AI image generators have pushed a difficult question into courts, policy debates, and licensing talks: when a model creates a new portrait or artwork, whose earlier work helped produce it? A new MIT CSAIL study argues that, for large image-generation systems, that question may sometimes have no precise answer.
The researchers identify a pattern they call attribution decay. As a generative model is trained on more data, the measurable role of any one image, artist, or photographed person can fade until removing that material no longer changes a generated result.
What Attribution Decay Means
Attribution is the attempt to connect a model output back to the training data that influenced it. In legal and creative disputes, that connection matters because artists want recognition, companies want predictable rules, and policymakers want responsibility to be assignable.
The MIT CSAIL work complicates that picture. The core claim is not simply that attribution tools are weak. It is that, at large enough scale, the link between a specific training example and a specific generated image can become absent in practice.
Zheng Dai SM ’21, PhD ’24, former MIT CSAIL researcher and lead author on the work, explains the logic directly: "If you take away a piece of data and the output of the model doesn't change, then that piece of data didn't affect the output."
That reasoning applies one item at a time. If removing an image has no effect, the researchers argue, that image should not be treated as responsible for the output. If the same is true across many possible removals, the usual idea of tracing a generated image to a particular source begins to break down.
How The Researchers Tested The Link
The hard part is proving what would have happened if a model had never seen a given input. A strict test would require retraining the model from scratch without that image, then repeating the process for other images. With millions of training examples, that approach quickly becomes impractical.
Earlier attribution work has therefore relied on approximations. Those methods estimate influence, but they do not fully remove an input and all of its effects from the system.
Dai and MIT Professor David Gifford, an MIT CSAIL principal investigator, used a different route. They built an architecture called a diffusion ensemble. Instead of one large model, the system is made of many smaller components, each trained on a different portion of the data.
That design makes deletion testable. To ask what the model would produce without a particular image, the researchers can turn off the components that saw it. The remaining system acts as a counterfactual version of the model without needing full retraining.
Gifford describes the distinction as important because the method is exact rather than approximate. In his words, "This paper introduces the first method that is absolute."
The Results Across Larger Datasets
The team still needed to show that the ensemble approach could generate competitive images. They compared the ensembles with 24 conventional diffusion models trained on the same data, and the generated images were about as strong by standard measures.
The researchers also found that the ensembles performed better relative to conventional models as training data increased. Dai summarized the pattern this way: "When you have low amounts of data, they do very poorly. But if you have more data, it actually scales better compared to the vanilla diffusion model."
With the system in place, the team examined what they call a generated image’s counterfactual universe: the collection of alternate versions produced by removing different training examples. The largest distance between the original output and any alternate version is the counterfactual radius, a measure of how much one training item could have mattered.
They trained 24 ensembles on datasets ranging from 256 images to more than 160,000. The images came from seven public collections, including CIFAR-10, CelebA, MetFaces, and ArtBench.
The result was consistent. As the training set grew, the counterfactual radius shrank along an inverse power law. The pattern held whether image differences were measured pixel by pixel or by semantic meaning, with statistical significance in both cases.
The researchers also checked whether the result might be an artifact of their own method. At small scale, they repeated the experiment by training 1,282 separate models. Attribution decay still appeared.
Other tests also preserved the finding, including fixed epochs, text-prompted models, class-conditioned models, four similarity metrics, and a setup in which the removed fraction of data was held constant.
Why It Matters For Copyright And Privacy
The study lands directly in the debate over AI-generated images, derivative works, fair use, and creator compensation. If an output cannot be tied to any individual training image, then familiar arguments about copying become harder to apply in a simple way.
Gifford frames the finding as evidence that these models are not merely reproducing their inputs. He says the issue raises questions about "fair use," whether outputs are copyrightable as novel works, and how authors should be paid when a model’s result is not attributable to material online.
The same work also points to a possible technical obligation for companies. Gifford argues that if companies want to claim their outputs are not infringing derivatives of internet material, they should revise models so they can demonstrate they are not producing derivatives of individual people or items.
That has a privacy dimension as well. If systems can be designed to produce outputs guaranteed to be unattributable, the capability could become part of how developers reduce the chance that generated media points back to a specific person or image.
The Open Question Beyond Images
The research focuses on diffusion models. The source article describes these models as dominant in audiovisual media generation and also prevalent in scientific uses such as protein structure modeling and therapeutic discovery.
Whether the same attribution decay applies to large language models remains unresolved. That distinction matters because large language models are central to major copyright disputes, but the MIT CSAIL work does not claim to settle that broader question.
James Grimmelmann, a law professor at Cornell Law School and Cornell Tech, says attribution would be useful if it could reliably separate copying from coincidence. But he adds that the paper gives reason to think attribution may fail for important models, meaning technologists and courts may need other ways to evaluate copying.
Dai and Gifford’s project is described in an open-access paper published today in Nature Communications. The work was supported by Schmidt Futures.