In January 2023, illustrator Sarah Andersen and two other plaintiffs filed suit against Stability AI, Midjourney, and DeviantArt in the U.S. District Court for the Northern District of California. The plaintiffs' argument was straightforward: the defendants had scraped artists' work without permission and built models that imitate their artistic styles. This case (Andersen et al. v. Stability AI Ltd., Case No. 3:23-cv-00201-WHO) remains in litigation as of 2026, with a jury trial scheduled for April 5, 2027. During discovery, Midjourney turned over more than 150 terabytes of LAION data to the plaintiffs via hard drives.
Lawsuits of this kind confront a fundamental technical problem. When a model generates an image, how can one determine whether it "derives from" a specific work included in the training data, or whether it "emerged" from statistical patterns extracted across countless data points? If a technology could reliably answer this question, it would open the door to proving copyright infringement, adjudicating fair use, and designing compensation schemes for artists. Dai and Gifford began this research precisely in an attempt to build that technical foundation.
The More Training Data You Add, the More the "Evidence" Disappears
The method developed by Dai and Gifford is called Ablation Based Counterfactuals (ABC). The core of the approach works as follows. First, the entire training dataset is split into different subsets, and an independent diffusion model is trained on each. These models are then combined as an ensemble, which together constitutes a single generative model. To examine the influence of a particular training sample, the model that saw that sample is removed from the ensemble. Feeding the same noise input into the ensemble with that model excluded yields a "counterfactual output"—what would have been generated if that training data had never existed. If the difference between the original output and the counterfactual output is large, it can be concluded that the training data strongly influenced the output.
Using this method, the research team trained 23 different ensembles and systematically examined the relationship between dataset scale and attributability. The results were unambiguous: as the amount of training data increases, the difference between the counterfactual output and the original output—defined in the paper as the "counterfactual radius"—shrinks. This negative correlation was highly statistically significant, with .
The paper further extrapolates this trend. When the number of training samples reaches $10^8$ (100 million), the counterfactual radius drops to roughly 7 in Euclidean distance—a point at which the original image and the counterfactual image become indistinguishable to the human eye. Given that commercial image generation models are trained on hundreds of millions to billions of images, it is estimated that the outputs of these models are, in effect, unattributable to any single piece of training data.
| Metric | Small-Scale Dataset | Large-Scale Dataset (Extrapolated) |
|---|---|---|
| Number of training samples | Thousands (experimentally verified) | $10^8$ (extrapolated estimate) |
| Counterfactual radius (Euclidean distance) | Hundreds (visually clear difference) | ~7 (imperceptible difference) |
| Attribution determination | Possible | Effectively impossible |
| Number of ensembles used for verification | 23 | 23 (same experimental series) |
What "Unattributability" Means Legally
The problem this finding raises extends beyond the technical realm into the legal and institutional domain. As Gifford stated in an MIT press release: "If the output has nothing to do with any individual piece in the training data, then there's a question of fair use, there's a question of whether the output itself deserves copyright protection as a new piece of work, and there's a question of how you would compensate creators if the model's output can't be attributed to anything on the internet."
James Grimmelmann, a professor at Cornell Law School, points to the implications this paper has for legal enforcement practice. "If attribution worked, you could reliably determine whether a similarity between a model's output and a copyrighted work resulted from copying or from coincidence. But this paper shows why attribution fails for interesting models. Technologists and courts will need to fall back on other ways of assessing copying."
However, Grimmelmann also carefully notes that this research cannot be immediately applied to current litigation. In an email to The Register, he added that a German court ruling involved a music model that memorized and reproduced lyrics, while U.S. case law has focused on whether the act of training itself constitutes fair use—and that there are almost no cases in which the similarity of image model outputs has been directly litigated in court. The issue of unattributability will only become legally relevant once future lawsuits place the similarity of outputs itself at the center of the dispute.
Here a paradox emerges. The larger a model becomes, the less its outputs can be attributed to any specific training data. While this makes proving copyright infringement more difficult, it could also become a deliberate risk-avoidance strategy for companies. A model trained at sufficient scale could use the very unattributability of its outputs as grounds for the claim, "We did not copy."
Where Is the Line Between "Memorization" and "Creation"?
Gifford also argues that this finding has a side that supports the model's "creativity." If the output does not depend on any specific training data, then the model is not a copying machine but is generating something new from the distribution it has learned. However, this logic is a double-edged sword. If a model is creative, its output itself may be eligible for copyright protection—but the grounds for compensating training data providers weaken correspondingly.
There is an interesting contrast here. In November 2025, a German court found that OpenAI had infringed copyright when ChatGPT "memorized" and reproduced a songwriter's lyrics. That ruling relied on the analysis in the co-authored paper "The Files Are in the Computer" by Grimmelmann and A. Feder Cooper, which holds that when a model can sequentially reproduce a specific work, this can be regarded as copying. Memorization is infringing precisely because it is attributable. Dai and Gifford's finding shows that this "memorization" disappears as a model grows. In other words, the structural tendency for larger models to make copyright infringement harder to prove is technically built in.
Limitations of the Method and Remaining Questions
The ABC method itself has constraints. Training an ensemble requires 10 to 50 times the computational resources of a single model, and it cannot be retroactively applied to existing commercial models. The datasets verified experimentally topped out at tens of thousands of samples at most, so behavior at $10^8$ samples remains an extrapolated estimate. In discrete spaces (such as MNIST handwritten digits), 14 out of 3,731 samples were confirmed to be "truly unattributable samples" with a counterfactual radius of zero. In continuous image spaces, however, true unattributability is theoretically unlikely to occur, and in practice the concept of "near-unattributability" (a counterfactual radius below a threshold $\tau$) must be used instead. Setting an appropriate value for this threshold $\tau$ is context-dependent, and no legally meaningful standard has yet been established.
Since publishing their first method in 2023, Dai and Gifford have consistently pursued the same question. The very goal of pinpointing a causal relationship between training data and output becomes unachievable as models scale up. What this research demonstrates is that one of the technical premises AI regulation had hoped to rely on collapses with scale. Courts and legislatures are now being forced to rebuild frameworks for adjudicating copyright issues without the tool of attribution.