reviews: 
Comments: The authors introduce the Diffusion Attribution Score (DAS) to address limitations found in D-TRAK, a data attribution method for diffusion models. This is a timely and surprisingly under-explored task: While data attribution task (AKA data valuation), which strives to assess training samples' impact on trained model's predictions, has a long history - only recently methods for diffusion models emerged, motivated by the timely copyrights issues that such models present. The previous method D-TRAK approximates comparisons between prediction loss of diffusion models trained with and without specific training samples. However, the authors argue that the reliance on diffusion loss leads to indirect comparisons, and hypothesize that this indirect approach does not accurately capture the influence of training samples on model outputs. To overcome this, they propose DAS, which approximates a direct comparison. As demonstrated in thorough evaluations, this approach indeed provides more precise data attribution scores, when compared to D-TRAK and other baselines.
Strengths: 1. The authors picked up on the counterintuitive finding of D-TRAK that switching loss functions in their method, to a loss that is not used during training, increases attribution correctness. Though D-TRAK proposed an explanation, I personally share the author’s belief that this finding calls for further exploration (in my view D-TRAK's explanation requires further substantiation in itself). 

2. The authors provide a significant observation: D-TRAK’s attribution scores, as expressed in Eq. (7), do not directly compare (approximate) predictions with/ without training samples. I agree with this found limitation.

3. They propose to derive attribution formulas, that fall within the TRAK methodology, but starting from a direct comparison between the predictions (Eqs. 9). This original paradigm not only solves the newfound limitation, but also sheds light on the counterintuitive finding of D-TRAK: L_square does indeed differ from L_simple by providing a direct comparison of the predictions (Eq. 10).

4. Sufficient performance experiments: The authors demonstrate that DAS indeed outperforms D-TRAK (and several other baselines) across four datasets, and in several settings. Evaluations are in terms of LDS - a widely accepted choice in evaluating TRAK-based methods. Ontop of being appropriate, it is also extensive as it requires multiple training.
Weaknesses: 1. The paper lacks a "Previous Work" section—a significant omission, as it currently mentions only one attribution method for diffusion models (D-TRAK) in the introduction. The authors appear to have overlooked other relevant approaches, such as [1], [2], and [3], which should be acknowledged, even if not necessarily included in direct comparisons. Acknowledging these methods is especially important, given that this domain is still underexplored, and the current structure of the paper will give researchers a misleading impression that only gradient-based methods are available. Additionally, key baselines like Journey TRAK, TracInCP and others are introduced in the evaluation tables without prior context - an earlier introduction would clarify their relevance.

2. The mathematical claims lack direct verification through numerical experiments or even qualitative examples, and the improved performance alone is too indirect to serve as convincing validation  **[Edit: i.e. better LDS scores against competitors on standard benchmarks is not enough to substantiate the mathematical claims]**. With that said, given that it is common practice in ML to present mathematical derivations and substantiate them only via improved performance, this is not a critical flaw in terms of acceptance. However, it would significantly improve the impact if such experiments were added - here is a possible idea (other convincing experiments can work as well): Find cases where DAS succeeds and D-TRAK fails, and show that D-TRAK is indeed limited by its indirect comparisons (Sec. 3.1), where DAS solves this. 

[1] Wang et. al, ICCV 2023, “Evaluating Data Attribution for Text-to-Image Models”

[2] Brokman et. al, ECCV 2024, “MONTRAGE: Monitoring Training for
Attribution of Generative Diffusion Models”

[3] Kwon et. al, ICLR 2024, “DataInf: Efficiently Estimating Data Influence in LoRA-tuned LLMs and Diffusion Models”
Recommendation: 10
Reviewer confidence: 4
Soundness/correctness: 3
Clarity: 3