Bridging the Data Gap: Source-Informed Task-Space Transport for Few-Shot Diffusion
Organizations: University of Warwick · Columbia University · Independent Researcher · Queen Mary University of London
Abstract
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.
Figures & tables
| A. Zero-target controls: 60 validation episodes | ||||
|---|---|---|---|---|
| Route | SW | SW | Class consistency | class |
| correct source transport | – | – | ||
| Strict source reuse | ||||
| Wrong source | ||||
| Relation-only | ||||
| B. Final-test SW: 180 episodes, 60 per budget | ||||
| Paired SW comparison | |||
|---|---|---|---|
| FiLM basis | |||
| Linear MLP (basis) | |||
| MLP linear (FiLM) |
| Setting | Representation / transport evidence | Generative implication |
|---|---|---|
| GMM | Bayes-ID can be perfect while learned-ID is weaker; at , learned-ID and transported retrieval . Shift sweep: transport-over-reuse as headroom grows. | Correct-vs-wrong SW gain at ; usable identity tracks the gain more closely than Bayes-ID |
| CIFAR | Transported target-coordinate retrieval – across relations | Correct source transport improves on wrong/relation-only at ; the separate final-test budget comparison is in Table 1 |
| Office-Home | Product- retrieval ; transport raises target-coordinate retrieval | Clipart share ; low object ID persists even with abundant direct , showing that transport error alone is insufficient to explain the failure. |
Appendix figures & tables52 assets
Supplementary material from the paper’s appendix.
Appendix
| Task family | Own | Mean | |
|---|---|---|---|
| Perturbation .10 | |||
| Perturbation .25 | |||
| Perturbation .50 | |||
| Perturbation 1.00 | |||
| Unrelated |
| 0 | 0.1 | 0.25 | 0.5 | 1 | 2 | |
|---|---|---|---|---|---|---|
| 0 | 0.000 | 0.000 | -0.000 | 0.000 | -0.000 | -0.002 |
| 0.1 | 0.008 | 0.010 | 0.006 | 0.006 | 0.002 | 0.002 |
| 0.25 | 0.093 | 0.102 | 0.098 | 0.066 | 0.038 | 0.023 |
| 0.5 | 0.242 | 0.209 | 0.205 | 0.220 | 0.140 | 0.091 |
| 0.75 | 0.387 | 0.390 | 0.370 | 0.321 | 0.256 | 0.142 |
| 1 | 0.523 | 0.563 | 0.523 | 0.447 | 0.404 | 0.228 |
| Correct | Wrong | Relation-only | Source reuse | Abundant-target reference | ||
|---|---|---|---|---|---|---|
| 0 | 0 | 0.09386 | 0.09396 | 0.09361 | 0.64158 | 0.09311 |
| 0 | 0.1 | 0.14144 | 0.14170 | 0.14129 | 0.70917 | 0.14840 |
| 0 | 0.25 | 0.16930 | 0.16911 | 0.16933 | 0.63886 | 0.16775 |
| 0 | 0.5 | 0.32266 | 0.32270 | 0.32317 | 0.77757 | 0.31470 |
| 0 | 1 | 0.58670 | 0.58635 | 0.58467 | 0.71809 | 0.52292 |
| 0 | 2 | 1.04219 | 1.04036 | 1.04108 | 1.16237 | 0.90496 |
| Wrong correct | Relation-only correct | ||
|---|---|---|---|
| 0 | 0 | ||
| 0 | 0.1 | ||
| 0 | 0.25 | ||
| 0 | 0.5 | ||
| 0 | 1 | ||
| 0 | 2 |
| Source reuse correct | Abundant-target ref. correct | ||
|---|---|---|---|
| 0 | 0 | ||
| 0 | 0.1 | ||
| 0 | 0.25 | ||
| 0 | 0.5 | ||
| 0 | 1 | ||
| 0 | 2 |
| Correct | Wrong | Relation-only | Source reuse | Abundant-target reference | ||
|---|---|---|---|---|---|---|
| 0 | 0 | 0.01827 | 0.01820 | 0.01813 | 0.88275 | 0.01782 |
| 0 | 0.1 | 0.03767 | 0.03772 | 0.03767 | 1.01943 | 0.04387 |
| 0 | 0.25 | 0.06638 | 0.06640 | 0.06653 | 0.87212 | 0.06448 |
| 0 | 0.5 | 0.14388 | 0.14391 | 0.14401 | 1.02813 | 0.13898 |
| 0 | 1 | 0.32266 | 0.32176 | 0.32035 | 0.71514 | 0.24480 |
| 0 | 2 | 0.72649 | 0.72400 | 0.72402 | 1.19824 | 0.52956 |
| Wrong correct | Relation-only correct | ||
|---|---|---|---|
| 0 | 0 | ||
| 0 | 0.1 | ||
| 0 | 0.25 | ||
| 0 | 0.5 | ||
| 0 | 1 | ||
| 0 | 2 |
| Source reuse correct | Abundant-target ref. correct | ||
|---|---|---|---|
| 0 | 0 | ||
| 0 | 0.1 | ||
| 0 | 0.25 | ||
| 0 | 0.5 | ||
| 0 | 1 | ||
| 0 | 2 |
| Bayes-ID | learned-ID | Collapse gap | |
|---|---|---|---|
| 0.00 | .016 | .016 | |
| 0.10 | .400 | .073 | .327 |
| 0.25 | .953 | .325 | .628 |
| 0.50 | 1.000 | .708 | .292 |
| 0.75 | 1.000 | .839 | .161 |
| 1.00 | 1.000 | .874 | .126 |
| Predictors | Fit | Key coefficient | 95% CI |
|---|---|---|---|
| Bayes-ID interaction | .587 | ||
| learned-ID interaction | .843 | ||
| Bayes-ID learned-ID | .814 | ||
| Bayes-ID | learned | transported | raw | |
|---|---|---|---|---|
| 0.00 | .016 | .015 | .013 | .016 |
| 0.10 | .400 | .071 | .019 | .015 |
| 0.25 | .953 | .323 | .089 | .023 |
| 0.50 | 1.000 | .691 | .169 | .039 |
| 0.75 | 1.000 | .831 | .258 | .074 |
| 1.00 | 1.000 | .883 | .315 | .109 |
| Correct | Wrong | Relation-only | Source reuse | Transport over reuse | ||
|---|---|---|---|---|---|---|
| 0.00 | .759 | 1.241 | 1.062 | .783 | +.482 | +.024 |
| 0.25 | .765 | 1.252 | 1.048 | .828 | +.487 | +.063 |
| 0.50 | .802 | 1.315 | 1.115 | .905 | +.513 | +.102 |
| 1.00 | .835 | 1.355 | 1.157 | 1.066 | +.520 | +.231 |
| 2.00 | 1.037 | 1.667 | 1.443 | 1.577 | +.631 | +.541 |
| Configuration | No adapt. | Oracle | Full FT ref. | Captured |
|---|---|---|---|---|
| , 80k | .8821 | .6320 | .1276 | 33.2% |
| , 320k | .8741 | .5965 | .1508 | 38.4% |
| , 80k | .8868 | .5396 | .1267 | 45.7% |
| , 320k | .8779 | .4690 | .1565 | 56.7% |
| Task family | No adapt. | Oracle | Best-grid FT | Captured |
|---|---|---|---|---|
| Perturbation .10 | .7513 | .3835 | .1179 | 58.1% |
| Perturbation .25 | .8910 | .5583 | .1220 | 43.3% |
| Perturbation .50 | .9516 | .6949 | .1359 | 31.5% |
| Perturbation 1.00 | .9679 | .7808 | .1239 | 22.2% |
| Route / comparison | |||
|---|---|---|---|
| correct source transport | |||
| Source-init. adaptation | |||
| Target-only | |||
| Mean source | |||
| Shuffled source | |||
| Relation-only |
| Target budget | Full-FT steps | Learning rate |
|---|---|---|
| 25 | ||
| 25 | ||
| 400 |
| Refinement gain [95% CI] | |
|---|---|
| 1 | |
| 2 | |
| 5 | |
| 10 | |
| 20 |
| Configuration / comparison | |||
|---|---|---|---|
| Basis: correct source transport | |||
| FiLM: correct source transport | |||
| FiLM basis | |||
| Basis residual MLP | |||
| Basis linear | |||
| Linear MLP |
| Group | Relation | Metric | Raw | Main | Wrong-source + transport | Relation only |
|---|---|---|---|---|---|---|
| Seen | Blur | L2 | ||||
| Cosine | ||||||
| Seen | Noise | L2 | ||||
| Cosine | ||||||
| Seen | Contrast | L2 | ||||
| Cosine |
| Group | Relation | Main raw source (pp) [95% CI] | Main wrong source (pp) [95% CI] |
|---|---|---|---|
| Seen | Blur | ||
| Seen | Noise | ||
| Seen | Contrast | ||
| Held-out | Blur | ||
| Held-out | Noise | ||
| Held-out | Contrast |
| Group | Relation | Generated identity (%) | Real identity (%) | DINO-SW | DINO-MMD |
|---|---|---|---|---|---|
| Seen | Blur | 5.52 | 50.80 | 0.02176 | 0.15937 |
| Seen | Noise | 3.78 | 29.27 | 0.01671 | 0.09777 |
| Seen | Contrast | 6.84 | 78.10 | 0.02983 | 0.27962 |
| Held-out | Blur | 3.59 | 51.20 | 0.02338 | 0.18884 |
| Held-out | Noise | 3.85 | 34.50 | 0.01888 | 0.13402 |
| Held-out | Contrast | 2.71 | 70.90 | 0.03059 | 0.28967 |
| Relation | Identity (pp) [95% CI] |
|---|---|
| Blur | |
| Noise | |
| Contrast |
| Group | Relation | Timesteps | Correct MSE | Wrong MSE | [95% CI] |
|---|---|---|---|---|---|
| Seen | Blur | 0–199 | 0.069118 | 0.069843 | |
| 200–399 | 0.025385 | 0.026199 | |||
| 400–599 | 0.014950 | 0.015695 | |||
| 600–799 | 0.008320 | 0.008864 | |||
| 800–999 | 0.002333 | 0.002566 | |||
| Seen | Noise | 0–199 | 0.575592 | 0.576098 |
| Check | Result |
|---|---|
| CLIP top-1, Product / Clipart | 89.03% / 65.96% |
| Test classes with Clipart top-1 | 10/10 |
| DINOv2 held-out domain accuracy | 98.30% |
| Same-class centroid top-1 / median rank | 100.0% / 1 |
| Same-minus-different centroid cosine gap | .5077 |
| Checkpoint step | Main DINO-SW |
|---|---|
| 20,000 | .040525 |
| 25,000 | .039609 |
| 30,000 | .038712 |
| 35,000 | .038019 |
| 40,000 | .037572 |
| 45,000 | .037351 |
| Route | DINO-SW | MMD | Object ID (%) | Clipart (%) |
|---|---|---|---|---|
| Correct transport | .038969 | .407846 | 1.67 | 86.50 |
| Wrong transport | .039394 | .419016 | 1.44 | 86.27 |
| Relation-only | .039251 | .415280 | 1.37 | 86.71 |
| Source reuse | .041641 | .457524 | 1.18 | 63.80 |
| Route | DINO-SW | MMD | Object ID (%) | Clipart (%) | |
|---|---|---|---|---|---|
| 1 | Correct transport | 0.038969 | 0.407846 | 1.67 | 86.50 |
| 1 | Target-only | 0.040346 | 0.439860 | 2.23 | 75.73 |
| 1 | Full FT | 0.039336 | 0.468223 | 5.33 | 87.49 |
| 5 | Correct transport | 0.038969 | 0.407846 | 1.67 | 86.50 |
| 5 | Target-only | 0.039031 | 0.409734 | 1.81 | 81.22 |
| 5 | Full FT | 0.034550 | 0.349838 | 12.55 | 83.11 |
| Comparator | DINO-SW [95% CI] | MMD [95% CI] | |
|---|---|---|---|
| 0 | Wrong + transport | [0.000213, 0.000643] | [0.006870, 0.015706] |
| 0 | Relation-only | [0.000109, 0.000456] | [0.002360, 0.012075] |
| 0 | Source reuse | [0.002270, 0.003036] | [0.039741, 0.060430] |
| 1 | Target-only | [0.000568, 0.002311] | [0.015413, 0.047276] |
| 1 | Full FT | [-0.001578, 0.002312] | [0.019137, 0.101637] |
| 5 | Target-only | [-0.000754, 0.000800] | [-0.019453, 0.018779] |
| Comparator | object ID [95% CI] | Clipart [95% CI] | |
|---|---|---|---|
| 0 | Wrong + transport | [-0.043, 0.543] | [-0.438, 0.955] |
| 0 | Relation-only | [-0.078, 0.885] | [-0.885, 0.443] |
| 0 | Source reuse | [-0.221, 1.406] | [20.820, 24.661] |
| 1 | Target-only | [-2.031, 0.404] | [2.760, 19.062] |
| 1 | Full FT | [-8.737, 0.195] | [-4.844, 2.734] |
| 5 | Target-only | [-0.703, 0.286] | [1.667, 9.532] |
| Query route | L2 top-1 | Cosine top-1 | L2 margin | Cosine margin |
|---|---|---|---|---|
| Raw | 12.0% | 26.5% | -.0500 | -.1749 |
| Correct source transport | 42.0% | 44.5% | -.0153 | -.0620 |
| Wrong-source transport | 20.0% | 19.0% | -.0897 | -.2654 |
| Relation-only | 10.0% | 10.0% | -.0545 | -.1510 |
| Comparator | L2 [95% CI] | Cosine [95% CI] |
|---|---|---|
| Raw | ||
| Wrong-source transport | ||
| Relation only |
| Group | Generated ID | Real ID | DINO-SW | DINO-MMD | Clipart |
|---|---|---|---|---|---|
| Seen (45 classes) | 2.38% | 50.33% | .03679 | .35175 | 87.34% |
| Held-out (10 classes) | 1.56% | 52.00% | .03902 | .40642 | 88.33% |
| Group | Timesteps | Correct MSE | Wrong MSE | [95% CI] |
|---|---|---|---|---|
| Seen | 0–199 | 0.056513 | 0.056724 | |
| 200–399 | 0.019655 | 0.019785 | ||
| 400–599 | 0.013028 | 0.013164 | ||
| 600–799 | 0.008825 | 0.008963 | ||
| 800–999 | 0.003287 | 0.003342 | ||
| Held-out | 0–199 | 0.059910 | 0.059928 |
| Seen-class route | Generated identity (%) | Real identity (%) | DINO-SW | DINO-MMD | Clipart (%) |
|---|---|---|---|---|---|
| Original direct | 2.38 | 50.33 | 0.03679 | 0.35175 | 87.34 |
| Explicit class embedding | 6.90 | 50.33 | 0.03507 | 0.32768 | 87.45 |
| Metric | Favor-control [95% CI] |
|---|---|
| Requested-class identity | |
| DINO-SW reduction | |
| DINO-MMD reduction | |
| Clipart-share increase |
| Method | |||||
|---|---|---|---|---|---|
| No adaptation | .3696 | .3696 | .3696 | .3696 | .3696 |
| Target-only | .1397 | .1406 | .1398 | .1405 | .1408 |
| Relation-only | .3680 | .3680 | .3680 | .3680 | .3680 |
| Wrong-source transport | .1407 | .1407 | .1407 | .1407 | .1407 |
| Correct source transport | .1407 | .1407 | .1407 | .1407 | .1407 |
| Full fine-tuning | .2981 | .2802 | .2304 | .1800 | .1591 |
| Protocol | Route | Statistic | SW | MMD |
|---|---|---|---|---|
| Disease IV–VI | Source reuse | 2.5248 | .3642 | 7.1765 |
| Wrong disease, same family | 2.5020 | .3638 | 7.1466 | |
| Wrong disease, different family | 2.5025 | .3639 | 7.1444 | |
| Correct source transport | 2.5030 | .3638 | 7.1429 | |
| Family IV–VI | Source reuse | 1.7452 | .3081 | 5.7946 |
| Wrong-family transport | 1.7185 | .3064 | 5.7468 |
| Check | Result |
|---|---|
| Target tissue balanced accuracy | 88.25% |
| Minimum target tissue recall | 60.57% |
| Domain balanced accuracy, fold 1 | 59.01% |
| Domain balanced accuracy, fold 2 | 58.24% |
| Domain balanced accuracy, fold 3 | 57.00% |
| Same-tissue centroid retrieval | 100% top-1 in each fold |
| Route | SW | Energy MMD | DINO-100 (%) |
|---|---|---|---|
| Correct source transport | |||
| Clean-source generation corruption | |||
| Paired effect |
| Updates | Learning rate | Mean validation SW |
|---|---|---|
| 25 | 0.218506 | |
| 25 | 0.259794 | |
| 100 | 0.217296 | |
| 100 | 0.310748 |
| Route and metric | |||
|---|---|---|---|
| Transport: SW | |||
| Transport: MMD | |||
| Transport: DINO-100 (%) | |||
| Target-only: SW | |||
| Target-only: MMD | |||
| Target-only: DINO-100 (%) |
| Comparison | / change | ||
|---|---|---|---|
| Target-only transport: SW | |||
| Full FT transport: SW | |||
| Full FT: minus 1 | – | – | |
| Full FT: minus 1 | – | – |
| Route / paired effect | |||
|---|---|---|---|
| Transport | |||
| Target-only | |||
| Full FT | |||
| Real-query calibration | |||
| Transport target-only | |||
| Transport full FT |
| Metric / paired effect | |||
|---|---|---|---|
| Full FT: SW | |||
| Full FT transport: SW | |||
| Full FT: energy MMD | |||
| Full FT transport: MMD |
| Route / paired effect | |||
|---|---|---|---|
| Transport | |||
| Target-only | |||
| Full FT | |||
| Real-query calibration | |||
| Transport target-only | |||
| Transport full FT |
| Comparison | Data and sampling | Evaluation and uncertainty |
|---|---|---|
| GMM factorial | 42 cells; five seeds; 64 held-out tasks per seed | SW/MMD paired by seed and task; hierarchical intervals; abundant-target encoding reference uses 512 target points. |
| CIFAR main zero-target | 20 validation classes three corruptions; 64 source images; 96 generated/128 query images | Pixel SW: 256 projections; energy MMD: 64/64 samples. Frozen semantic instrument from the original package. Class-cluster intervals. |
| CIFAR original adaptation comparison | 20 test classes three corruptions at each ; 96 generated/128 query images | Pixel SW and energy MMD as above. Budget-specific full-FT settings; class-cluster intervals. |
| CIFAR conditioning, transport and source-budget ablations | Separately matched validation comparisons; nested source prefixes for | Each comparison uses its own trained model and matched class–corruption episodes. Paired class-cluster intervals; one training seed per arm. |
| CIFAR independent direct- diagnostic | Its separate 200-support/50-query repartition | Its stated DINO identity instrument and real-query calibration; class intervals. The coordinate-retrieval probe instead resamples supports conditional on its class set. |
| Office-Home main routes | 10 held-out classes; eight repeats; 96 generated images per repeat; 20 fixed real queries per class | DINO feature-space distances and 65-way CLIP identity are distinct metrics. Repeats are averaged within class; class intervals. |