\section{Conclusion}
\label{sec:conclusion}
% rivedere conclusioni per riallinearle a i contributi iniziali. aggiungere come main direction of future work il miglioramento della generazione nelle regioni ad alta frequenza come i denti.
In this work, we investigated the use of Flow Matching with Optimal Transport to generate 3D craniofacial skeletal data.
Despite the challenges posed by the three-dimensional nature of medical data and the high level of clinical accuracy required, we showed that this generative modelling paradigm succeeds in generating high quality synthetic data.
% Despite the complexities deriving from this kind of data, as its 3D nature and the clinical accuracy required, we showed that this generative modelling paradigm succeeds in generating high quality synthetic data. 
In addition to the quantitative and qualitative analysis, we validated the results on two medical downstream tasks, confirming the validity of the data generated with our solution for various settings.
The robust generation broadens the spectrum of available tools in 3D medical data synthesis, and the performance in the downstream tasks confirms their relevance in augmenting real datasets, in replacing them when they are not available and in balancing them, which can be critical for various tasks.
% il successo nella generazione ed in queste doenstream tasks permette di ampiare il panorama di strumenti utilizzabili nella generazione di immagini mediche e ha dimostrato l'importanza dei dati sintetici nell'augmentation di dati reali sia per incrementare il numero di dati, sia per rimediare all'unbalancing dei dataset, che in certe tasks può essere estremamente rilevante e problematico.
Moreover, the synthetic dataset obtained with OTFM was compared to data generated with DDPMs, the dominant paradigm in 3D medical images generation.
The results showed how OTFM surpasses DDPM in terms of generation quality, robustness of the model, and ability in conditioning the generation with Quality Scores.
% il fatto che sia più facile alleare e generare con OTFM rispetto a DDPM potrebbe essere dovuto al simpler forward process e alla simpler trajectory ricostruita dal backward process.
Despite this, there are still a few cases in which OTFM generations contain small errors. 
Therefore, future work will focus on injecting anatomical knowledge into the model and enhancing the generation of high-frequency details of the volumes.


%Surprisingly, while being generally worse, some DDPM generations achieved higher quality.
%, but more work is needed to fully understand this behaviour.
%We have also validated the importance of image resolution in the final generation quality and proposed a modified architecture to retain high resolution information in the training of the autoencoder. This architecture resulted in better reconstruction performance and thus higher quality generations.


