  Recent advances in score-based generative models have led to a huge spike in
the development of downstream applications using generative models ranging from
data augmentation over image and video generation to anomaly detection. Despite
publicly available trained models, their potential to be used for privacy
preserving data sharing has not been fully explored yet. Training diffusion
models on private data and disseminating the models and weights rather than the
raw dataset paves the way for innovative large-scale data-sharing strategies,
particularly in healthcare, where safeguarding patients' personal health
information is paramount. However, publishing such models without individual
consent of, e.g., the patients from whom the data was acquired, necessitates
guarantees that identifiable training samples will never be reproduced, thus
protecting personal health data and satisfying the requirements of policymakers
and regulatory bodies. This paper introduces a method for estimating the upper
bound of the probability of reproducing identifiable training images during the
sampling process. This is achieved by designing an adversarial approach that
searches for anatomic fingerprints, such as medical devices or dermal art,
which could potentially be employed to re-identify training images. Our method
harnesses the learned score-based model to estimate the probability of the
entire subspace of the score function that may be utilized for one-to-one
reproduction of training samples. To validate our estimates, we generate
anomalies containing a fingerprint and investigate whether generated samples
from trained generative models can be uniquely mapped to the original training
samples. Overall our results show that privacy-breaching images are reproduced
at sampling time if the models were trained without care.
