PaperlayerView exact revision on arXiv

Source-linked AI summary

Bridging the Data Gap: Source-Informed Task-Space Transport for Few-Shot Diffusion

Jinjian Jiang, Jing Peng, Rehan Deen, Yu Cao, Ziquan Liu, Muhammad Salman Haleem, David Mguni

arXiv:2610.31323v1cs.LGcs.AI

TL;DR

When target data are scarce, repeated target-specific generator adaptation is costly and can be unreliable. Meta-Diff learns a recurring source–target relation in task space; CIFAR-100 supports source-specific gains under controlled shifts, while Office-Home exposes a semantic limitation.

  • Problem

    Adapting a high-capacity generator for each sparsely observed target is costly, motivating reuse of recurring source–target structure across semantic tasks.

    Source: §1 · pp. 1–2

  • Method

    Meta-Diff encodes distributions in a shared task space, transports a new source coordinate using a learned relation, and generates without target-time optimisation.

    Source: §1 · p. 2, §3 · p. 3

  • Results

    CIFAR supports source-specific improvement in measured distributional metrics with zero target images and a known relation, while Office-Home shows target-domain alignment without reliable object identity.

    Source: §7 · p. 11, §6 · p. 11

  • Takeaways & Limitations

    The results define a measurable operating regime involving usable task identity, relation predictability, transport headroom, and semantic use of the coordinate.

    Source: §6 · p. 11, §7 · p. 11

    CIFAR evidence is limited to measured distributional metrics under controlled shifts and tested checkpoints; Office-Home alignment does not yield reliable object-specific generation.

    Source: §6 · p. 11

Abstract

from arXiv · show

Many deployments require a model to move rapidly from a data-rich source to a related target observed only sparsely. This is especially consequential where target data are difficult to collect, as in healthcare settings with persistent population or acquisition imbalances. Retraining or fine-tuning a high-capacity generator for every target is costly and can be statistically unreliable when target data are scarce. We introduce Meta-Diff, which instead learns a recurring source--target relation once in a compact task space. A shared encoder maps each distribution to a low-dimensional coordinate; a learned relation transports a new source coordinate to its predicted target, and a shared diffusion backbone generates from that prediction without target-specific retraining. Controlled Gaussian-mixture experiments identify when this works: task identity must survive the representation, the relation must generalise across tasks, and the source--target shift must leave useful headroom for transport. On held-out CIFAR-100 validation tasks, correct source $+$ transport achieves 13.9% lower mean SW than transport from the wrong source. With validation-selected adaptation settings in the final-test one-target comparison, its mean SW is 14.7% lower than target-only modelling and 32.7% lower than full fine-tuning; the main route itself uses no target image and assumes the applicable relation is known. On matched CIFAR test episodes, generating from the clean-source coordinate and then applying the known corruption yields lower SW than task-space transport. Office-Home exposes a complementary boundary: transport can align target-domain statistics without reliable object identity. Together, these results recast extreme-few-shot adaptation as reusable transport in task space, while making the conditions for its success and failure directly measurable.

1 INTRODUCTION

Meta-Diff addresses scarce target data by learning a recurring source–target relation across semantic tasks, then applying it in task space to a held-out task. The introduction frames its evaluations around when this transport helps and where it remains limited.

1 INTRODUCTION

  • The approach targets settings where target data are scarce or costly to collect, including healthcare settings affected by uneven population, institution, or acquisition coverage.Representative target-data collection remains the preferred long-term remedy.Source: §1 · p. 1
  • A shared encoder maps source and target distributions into task space, where a learned relation transports a held-out task’s source coordinate for generation.The main route generates from the transported coordinate without target images, coordinate refinement, or backbone updates.Source: §1 · p. 2, Figure 1 · p. 2
  • At one target image, SW is 0.1781 for direct transport, 0.2087 for target-only, and 0.2648 for full fine-tuning.The comparison uses validation-selected, budget-specific adaptation settings; full fine-tuning has lower mean SW at KT = 20.Source: §1 · pp. 2–3
  • The 210-run GMM study maps operating conditions, while CIFAR-100 tests source-specific generation and comparisons with target-adapted baselines.The study distinguishes usable task information, relation generalisation, and transport headroom as conditions for success.Source: §1 · p. 2
  • Office-Home shows target-domain alignment without reliable object-specific generation, while FiLM independently reproduces source specificity.The transport-structure ablations test whether nonlinearity is needed.Source: §1 · p. 3

2 RELATED WORK

Prior work compresses target adaptation and reuses experience across tasks, while Meta-Diff focuses on amortising a recurring source–target relation across semantic tasks. The related work also motivates data-asymmetric transfer while treating representative collection as necessary.

Few-shot diffusion and compact adaptation

Meta-learning and task representations

  • Meta-learning, Deep Sets, FiLM, and Transfer Guided Diffusion Processes provide related tools, but Meta-Diff requires the source–target relation to generalise to held-out semantic tasks.Success depends on task representation quality as well as adaptation capacity.Source: §2 · p. 3

Data asymmetry as motivation

  • Uneven population and institutional coverage can accompany subgroup degradation in medical imaging, motivating use of related abundant data without treating synthetic data as a substitute for representative collection.The clinical studies are framed as stress tests and limitations, not evidence for clinical deployment.Source: §2 · p. 3

3 PROBLEM AND METHOD

Meta-Diff embeds source and target distributions in a shared task space, then predicts a target coordinate from the source coordinate and a known relation. Its theory addresses coordinate estimation and stability, while leaving task identity and relational generalisation to experiments.

3 PROBLEM AND METHOD

  • The deployment protocol provides abundant source support and permits independent baselines target support; Meta-Diff’s main route uses only source support and the known relation.The comparison focuses on MS ≫ KT, with a disjoint target query set for evaluation.Source: §3 · p. 3
  • A shared permutation-invariant encoder places source and target distributions in a common task space, turning transfer into coordinate prediction rather than target-specific high-dimensional optimisation.The shared generator is conditioned through additive residual noise-prediction fields or, in a separate variant, FiLM modulation.Source: §3 · pp. 3–4
  • The final transport is ezT = AzS + bcS→T, using a relation-specific bias learned during meta-training; the applicable relation is assumed known at deployment.Unseen relations are outside the protocol, and the main route decodes the prediction without target-time refinement or backbone updates.Source: §3 · p. 4

3.1 META-TRAINING AND STABILITY UNDER LIMITED OBSERVATIONS

  • Meta-training supervises source, target, and transported-coordinate denoising losses on disjoint query sets, but deployment reads no target support or query and updates neither coordinates nor backbone weights.The transport map itself takes only the source coordinate and relation.Source: §3.1 · p. 4
  • The propositions establish source-coordinate estimation and continuous-time stability under stated assumptions, not semantic task identity, unseen-task relation generalisation, or small practical error for the trained DDIM sampler.The coordinate-estimation mean-squared error decays at O(M^-1); the stability result concerns an additive-score-conditioned process with uniform Lipschitz bounds.Source: §3.1 · pp. 4–5

4 EXPERIMENTAL DESIGN

The evaluation combines controlled GMM tasks, held-out CIFAR-100 corruption tasks, and a natural Product→Clipart domain shift. Comparisons are paired where possible, with uncertainty procedures and dataset splits specified for each benchmark.

4 EXPERIMENTAL DESIGN

  • Headline comparisons are paired on task, support draw, target query set, and sampling noise where possible; CIFAR intervals use class-cluster bootstrap resamples and omit training-seed variation.The 95% intervals are pointwise without multiplicity adjustment, and adaptation hyperparameters are selected on validation tasks before final testing.Source: §4 · p. 5
  • The GMM study varies task separation and relation heterogeneity across 210 trained cells and 13,440 held-out task evaluations, with a separate shift-magnitude sweep.Known distributions allow intrinsic Bayes task identification, learned-coordinate identification, and held-out affine relation predictability to be distinguished.Source: §4 · p. 5
  • CIFAR-100 holds out entire superclasses, uses clean sources and fixed-severity blur, noise, or contrast targets, and compares source controls with target-only modelling and full fine-tuning.Sliced Wasserstein is the headline distribution metric; energy MMD and semantic consistency are complementary measures.Source: §4 · p. 5
  • Office-Home evaluates Product→Clipart across 65 object categories with a 45/10/10 train-validation-test class split, then probes semantic limitations using frozen-checkpoint diagnostics.Real-image audits check the semantic evaluator and domain distinction before generated images are scored.Source: §4 · p. 5

5 RESULTS

On final-test CIFAR episodes, correct-source transport outperforms target-only modelling at one target image, while a clean-source image-space corruption route has lower SW than transport. The results also show that transport’s distributional gains are bounded by task-identity and semantic-fidelity limitations, with different boundaries in controlled GMMs and Office-Home.

5.1 GMM: A CONTROLLED OPERATING REGIME

  • In GMMs, correct-source advantage disappears without source identity and weakens as relation predictability declines; usable learned-coordinate identity is more closely associated with gain than intrinsic identity.At α = .25, Bayes identification is .953 while learned-coordinate nearest-centroid identification is .325; across cells, their correlations with source gain are ρ = .89 and .98, respectively.Source: §5.1 · pp. 5–6, Figure 3 · p. 6
  • With α = 1, increasing relation heterogeneity from 0 to 2 lowers held-out affine relation R2 from 1.000 to .408 and correct-over-wrong SW advantage from .523 to .228.Transport improves over source reuse by an unresolved .024 SW at near-zero shift but by .541 at λ = 2, where source–target headroom reaches 1.59 SW.Source: §5.1 · p. 6, Figure 4 · p. 7

5.2 CIFAR: SOURCE SPECIFICITY AND TARGET-BUDGET COMPARISONS

  • CIFAR ablations find FiLM correct-source transport improves SW and class consistency over controls, while basis linear versus residual MLP remains unresolved and FiLM linear has lower SW than nonlinear.The source-budget SW changes from MS = 16 to 300 are small, but paired intervals contain zero; this does not establish equivalence or an exact plateau.Source: §5.2 · p. 7
  • CIFAR distributional gains do not establish reliable requested-class generation: headline class consistency is 0.1075 for transport and 0.1102 for strict reuse, with an unresolved difference.A separate direct-zT diagnostic uses a different support/query partition and identity instrument, so its percentages cannot be ranked against headline consistency.Source: §5.2 · p. 7
  • At KT = 1, CIFAR SW is 0.1781 for correct source + transport, 0.2087 for target-only, and 0.2648 for full fine-tuning.At KT = 20, transport and full fine-tuning have SW 0.1844 and 0.1483, respectively; adaptation settings vary, so this comparison does not isolate target-data quantity.Source: §5.2 · p. 7, Table 1 · p. 8
  • On matched CIFAR test episodes, clean-source generation followed by known corruption has lower SW than transport: 0.1688 versus 0.1781.The baseline-minus-transport difference is −0.0092 [−0.0138, −0.0045], so these results do not establish an advantage for task-space transport over this baseline.Source: §5.2 · p. 9

5.3 OFFICE-HOME: NATURAL-DOMAIN ALIGNMENT AND UNRESOLVED SEMANTIC LIMITATIONS

  • In Office-Home, correct-source transport improves DINO-SW over wrong-source transport, relation-only prediction, and source reuse, while requested-object identity remains only 1.67%.The feature-space alignment and Clipart-like appearance do not ensure preservation of the requested object; with more target support, full fine-tuning is clearly better by KT = 5 and 10.Source: §5.3 · p. 9, Figure 6 · p. 10
  • Office-Home diagnostics show transport error alone cannot account for weak object identity: direct target coordinates yield only 2.38% seen-class and 1.56% held-out identity accuracy.An explicit learned class embedding raises generated identity to 6.90% on seen classes, still far below real-image calibration; the probes do not uniquely localise failure to the decoder.Source: §5.3 · p. 10

6 MECHANISTIC SYNTHESIS AND LIMITATIONS

The paper treats source-informed transfer as a chain of measurable requirements, from usable task identity and relation predictability to transport headroom and semantic use. Its results are bounded by the tested settings and by limitations in the theory and target-domain generation.

6 MECHANISTIC SYNTHESIS AND LIMITATIONS

  • The diagnostic chain tests usable identity, relation predictability, transport preservation, and headroom, then examines whether the generator uses coordinates semantically.Table 3 presents representative diagnostics for enabling conditions and limiting stages; its values are not a common metric across rows.Source: §6 · p. 10, Table 3 · p. 10
  • At KT = 1 and 5, transport has lower mean SW, while full fine-tuning has lower mean SW at KT = 20.Because optimisation steps and learning rates also vary, the comparison does not isolate target-data quantity.Source: §6 · p. 11
  • At k = 16, the single-relation affine map uses 272 active parameters; the three-relation CIFAR implementation uses 304 and performs no deployment update.Source-budget changes over 16–300 images are small but do not establish a precise plateau at 16.Source: §6 · p. 11
  • CIFAR evidence is limited to measured distributional metrics under controlled shifts and tested checkpoints, while Office-Home aligns target-domain statistics without reliable object-specific generation.The propositions establish concentration and continuity, not relational generalisation; on matched CIFAR test episodes, clean-source generation followed by known corruption yields lower SW than task-space transport.Source: §6 · p. 11

7 CONCLUSION

Meta-Diff studies whether a recurring source–target relation can replace repeated adaptation when target data are scarce, and reports measurable conditions and boundaries for task-space transport. The paper also documents AI assistance and directs readers to appendices for proofs, experiments, and implementation details.

7 CONCLUSION

  • The conclusion identifies usable task identity, relation predictability, and headroom as requirements, while Office-Home exposes semantic limitations not explained by transport error alone.CIFAR supports source-specific improvements in measured distributional metrics with zero target images and a known relation, conditional on validation-selected budgets for adaptation comparisons.Source: §7 · p. 11

AI USE STATEMENT

  • The authors used generative AI for language editing, drafting support, literature search, and some implementation and analysis tasks, and take responsibility for the final content.Authors reviewed AI-assisted text, technical claims, derivations, specifications, analyses, and code.Source: AI USE STATEMENT · p. 11

REPRODUCIBILITY STATEMENT

  • Appendices provide full proofs, GMM diagnostics, CIFAR controls and ablations, Office-Home experiments, clinical stress tests, and implementation and evaluation details.The paper also reports data splits, adaptation settings, parameter counts, statistical units, and checkpoint-selection procedures.Source: REPRODUCIBILITY STATEMENT · p. 11

IMPACT STATEMENT

The impact statement cautions that synthetic data may reproduce bias or create misleading detail and does not substitute generated clinical images for representative collection or validation. The proof excerpts distinguish coordinate-estimation and stability guarantees from semantic sufficiency.

IMPACT STATEMENT

  • Source-informed generation may reduce target-specific optimisation where representative target data are difficult to obtain, but synthetic data can reproduce bias or create misleading detail.Generated clinical images are not treated as substitutes for representative collection or clinical validation.Source: IMPACT STATEMENT · p. 11
  • Healthcare deployment requires independent clinical evaluation, governance, and privacy review beyond this work’s scope.Source: IMPACT STATEMENT · p. 12

A PROOFS FOR THE MAIN-TEXT GUARANTEES

  • The guarantees establish source-coordinate estimation and stability with respect to coordinate error, not low-dimensionality, semantic sufficiency, task identifiability, or cross-task relational generalisation.The Proposition 1 proof controls mean-squared estimation error around the population feature coordinate but does not imply semantic sufficiency.Source: A PROOFS FOR THE MAIN-TEXT GUARANTEES · p. 14, §A.1 · p. 14

A.2 PROOF OF PROPOSITION 2

The proof establishes continuity of the generated law with respect to the task coordinate under stated regularity conditions and a common initial law. Separate calibration diagnostics find coordinate sensitivity across five GMM families, but do not measure deployment superiority.

A.2 PROOF OF PROPOSITION 2

  • The proposition establishes generated-law continuity under stated regularity assumptions and a common identically coupled initial law.The proof uses synchronous coupling so stochastic increments cancel because the diffusion coefficient is coordinate-independent.Source: §A.2 · pp. 14–15
  • For FiLM-conditioned drift, a corresponding uniform Lipschitz bound in the coordinate is an additional assumption; FiLM experiments do not establish it.The proposition also does not imply that the learned coordinate is low-dimensional, task-identifying, or transferable across unseen semantic tasks.Source: §A.2 · p. 15

B.1 COORDINATE CALIBRATION

  • Mean-minus-own loss is positive in all five GMM families, indicating coordinate sensitivity in the tested calibration checkpoints.The diagnostics use 32 held-out tasks, KT = 5, and eight noise draws per task; they remain separate from the factorial boundary study.Source: §B.1 · p. 15
  • The calibration panels interpolate encoder coordinates using the 80k-step perturbation-0.1 GMM checkpoint and the 50k-step cifar ds3 checkpoint.These interventions diagnose conditioning rather than correct-source deployment superiority.Source: §B.1 · p. 15, Figure 7 · p. 16

B.2 COMPLETE FACTORIAL DIAGNOSTICS

The factorial diagnostics show that source-specific transport depends on usable task identity and relation predictability, while transport’s value varies with shift magnitude. CIFAR comparisons test source specificity, refinement, and transport structure; historical GMM diagnostics are kept separate from the final-route evidence.

B.2 COMPLETE FACTORIAL DIAGNOSTICS

  • In the GMM grid, correct-source transport had a resolved advantage over relation-only in 33 of 42 cells; source-reuse and abundant-target references were not uniformly favourable.Table 7 reports 34 resolved correct-versus-wrong cells.Source: Figure 9 · p. 18, Table 7 · p. 20

B.3 USABLE IDENTITY EXPLAINS THE SOURCE-SPECIFIC GAIN; B.4 IDENTITY THROUGH THE TRANSPORT PIPELINE

  • Across 42 cells, source-specific gain tracked learned-ID more closely than Bayes-ID (ρ = .98 versus .89); transported retrieval averaged .172 versus .061 for raw cross-domain retrieval.Transport improved task alignment but did not fully recover the correct target coordinate; mean transported retrieval was near chance at α = 0 and .1.Source: §B.3 · p. 25, §B.4 · pp. 25–26

B.5 SOURCE–TARGET SHIFT MAGNITUDE AND TRANSPORT HEADROOM

  • As shift magnitude increased from λ = 0 to 2, transport-over-reuse advantage grew from .024 to .541, while source-specific gain remained large even at λ = 0.Model-free source–target SW headroom rose from approximately .08 to 1.59, distinguishing source choice from transport utility.Source: §B.5 · p. 26, Table 15 · p. 26

B.6 HISTORICAL REPRESENTATION-CAPACITY AND RELATEDNESS DIAGNOSTICS

  • Historical GMM diagnostics probe representation capacity and task relatedness, but their aggregate summaries lack paired task-level records and are not evidence for the final correct-source transport route.Their privileged, budget-selected references are not guaranteed performance upper bounds.Source: §B.6 · pp. 26–27

C.1 PROTOCOL

  • CIFAR-100 evaluation uses superclass-disjoint train, validation, and test splits, with 20 reserved target-support images per class and 230 target-query images per class.Headline generation evaluations compare 96 generated samples against 128 sampled target queries per episode.Source: §C.1 · p. 27

C.2 SOURCE SPECIFICITY FROM ZERO TO TWENTY TARGETS

  • At KT = 1, SW target-only-minus-main was 1.1129 [0.5787, 1.7474] and full-FT-minus-main was 3.5666 [2.5424, 4.6245], both favouring transport.At KT = 5 and 20, both comparisons remain unresolved.Source: §C.2 · p. 27

C.3 VALIDATION-FROZEN FULL FINE-TUNING AND COORDINATE REFINEMENT

  • Validation-selected full-fine-tuning settings were frozen before final testing; matched refinement worsened transformation-statistic distance at KT = 1 and 5, while the other intervals included zero.The zero-containing intervals establish neither equivalence nor universal absence of benefit.Source: §C.3 · pp. 28–29, Table 20 · p. 29

C.4 SOURCE BUDGET AND CONDITIONING GENERALITY

  • Source-budget changes from MS = 16 to 300 were small but did not establish equivalence; linear transport was favoured over nonlinear transport at KT = 1 and 5, with KT = 20 unresolved.The matched conditioning SW comparison was unresolved at all three budgets.Source: §C.4 · p. 30

C.5 META-TRAINING-TASK SCARCITY

Meta-training-task scarcity leaves FiLM-versus-basis SW differences unresolved, while coordinate probes show retrieval gains without guaranteeing semantic generation. In Office-Home, correct-source transport improves zero-target distributional alignment, but higher-budget full fine-tuning leads on several metrics.

C.5 META-TRAINING-TASK SCARCITY

  • At 50% task scarcity, all FiLM-minus-basis SW intervals contain zero, while superclass-consistency effects favour FiLM at all three budgets; 25% SW effects are unresolved.Each scarcity arm has one training seed, so class-cluster intervals do not capture training-seed uncertainty.Source: §C.5 · pp. 30–31

C.6 COORDINATE RETRIEVAL AND DIRECT-TARGET DIAGNOSTICS

  • On 20 held-out CIFAR classes, correct-source transport retrieves target coordinates at 62.5%, 59.5%, and 49.0% for blur, noise, and contrast, versus 1.25%, .75%, and 2.25% for wrong-source transport.These retrieval resamples are conditional on the fixed class set and do not establish population-level class significance.Source: §C.6 · p. 31, Table 22 · p. 31, Table 23 · p. 31
  • Direct-target generation from 200 target images yields held-out identity of 3.59% for blur, 3.85% for noise, and 2.71% for contrast, despite correct target coordinates lowering denoising MSE in most held-out timestep bins.Coordinate use therefore does not by itself guarantee class-correct generation.Source: §C.6 · pp. 31–32, Table 24 · p. 31, Table 26 · p. 32

D.1 PROTOCOL AND EVALUATOR AUDIT

  • Office-Home inference treats ten held-out classes as independent units, averaging eight generation repeats and wrong-source assignments within class before bootstrap resampling.The generation grid compares real-domain images, source reuse, transport variants, and one-shot adapting baselines.Source: §D.1 · p. 32, Figure 11 · p. 34

D.2 VALIDATION-ONLY CHECKPOINT AND ADAPTATION SELECTION

  • Office-Home choices were fixed on ten validation classes before test evaluation, and zero-target validation scores serve only as selection and audit evidence.The final route comparisons use the held-out test routes, not validation superiority claims.Source: §D.2 · p. 33, Table 28 · p. 33

D.3 ZERO-TARGET AND TARGET-BUDGET RESULTS

  • At KT = 0, correct-source transport’s paired SW gains are .000425 over wrong-source transport, .000282 over relation-only, and .002673 over source reuse; at KT = 5 and 10, full fine-tuning is significantly better in SW, MMD, and requested-object accuracy.At KT = 1, transport improves DINO-SW over target-only by .001377, while its SW comparison with full fine-tuning is unresolved.Source: §D.3 · p. 33, Table 29 · p. 33, Table 31 · p. 34

D.4 SEMANTIC LIMITATIONS AFTER BYPASSING TRANSPORT

Semantic diagnostics and external-domain stress tests qualify distributional gains: alignment need not preserve requested identity, and several clinical or external benchmarks do not establish source-specific transfer. Supplementary CIFAR tests also find a known-corruption image-space route with lower SW than transport.

D.4 SEMANTIC LIMITATIONS AFTER BYPASSING TRANSPORT

  • Correct transport significantly improves target-coordinate L2 retrieval over raw zS, and L2 and cosine retrieval over relation-only, but correct-versus-wrong transport class intervals include zero, indicating partial coordinate alignment.Bypassing transport does not restore object identity.Source: §D.4 · p. 35

E.1 CHESTX-RAY14 AGE-GROUP TRANSFER

  • For ChestX-ray14, correct-source transport matches the broad target-image distribution better than no adaptation or relation-only, but its contrast with wrong-source transport is unresolved and identity evaluators do not validate requested age or finding.The authors therefore characterize this branch as distribution matching, not source-specific demographic transfer.Source: §E.1 · p. 37, Table 39 · p. 37, E CLINICAL AND EXTERNAL-DOMAIN STRESS… · p. 37

E.2 FITZPATRICK17K DISEASE AND PATHOLOGY-FAMILY TRANSFER

  • Fitzpatrick17k correct-source and wrong-source routes show no resolved difference on valid distributional metrics, and the semantic gate fails on every fold in the stronger pathology-family split.The authors do not treat this as equivalence or use task separability as the central explanation.Source: Table 40 · p. 37, §E.2 · p. 38

E.3 CRC HISTOLOGY PREFLIGHT

  • CRC generation was not run because all three domain-separation folds fell below the locked 70% threshold, despite passing tissue-evaluator and cross-domain alignment checks.This stopping decision provides no evidence for or against Meta-Diff generation performance.Source: §E.3 · p. 38, Table 41 · p. 38

F SUPPLEMENTARY CONTROLLED EXPERIMENTS

  • The supplementary CIFAR comparisons use one trained model and pointwise, unadjusted class-cluster intervals, so they do not estimate training-seed variability.Routes share queries and DDIM noise within episodes.Source: F SUPPLEMENTARY CONTROLLED EXPERIMENTS · p. 38

F.1 KNOWN-CORRUPTION IMAGE-SPACE BASELINE

  • The known-corruption image-space route has lower SW than task-space transport, so these results do not establish a transport advantage over that baseline.It uses the correct clean-source coordinate followed by the known target corruption, without target images or target-time optimisation.Source: §F.1 · pp. 38–39, Table 42 · p. 39

F.2 FIXED FULL-FT UPDATE BUDGET ACROSS TARGET-SET SIZES

  • Under a common full-fine-tuning schedule, transport has lower SW at KT = 1 and 5, while the KT = 20 full-FT-minus-transport effect of −0.0119 [−0.0429, 0.0213] is unresolved.The fixed schedule resolves a KT = 20 versus 1 SW reduction; the intervals do not cover training-seed uncertainty.Source: §F.2 · p. 39, Table 44 · p. 40, Table 45 · p. 40

F.3 MATCHED CIFAR SEMANTIC EVALUATION

  • In matched CIFAR semantic evaluation, full fine-tuning has higher DINO-100 requested-class fraction than transport at all three target budgets, while transport-versus-target-only differences remain unresolved.All generated-route means remain substantially below their matched real-query calibration.Source: §F.3 · p. 41, Table 46 · p. 41, Table 47 · p. 41

F.4 MATCHED OFFICE-HOME SEMANTIC EVALUATION

Matched Office-Home semantic evaluation finds no resolved transport-versus-target-only identity difference at any target budget, while full fine-tuning improves identity at KT = 5 and 10. These measurements remain below real-query calibration and do not isolate the source of semantic limitations.

F.4 MATCHED OFFICE-HOME SEMANTIC EVALUATION

  • On matched Office-Home queries, transport-versus-target-only semantic intervals contain zero at all budgets; full fine-tuning improves identity over transport at KT = 5 and 10, but not conclusively at KT = 1.Even the higher full-fine-tuning means remain well below the real-query calibration.Source: §F.4 · pp. 41–42, Table 48 · p. 42

G IMPLEMENTATION AND REPRODUCIBILITY

  • The CIFAR headline route decodes the predicted coordinate directly with a frozen diffusion backbone, using 304 active parameters for its three-relation linear transport.The Office-Home headline protocol uses a separate FiLM model and also has no refinement.Source: G IMPLEMENTATION AND REPRODUCIBILITY · p. 42

G.1 EVALUATION PROTOCOLS

  • Evaluation protocols retain their own models, task splits, evaluators, and statistical units rather than pooling independent comparisons.The protocol matrix distinguishes actual metric-evaluation counts from pool capacities.Source: §G.1 · p. 42, Table 49 · p. 43

Related papers

Loading 2610.31323v1…