Diffusion models are a class of generative models that generate high-quality samples, but at present it is difficult to characterize how they depend upon their training data. This difficulty raises scientific and regulatory questions, and is a consequence of the complexity of diffusion models and their sampling process. To analyze this dependence, we introduce Ablation Based Counterfactuals (ABC), a method of performing counterfactual analysis that relies on model ablation rather than model retraining. In our approach, we train independent components of a model on different but overlapping splits of a training set. These components are then combined into a single model, from which the causal influence of any training sample can be removed by ablating a combination of model components. We demonstrate how we can construct a model like this using an ensemble of diffusion models. We then use this model to study the limits of training data attribution by enumerating full counterfactual landscapes, and show that single source attributability diminishes with increasing training data size. Finally, we demonstrate the existence of unattributable samples.
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