The result lands on the central question in the AI copyright fights: whether what a model produces is a derivative of anything it was trained on.
Researchers at MIT's Computer Science and Artificial Intelligence Laboratory report that once an image model has been trained on a large dataset, the question of which training examples produced a given output often has no answer — not because tracing tools fall short, but because the link from training data to output has genuinely ceased to exist. They call the effect attribution decay: the more data behind a generative model, the less any one training example weighs in anything it produces. Past a large enough training scale, stripping out a single image, all the works of a particular artist, or every photo depicting a particular person often leaves what the model generates unchanged.
Lead author Zheng Dai, formerly a CSAIL researcher, told MIT News that if a piece of data is taken out and the model's output stays the same, that data had no bearing on the output — and data with no bearing on an output, the researchers argue, cannot be held responsible for it. The work is set out in an open-access paper in Nature Communications.
Testing removal directly would mean retraining a model from scratch with one image held out, then the next, and the next — computationally impossible once datasets run to millions of examples, which is why earlier attribution work estimated how much an example counted instead of genuinely taking it out. The team's answer is an architecture of their own, the diffusion ensemble: many small components, each trained on its own separate slice of the material, so dropping an image means switching off the components that saw it. What remains is a true counterfactual model, with no retraining and no approximation. David Gifford, an MIT professor and CSAIL principal investigator, told the same publication that every earlier approach had been an approximation, and that none could establish beyond doubt that taking out individual items left the output unaltered.
The team trained 24 ensembles on datasets running from 256 images up to more than 160,000, drawn from seven publicly available collections including CIFAR-10, CelebA, MetFaces and ArtBench. For each generated image they built alternate versions, each made by dropping a different training item, and measured what they call the counterfactual radius: the distance from the original to whichever alternate stands furthest from it, or the greatest influence any lone item could possibly have exerted. The radius shrank as training sets grew, along a consistent inverse power law, and the result was statistically significant whether the gap between images was assessed pixel by pixel or at the level of meaning. A smaller-scale brute-force run of 1,282 individually retrained models showed the same decline, ruling out the ablation method itself as the cause.
Set against 24 conventional diffusion models trained on the same data, the ensembles produced images of comparable quality by standard measures. Dai told MIT News that they perform very badly where only small amounts of data are available, though with more data they scale better than the ordinary diffusion model does.
In the same account, Gifford said the finding speaks straight to the legal question of whether a generative model's output counts as a derivative work. Where outputs bear no relation to any one item in the training material, he said, "that raises questions about fair use, about whether the outputs are themselves copyrightable as novel works, and about how authors get compensated when what comes out of a model isn't attributable to anything on the internet." He described generation guaranteed to be untraceable to any single training item as an obligation AI companies should take on rather than an escape hatch — a capability they would have to revise their models to use.
James Grimmelmann, who teaches law at Cornell Law School and Cornell Tech, told the outlet that if attribution worked, it would reliably show whether resemblances between what a model produces and a copyright-protected work come from copying or from coincidence. The paper, he said, gives grounds for thinking attribution will not work for the models that matter, so technologists and the courts will have to fall back on other ways of judging whether copying took place.
The study examined diffusion models, now the dominant approach for generating audiovisual media. Whether the same decay sets in for large language models, the systems at issue in the most prominent AI copyright suits, remains an open question.