A painter discovers that an artificial intelligence model was trained on their paintings, without permission or payment, and sues. If part of their claim depends on linking a generated image to their specific works, they may face a fiendishly difficult burden of proof: showing that those works causally influenced what the machine produced and that, had they been removed from training, the result would have changed. An MIT study published in Nature Communications in August 2026 has just shown that, in the models and datasets examined, such a test may in many cases find no appreciable individual causal influence. Not necessarily because the painter is wrong, but because of the scale and redundancy with which certain image-generation models work.
The study is titled 'Outputs of generative diffusion models are often unattributable'. Its authors, Zheng Dai and David K. Gifford, pose a counterfactual question: what would the model have generated if a specific data unit had not been in its training set? To answer this without retraining the whole machine each time, they design a system that allows them to remove the influence of a specific unit from the model and observe what changes. That unit is not just a single image: it can be all the photographs of a person or all the works of an artist within the corpus. They exclude each of these units separately, measure the difference in what the machine produces, and find a clear pattern: the larger the training set, the less the result tends to change when an individual piece is removed. In some of their experiments, even the unit corresponding to a person or an artist could be omitted without certain generated samples showing appreciable changes.
The study is precise about what this means, because the wrong conclusion would favour precisely those one would least want it to. The works do have influence. The machine depends on what it was trained on. What the study shows is that the causal influence of a specific unit may stop being appreciable under this test as the scale and redundancy of the training set grow. The authors consider data redundancy to be the main explanation. If many images contain similar patterns, removing one may produce no appreciable change, because the others still supply analogous information. A work need not be irrelevant to stop being necessary.
The logical trap the study exposes is to assume that, if a specific unit is not indispensable on its own, the whole ceases to matter. The model learns from the statistical patterns present in the aggregate and, at the same time, may show no causally detectable dependence on a particular image, person or artist under an individual exclusion test. It is the structure of a haystack: removing one straw may not alter its silhouette, but the haystack exists only as an accumulation of straws. This does not mean that every straw is essential, or that all have contributed equally. It means that the necessity of the whole can coexist with the substitutability of some of its parts.
Carried over into law and ethics, this structure can dilute certain forms of responsibility. If a dispute requires linking a specific output to a specific work, the creator faces a difficulty that grows with scale and redundancy: their work may have been part of the process without its removal making an appreciable difference to that sample. The question of possible appropriation arises at the level of the corpus, whereas some forms of legal attribution look for an individual chain between work and result. Between the two scales, an evidentiary gap opens up. Scale does not necessarily eliminate the problem; it may shield it from a test designed for individual causal relationships.
The study does not prove that there is infringement, or that the training is unlawful, nor does it exonerate anyone; it addresses a technical question, whether a result can be causally linked to a specific input, not a legal one. Moreover, it was tested only on diffusion models and academic image datasets, not on the large commercial models trained on corpora of a different scale and composition. We do not know whether the same behaviour occurs there, or how strongly: redundancy makes that hypothesis plausible, but the study does not test it. Nor does it set any magic threshold. There is no number of images beyond which attribution disappears; there is a slope along which it weakens as scale grows. None of this is a ruling. It is a finding about what can and cannot be proven.
Individual attribution is blurred here in the same way that responsibility is blurred in so many contemporary structures. The pollution of a river may come from accumulated discharges whose individual contribution is hard to isolate. Precarity may arise from decisions and incentives spread across institutions and companies. The addictive design of a platform may result from many partial decisions, none of which explains the aggregate effect on its own. In all these cases there may be harm whose origin is hard to locate when each contribution is examined separately. These diffusion models take that logic to a particularly clear form: a system that learns from the work of many and which, owing to the scale and redundancy of its data, can make the influence of certain specific contributions on a sample empirically undetectable under this counterfactual test. Dilution appears here not as an external obstacle to investigating the model, but as an emergent effect of the scale and redundancy of its data.
The study shifts the ground for one specific kind of proof, and it may do so in favour of whoever controls the scale. A creator may struggle to move from 'my painting was in the corpus' to 'my painting causally influenced this particular image'. The first claim concerns the provenance of the data; the second, the relationship between a training unit and a given result. The study shows that this second relationship may cease to be detectable through an individual exclusion test. That does not invalidate every legal claim, because the acquisition and reproduction of training data raise separate issues, but it can make proof harder in claims that depend on linking a specific work to a specific output. The answer, if there is one, can hardly always be confined to the relationship between one work and one result. It would also have to address how the dataset was obtained and used, not just the needle that cannot be singled out in the haystack. As long as the whole debate is focused on identifying one causally indispensable straw, the haystack can hide the prior question: where all the straws that made it possible came from.
About the open conversation
This text discusses a study by Zheng Dai and David K. Gifford, of MIT, published in Nature Communications on 18 August 2026, which shows that, in the diffusion models examined, the causal influence attributable to an individual training unit tends to decrease as the corpus grows. The authors take as units a single image, the photographs of one person or the works of an artist present in the dataset, and consider redundancy to be the main explanation for the phenomenon. The study does not show that the works lack influence, that the model is independent of the aggregate corpus, or that training is lawful or unlawful; nor does it absolve companies of liability. Its scope is technical: it examines whether a generated sample can be causally linked to a specific unit through its counterfactual exclusion, and it was tested only on diffusion models with academic datasets.
My interest lies in the structure the finding allows us to think through: scale can make an individual contribution undetectable without removing dependence on the whole, and it opens up a distance between the collective level at which data is obtained and the individual level at which certain forms of attribution operate. This is a different problem from the one discussed in Thaler v. Perlmutter, which concerned the registrability of a work without a human author, not the lawfulness of using protected works to train models. If anyone wishes to contribute from copyright law, statistics, the ethics of technology or artistic practice, this notebook remains open.
Sources
Zheng Dai and David K. Gifford, 'Outputs of generative diffusion models are often unattributable', Nature Communications, vol. 17, art. 6974, 18 August 2026. DOI: 10.1038/s41467-026-75667-5. Peer-reviewed article. Using counterfactual ablation on diffusion ensembles, checked against full retraining at small scale, it shows that the causal influence attributable to an individual training unit (an image, a person or an artist) decays roughly according to an inverse power law as the corpus grows. In the larger sets studied, certain samples may remain without appreciable change when any one of those units is omitted. The authors attribute the phenomenon mainly to data redundancy. Tested on diffusion models and academic datasets (MNIST, Fashion-MNIST, CIFAR-10/100, CelebA, MetFaces and ArtBench), ranging from 256 to 162,770 images; not on commercial models, autoregressive models or large language models.
Open peer-review file for 'Outputs of generative diffusion models are often unattributable'. The authors distinguish causal attribution through individual exclusion from aggregate, subset-based or approximate forms of attribution, which may remain useful. The study neither denies dependence on the aggregate corpus nor takes a position on the legality of training, the liability of companies or the existence of infringement. David K. Gifford's remarks on the possible legal implications appear in the MIT News article, not in the peer-reviewed paper.
Legal context, as a separate matter: the Supreme Court of the United States declined to review Thaler v. Perlmutter, No. 25-449, on 2 March 2026. The denial left standing in that case the decision of the Court of Appeals for the District of Columbia Circuit, which requires human authorship for a work to receive copyright protection. The matter concerns the registrability of a work without a human author, not the lawfulness of using protected works to train models.