every compared allocation at equal or shorter wall-clock time across six selection strategies and three model families.It replaces only the allocation component of existing pipelines.Source: §1 · p. 2

2. Related Work

Prior block-sparse attention work includes trained and training-free approaches, while allocation methods vary in what they allocate and which signals or rules guide them. ALLOT retains existing selection strategies and kernels but calibrates layer-step allocations against final-video effects.

2. Related Work

  • Training-free methods use static masks or runtime block selection, while trained methods train or fine-tune models with sparse attention.ALLOT preserves existing selection strategies and kernels, replacing only allocation.Source: §2 · p. 2
  • Existing methods allocate density or patterns at layer, head, step, or combined levels using local metrics such as attention mass, Hellinger distance, or one-step error.Across steps, many use heuristic warm-up, preset shapes, or equal treatment.Source: §2 · p. 2
  • ALLOT allocates per layer-step cell but calibrates against final-video error to capture cross-step amplification and jointly optimizes cells under measured latency.Source: §2 · p. 2

3. Motivation and Key Observations

Directly measuring every layer-step cell's final-video sensitivity would require thousands of generations, so the analysis decomposes sensitivity into cheaper signals. Its observations show that layer and step effects vary substantially, while sensitivity rankings remain stable across inputs.

3. Motivation and Key Observations

  • The analysis defines cell sensitivity as final-video degradation relative to dense output and decomposes it into one-layer, one-step error and final-video error from sparsified step windows.Direct measurement for every cell would require thousands of full generations.Source: §3 · p. 2
  • Layer sensitivity varies widely: the first one or two layers can have one-step errors up to 154 times the median-layer error, and attention-map metrics produce different rankings.The most sensitive layer differs across models, limiting fixed first-layer rules.Source: §3 · p. 2, Figure 2 · p. 3
  • Earlier windows cause markedly larger final-video errors than later windows under the same sparsification, with first-to-last MSE ratios reaching several hundred for some models.One-step errors show smaller differences and can reverse the first-versus-last ordering on Wan2.2.Source: §3 · p. 3, Figure 2 · p. 3
  • Across tested models, per-input sensitivity rankings closely match rankings aggregated over calibration inputs, with median Spearman correlations of 0.80–1.00.This supports offline measurement and reuse across prompts for a fixed model and selection strategy.Source: §3 · p. 3

4. ALLOT

ALLOT estimates each layer-step cell’s contribution to final-video error, then jointly allocates cell densities under a measured-latency budget. It uses cell probes and trajectory calibration while retaining existing attention selection strategies and kernels.

4. ALLOT

  • ALLOT combines cell probing, trajectory calibration, and latency-constrained allocation to optimize every layer-step cell’s density.The method approximates final-video error as a sum of per-cell contributions and solves for densities under a measured-latency budget.Source: §4 · p. 3, §4.1 · p. 3

4.1. Problem formulation

  • A first-order estimate factorizes each cell’s final-video sensitivity into within-step output error and downstream amplification, assuming additive layer errors and step-wise separability.The trajectory gain is calibrated from final videos generated with a window of steps sparsified; only relative sensitivities affect allocation.Source: §4.1 · pp. 3–4

4.2. Cell probing on the model output

  • Each cell probe measures one layer’s velocity-prediction MSE against the dense model at a given noise level and candidate density.Probes use a small number of videos; layer rankings are input-stable, and probes are measured using the deployment selection strategy by default.Source: §4.2 · p. 4

4.3. Trajectory calibration against the final video

  • Trajectory calibration sparsifies all layers within a step window and divides its final-video pixel MSE by summed cell-probe errors to estimate a shared step gain.The calibrated gain captures downstream propagation, average cross-layer interactions, and latent-to-pixel conversion; each window requires one generation per prompt.Source: §4.3 · pp. 4–5

4.4. Latency-constrained allocation

  • The solver minimizes estimated sensitivity plus a Lagrangian penalty for measured latency, selecting cell densities and finding an exact optimum of the discrete surrogate at its attained budget.Measured sparse-kernel latency is not proportional to density; warm-up length and which cells remain dense emerge from the solution rather than heuristic rules.Source: §4.4 · p. 5

4.5. Inference and integration with existing selection strategies

  • At inference, ALLOT looks up each cell’s precomputed density and applies the existing dense or sparse kernel, changing only the allocation while retaining the strategy’s selection and ranking.It applies where per-cell density is controllable and latency measurable; fixed-mask strategies are limited to densities reachable through their mask parameters.Source: §4.5 · p. 5

5. Experiments

Across allocation comparisons, published-pipeline integrations, and model settings, ALLOT generally improves or matches fidelity at equal or shorter wall-clock time. Experiments also test its components, sensitivity estimates, calibration stability, and offline cost.

5.1. Experimental setup

  • The evaluation uses four models, 50 denoising steps, and 32 VBench prompts; fidelity metrics compare outputs with dense references rather than measuring absolute generation quality.A win requires a positive lower bound of the paired 95% PSNR-difference interval and lower mean LPIPS; other cases may be ties.Source: §5.1 · p. 5

5.2. Comparison with other allocation methods

  • With XAttention’s selection strategy and kernel fixed, ALLOT outperforms every compared allocation method by 1.53–7.31 dB.The comparison is organized by wall-clock time, with ALLOT re-solved for the first two groups.Source: §5.2 · p. 6, Table 1 · p. 7

5.3. Integration with published pipelines

  • ALLOT beats the default in six of nine published-pipeline settings and ties in three, with up to 5.03 dB PSNR gain at equal or shorter wall-clock time.On HunyuanVideo with SVOO, it improves PSNR by 3.38 dB while increasing end-to-end speedup from 1.75× to 1.90×.Source: §5.3 · p. 6

5.4. Cross-model comparison

  • On three Wan models, ALLOT outperforms uniform and strengthened density baselines, and it remains above the uniform baseline across tested budgets at 720p×81.At 480p×33, it also beats the strengthened baseline when that baseline’s warm-up is re-searched at each of three budgets.Source: §5.4 · p. 6

5.5. Ablation study

  • Trajectory calibration is the dominant ablation component: setting w(s)=1 lowers PSNR by 7.05 dB, while a greedy rule on the same one-step errors reaches 19.38 dB.A shared density across layers and a parametric shape rule also underperform; density-proportional cost makes no significant difference after wall-clock alignment.Source: §5.5 · p. 6

5.6. Verification, robustness and offline cost

  • Across 80 held-out-prompt tables at multiple budgets, predicted and measured sensitivity rankings agree strongly (pooled Kendall τ=0.83).Permuting ALLOT’s densities among cells lowers PSNR on every prompt at fixed total cost.Source: §5.6 · p. 6
  • Four probing videos and eight calibration prompts suffice for stable cell decisions; eight probing videos add no significant gain over four, and one or two lose less than a tenth of ALLOT’s gain.Calibration with SpargeAttn rather than mean-pooled top-k yields 0.993 correlation in w and 96.0–96.5% cell-decision agreement.Source: §5.6 · p. 6
  • Offline measurement takes roughly 6–23 GPU-hours per model, or over 30 hours for Wan2.2’s two experts; changing budget or step count requires only about four seconds to re-solve.Measurements are performed once per model and selection strategy.Source: §5.6 · p. 6

6. Conclusion

ALLOT addresses layer–step sensitivity that varies substantially but is nearly input-invariant for a fixed model and selection strategy. Across the tested model families and pipelines, it improves or ties allocation baselines, while retaining offline-calibration and modeling constraints.

6. Conclusion

  • Layer–step sensitivity is not reliably captured by local metrics, yet is nearly input-invariant for a fixed model and selection strategy.ALLOT calibrates one-step errors against final-video damage and optimizes a latency-constrained density table; trajectory calibration is the dominant ablation component.Source: §6 · p. 8
  • Across three model families, ALLOT outperforms every compared allocation method on XAttention and outperforms or ties defaults on four other published pipelines at equal or shorter wall-clock time.The conclusion also identifies offline calibration, strategy-specific probes, and limitations of the additive layer-separable estimate.Source: §6 · p. 8
  • ALLOT requires offline calibration, new cell probes when selection strategies change, and uses an additive layer-separable estimate that predicts rankings more reliably than error magnitudes.The conclusion names modeling cell interactions and preserving adaptive thresholds as future work.Source: §6 · p. 8

Supplementary Material

The supplement specifies how fidelity verdicts and timing comparisons are defined, along with the calibration scope for trajectory gains.

A.1. Metrics and verdicts

  • A win requires a positive lower bound of the paired PSNR interval and lower mean LPIPS; a loss requires a negative upper bound and higher mean LPIPS, with all other outcomes tied.DISTS is listed only as a supplement, and paired differences are ALLOT minus baseline.Source: §A.1 · p. 11
  • Trajectory gain is calibrated once per model family and shared across that family’s tables, but SVG2’s different flow shift requires rerunning window experiments on its schedule.Calibration families include Wan2.1, Wan2.2-A14B, and HunyuanVideo.Source: §A.1 · p. 11

A.2. Timing and equal wall-clock time

  • Wall-clock time is the per-video median including text encoding, denoising, and VAE decoding; ALLOT counts as matched when its time is no more than 1.01× the baseline’s.Speedups are measured relative to each pipeline’s own dense time.Source: §A.2 · p. 11

B.1. Cell probes and attention-map metrics

The supplementary analyses compare cell probes with attention-map metrics, test alternative cross-layer and per-head allocations, and describe the window calibration runs.

B.1. Cell probes and attention-map metrics

  • Attention-map metric rankings partly agree with cell probes on 1.3B, are essentially unrelated on 14B, and reverse on HunyuanVideo; on 14B, the cell-probe ratio reaches 154×, 75×, and 71× at the tested steps.SVOO’s released per-layer densities have Spearman correlation −0.14 with probes, versus +0.59 on 1.3B when probes use SVOO’s selection strategy.Source: §B.1 · p. 11

B.2. Allocating by other cross-layer metrics

  • Against Hellinger2-guided allocation, ALLOT’s paired PSNR differences are +3.62 dB on 1.3B 480p, +5.88 dB on 14B 480p, and +1.38 dB on HunyuanVideo 480p.On HunyuanVideo 480p×33, ALLOT also exceeds allocation proportional to SVOO’s default per-cell densities by +2.40 dB paired PSNR.Source: §B.2 · p. 11

B.3. Per-head allocation within a cell

  • On SVOO 1.3B 720p×81, ALLOT’s equal head split yields 1.44 dB higher PSNR than a per-head split proportional to SVOO’s default densities.LPIPS and DISTS also favor ALLOT’s equal split.Source: §B.3 · p. 11

C.1. Window experiments

  • The window experiments divide 50 steps into ten five-step windows, sparsify all layers to 0.30 in one window at a time, and use eight VBench prompts per window.Source: §C.1 · p. 11

C.2. One-step error with all layers sparse

Sparsity errors vary sharply across denoising steps, and one-step measures can misstate their final-video impact. ALLOT’s trajectory calibration addresses this difference, while sensitivity rankings remain stable across inputs.

C.2. One-step error with all layers sparse

  • Final-video first-to-last-window MSE ratios reach 463×, 186×, 69×, and 109× across the four models, while one-step errors understate those ratios by 72×, 78×, 2.3×, and about 600×.The first/last one-step-error ratios are 6.4×, 2.4×, 31×, and 0.18×, respectively.Source: §C.2 · p. 12

C.3. Local variation and attention concentration

  • PASA’s local-variation score has Spearman correlation +0.02 with final-video window error, while attention-concentration ratios are smaller than the one-step and final-video ratios.The Hellinger2 ratio is 2.72× and the 90%-attention-coverage density ratio is 2.20×, compared with 6.4× for one-step error and 463× for final video.Source: §C.3 · p. 12, §C.2 · p. 12

C.4. Comparison differing only in step-wise allocation

  • +1.77, +3.18, and +4.46 dB: trajectory-gain allocation beats the fixed-first-15-steps allocation at the three 1.3B budgets, with wall-clock time differing by at most 1.3%.On 14B 480p, the gain is +3.00 dB at 264.5 / 269.9 s; LPIPS is better in all four groups.Source: §C.4 · p. 13

D. Observation 3: Across Inputs

  • Across inputs, layer and step sensitivity rankings remain stable: per-video layer-ranking correlations are 0.80–0.91 in the reported settings, and step-window ranking medians are 0.95–1.00.The first/last-window MSE ratio varies across prompts even when rankings remain stable.Source: D. Observation 3: Across Inputs · p. 13

E.1. First-order error propagation

  • A first-order propagation model carries each step’s sparse velocity error through subsequent denoising; ALLOT combines within-step cell probes with a trajectory gain calibrated from sparse-window generations.For Wan’s multistep UniPC sampler, past velocities are included in the state; the calibrated gain also captures average cross-layer interactions and latent-to-pixel conversion.Source: §E.1 · p. 13

E.2. Proof of Eq. (2) and Proposition 1

This section establishes the discrete optimization result and tests the sensitivity estimate and its deployment components. The tests expose strategy- and model-specific qualifications alongside favorable comparisons.

E.2. Proof of Eq. (2) and Proposition 1

  • For any λ, the per-cell minimizing table is an exact discrete optimum of the estimated objective over candidate densities at its attained budget, without requiring convexity.A requested budget may not be attainable exactly; the returned within-budget table is bounded by the two bracketing solutions.Source: §E.2 · p. 14

E.3. Final video with a single layer sparse over all steps

  • Predicted and measured layer rankings match exactly on 1.3B and HunyuanVideo (Spearman 1.00) and nearly match on 14B (0.94); coverage density misranks sensitive HunyuanVideo layers.Layers 54 and 58 are ranked most sensitive by coverage density, yet sparsifying them yields 11.83 and 15.93 dB higher PSNR than sparsifying layer 1.Source: §E.3 · p. 14

E.4. Separability and additivity

  • In the tested 1.3B layer-group comparisons, final-MSE-to-injected-energy ratios differ by less than 2× in window 6 and energy-matched early windows, but by 2.17× in window 4.The test covers only the stated groups and densities.Source: §E.4 · pp. 14–15

E.6. Reassigning the same densities

  • Reassigning ALLOT’s same densities across cells worsens all five tested tables on all three metrics; layer shuffling alone is 3.40 dB lower.The measured order matches the additive-model prediction (Kendall τ = 1.0).Source: §E.6 · p. 15

E.7. Oracle diagnostic of trajectory calibration

  • Across six Wan2.1 oracle settings, both transformed-error controls yield higher PSNR than ordinary sparse runs for every prompt; this tests pattern sensitivity, not a universal propagation gain.Wan2.2 and HunyuanVideo interventions remain untested, and the first window approaches saturation.Source: §E.7 · p. 16

F.1. Cell probes: definition, grid and interpolation; F.2. In-context check

  • Cell probes isolate one layer’s velocity-prediction error at a noise level, but in-context correction is model-specific and is not applied to the paper’s tables.The correction raises HunyuanVideo PSNR by 0.46 dB but lowers it by 6.09 dB on Wan2.1-1.3B and 0.78 dB on both Wan2.2 experts.Source: §F.2 · p. 16, §F.1 · p. 16

F.3. Latency tables of each path; F.4. Solving: Algorithm 1, candidate densities and density cap; F.6. Offline cost

  • The solver uses measured latency rather than density or FLOPs as cost, selects densities by per-cell minimization under a budget, and prepares probe and latency tables offline.For Wan2.2-A14B, the two experts’ probes take 26 GPU-h and trajectory gain generation takes 6.5 GPU-h.Source: §F.4 · p. 17, §F.3 · p. 17, §F.6 · p. 17

F.5. Integration

  • +5.98 dB: at equal wall-clock time, ALLOT remains above XAttention’s strengthened threshold-based default.Replacing XAttention’s thresholds with induced densities improves PSNR by 2.27 dB at 1.9% more wall-clock time; density truncation’s effect differs for SVOO.Source: §F.5 · p. 17

G.2. XAttention and HEART

The XAttention evaluations compare ALLOT with allocation alternatives at matched or shorter wall-clock time, including HEART-related baselines and settings on HunyuanVideo and 720p Wan2.1. Across these evaluations, ALLOT improves fidelity against several alternatives, with results varying by metric and comparison.

G.2. XAttention and HEART

  • ALLOT’s VBench difference over original FAST is +0.30, while its +0.13 difference over original PASA is not significant.The reported VBench composite weights six dimensions; VBench does not determine the win/loss verdict.Source: §G.2 · p. 19
  • ALLOT’s PSNR gains over FAST, PASA, and the DFSAttn-style rule are 3.76 dB, 4.57 dB, and 1.48 dB, respectively.LPIPS and DISTS are better in every row; the held-out-prompt rerun leaves every verdict unchanged.Source: §G.2 · p. 19, Table G.1 · p. 19

G.3. XAttention on HunyuanVideo

  • At default wall-clock time, HunyuanVideo ALLOT gains 11.84 dB over the default, 10.88 dB over EBC, and 7.16 dB over FAST in PSNR.SSIM, LPIPS, and DISTS are also better on all 32 prompts in each comparison.Source: §G.3 · pp. 19–20, Table G.3 · p. 20

G.4. XAttention on 1.3B 720p×81

  • On Wan2.1-1.3B at 720p×81, ALLOT gains 6.35 dB in PSNR over the default, 5.16 dB over EBC, and 5.21 dB over HEART (EBC + TMR).It is faster than the default and EBC; ALLOT + TMR runs at HEART’s wall-clock time.Source: §G.4 · pp. 20–21, Table G.4 · p. 21

H. Published Pipelines and Fidelity–Speedup Curves

  • Table 2 speedups use dense wall-clock times from Table H.1 as their reference, with the dense path matched to each pipeline.SpargeAttn and Radial use the dense path of the same kernel; SVOO and SVG2 use their own dense pipeline runs.Source: H. Published Pipelines and… · p. 21

H.1. SVOO

This section evaluates ALLOT across published sparse-attention pipelines and includes ablations on allocation shape and cost modeling. Results are favorable in several settings, but some metrics and comparisons show ties or favor the default.

H.1. SVOO

  • On Wan2.1-14B at 720p, ALLOT reaches the default’s wall-clock time with 31.70 dB PSNR, a 3.55 dB gain over the default.SSIM, LPIPS, and DISTS are also better; on Wan2.1-1.3B at 720p, PSNR rises by 0.66 dB while LPIPS and DISTS favor the default.Source: §H.1 · p. 21, Table H.3 · p. 22
  • At equal wall-clock time on HunyuanVideo 720p×129, ALLOT gains 3.38 dB in PSNR over the default and improves SSIM, LPIPS, and DISTS.It runs 7.9% faster than the default; the reported paired intervals for the other three fidelity metrics also favor ALLOT.Source: §H.1 · p. 21, Table H.2 · p. 22

H.2. SpargeAttn

  • On SpargeAttn’s 720p settings, retuning raises PSNR from 28.64 to 30.88 dB for the official checkpoint and from 29.30 to 31.29 dB for the retuned checkpoint.The corresponding wall-clock times and speedups also change with tuning; ALLOT’s tables leave 40–55% of cells dense, using SDPA.Source: §H.2 · p. 21

H.3. Radial

  • At 720p×81, ALLOT’s PSNR is 30.45 dB versus 28.45 dB for the Radial default at equal wall-clock time in the decay-1.0 operating point.For HunyuanVideo, the PSNR difference is −0.55 dB and the SSIM, LPIPS, and DISTS intervals all contain zero.Source: §H.3 · p. 21, Table H.4 · p. 22

H.4. SVG2

  • SVG2 results are mixed: ALLOT reaches 25.60 dB PSNR with a 1.34 dB gain, but DISTS favors the default.Mean SSIM is slightly better and mean LPIPS slightly worse; the VBench difference is not significant.Source: §H.4 · pp. 22–23

H.5. Fidelity–speedup curves at 720p×81

  • The fidelity–speedup sweep solves one table per budget and pairs it with a uniform baseline at matched wall-clock time, with group times differing by at most 2%.The figure distinguishes ALLOT, the equal-time uniform baseline, and a strengthened baseline.Source: §H.5 · p. 23

I.1. Ablation on XAttention

  • The XAttention parametric shape rule keeps the first 10 steps and layer 0 dense, then lowers other layers’ density linearly from 0.59 to 0.05.Its shape is taken from an XAttention solved table and its coefficient is chosen to match ALLOT’s cost.Source: §I.1 · p. 23

I.2. Density-proportional cost

  • With density-proportional cost in the solver, the resulting table has mean density 0.48 but latency-table cost 0.73 of dense, and its PSNR, SSIM, and LPIPS do not differ significantly from ALLOT’s.The table contains 446 dense cells, compared with ALLOT’s 587.Source: §I.2 · p. 23

I.3. Calibration metric of the trajectory gain

The section tests trajectory-gain calibration, cross-model behavior, solved density patterns, and robustness to calibration and inference changes. The reported results show that calibration choices and budgets matter, while several measurement choices preserve most allocation decisions.

I.3. Calibration metric of the trajectory gain

  • Calibrating trajectory gain with LPIPS or DISTS instead of pixel MSE lowers PSNR by 0.84 dB or 2.06 dB, respectively.The perceptual metrics saturate at large errors and underweight early steps; the first-to-last-step weight ratio is 1/9 for LPIPS and 1/29 for DISTS relative to MSE.Source: §I.3 · p. 23

J. Cross-Model Comparison; J.1. Summary of four models

  • On the reported held-out Wan models, ALLOT gains 2.18 dB over the strengthened baseline and 6.49 dB over the uniform baseline on 1.3B, and 0.44 dB and 8.82 dB, respectively, on 14B 480p.The 14B strengthened-baseline comparison is not significant on DISTS.Source: §J.1 · p. 23

J.2. Wan2.2-A14B

  • For Wan2.2-A14B, the two experts share one table, with probe noise levels mapped onto each expert’s own schedule steps.The table uses Wan2.2’s measured trajectory gain, 14B’s latency table, and the same layer-step budget across groups.Source: §J.2 · p. 23

J.3. Solved tables

  • Solved warm-up length increases with budget, while the pattern of fully dense layers differs across Wan models and HunyuanVideo.At the same budget, Wan models have a 15-step warm-up; HunyuanVideo has no fully dense step, while layers 0 and 1 are dense throughout on HunyuanVideo and for at least 47 steps on Wan.Source: §J.3 · pp. 23–24

J.4. Strengthened baseline at other budgets

  • At budgets 0.20 and 0.45, reusing the k=20 strengthened baseline selected at 0.30 trails the best k by 1.10 dB and 2.32 dB, respectively.After re-searching k, ALLOT remains a win at both budgets; all k values are selected on the evaluation set.Source: §J.4 · pp. 24–25

K.1. Number of calibration inputs

  • With two probing videos, 96–99% of cells retain the same dense/sparse status across models; on XAttention 1.3B, one or two videos lose less than 0.6 dB.Eight videos bring no significant improvement, while step-wise rankings are more sensitive to calibration inputs than layer-wise rankings.Source: §K.1 · p. 25

K.2. Robustness of the trajectory gain; K.3. Probe resolution

  • Changing calibration density changes 0.6% of cells and PSNR by −0.02 dB, while recalibrating trajectory gain on held-out prompts yields a log correlation of 0.999.Across re-solved tables, 98.4–99.3% of cells retain their dense/sparse status; at SVOO 720p, the probe-resolution PSNR change is +0.05 dB with an interval containing zero.Source: §K.2 · p. 25, §K.3 · p. 25

K.4. Inference settings

  • With 30 steps, CFG 7.5, or the Euler sampler, ALLOT wins at equal wall-clock time by 5.93 dB, 6.80 dB, and 7.18 dB in PSNR, respectively.The CFG and sampler changes reuse the existing table; for 30 steps, the table is re-solved using the nearest 50-step trajectory-gain noise levels.Source: §K.4 · pp. 25–26, Table K.2 · p. 26

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