For example: for even moderately sized datasets, the trained diffusion models' marginal probability distribution stays the same irrespective of which examples were removed from the training data, potentially making the influence functions task vacuous.

In our paper, we empirically show that the choice of GGN and K-FAC approximation is crucial for the performance of influence functions, and that following our recommended design principles leads to the better performing approximations.

Influence functions require the training loss Hessian matrix. Typically, a K-FAC approximation to a Generalised Gauss-Newton (GGN) matrix is used instead of the Hessian. However, it's not immediately obvious which GGN and K-FAC approximations to use in the diffusion

How do you identify training data responsible for an image generated by your diffusion model? How could you quantify how much copyrighted works influenced the image?

In our ICLR oral paper we propose how to approach such questions scalably with influence functions.