\section{Related work}
\vspace{-4pt}
\subsection{Sharing synthetic medical image data}
\vspace{-2pt}

Synthesizing medical data for sharing purposes so as to avoid privacy issues is an established idea in the literature~\cite{goncalves_generation_2020}. %dube_approach_2014
Medical \emph{image} data can be synthesized by GANs~\cite{bowles_gan_2018, yi_generative_2019, sun_hierarchical_2022}, % dikici_constrained_2021, 
but for supervised learning to be possible, an annotation needs to be associated with a synthetic image. While conditioning GANs on an image class is straightforward when generating data for classification tasks~\cite{hu_prostategan_2018}, conditioning on segmentation maps~\cite{chang_mining_2023} to generate data for segmentation tasks requires the additional complexity of sharing segmentations to condition on (e.g., by training a separate GAN for them~\cite{guibas_synthetic_2018, greenspan_medgen3d_2023}). \citet{thambawita_singan-seg_2022} propose a GAN for joint unconditional generation of polyp images and segmentations that improves performance but requires a separate GAN to be trained for each input image, likely impeding scaling to larger datasets. 

\begin{figure}
    \centering
    \includegraphics[width=\linewidth]{_figures/3_method/hyfree-s3-overview-1.pdf}
    \vspace{-11pt}
    \caption{Overview of HyFree-S3 for two sites. Synthetic datasets are generated at each site independently, merged at a central site, and used in training a general segmentation model. That model is copied to all sites and independently fine-tuned on the local data. All models automatically adapt to the properties of the data.}
    \label{fig:method}
    \vspace{-20pt}
\end{figure}


\subsection{Distributed learning with medical image data}
\vspace{-1pt}

Federated learning~\cite{konecny_federated_2016} can be applied to medical imaging data~\cite{rieke_future_2020, adnan_federated_2022} where it allows the global model to be trained on diverse data from multiple hospitals~\cite{ng_federated_2021} without sharing local data.

Federated learning algorithms for training a GAN~\cite{rasouli_fedgan_2020} can be applied to medical data~\cite{chang_mining_2023} but they incur privacy costs because real data could be reconstructed from the gradients passed between sites~\cite{zhu_deep_2019}. A common solution~\cite{chang_synthetic_2020, chang_mining_2023, wang_fedmed-gan_2023} is to train only the generator globally while the discriminators are trained per-site using the local data and the synthetic data from the global generator. 

Our method differs from the existing distributed learning techniques in three ways. Firstly, it is asynchronous and does not require simultaneous online access to sites. Secondly, the generated data is filtered to not contain memorized data (in contrast to sharing a black-box generative neural network with potentially undiscovered vulnerabilities). Finally, HyFree-S3 is adaptable and hyperparameter-free, thus making it potentially easier to use.