Optimal transport driven flow matching: an efficient framework for volumetric generation

The development of robust machine learning models for 3D medical imaging is severely hindered by data scarcity, privacy regulations, and dataset heterogeneity. While generative artificial intelligence, particularly Latent Diffusion Models and Flow Matching, represents the state-of-the-art through synthetic data generation, scaling these models to high-dimensional 3D volumes remains a demanding computational challenge. In this thesis, we address the architectural bottlenecks of 3D volumetric generation by optimizing the latent generative core of the MAISI (Medical AI for Synthetic Imaging) framework. We conduct a rigorous theoretical and empirical comparison between Independent Conditional Flow Matching (I-CFM),Variance-Preserving CFM (VP-CFM) , and Minibatch Optimal Transport CFM (OT-CFM). Our extensive evaluation on the CT-RATE dataset reveals a critical "Loss-Fidelity Paradox": while under-parameterized 3D U-Nets achieve similar training convergence across all methods, I-CFM and VP-CFM suffer from severe macroscopic topological failures during inference. We mathematically diagnose this collapse as "Mode Averaging," where in the network’s limited capacity forces it to predict the spatial mean of highly intersecting, conflicting target trajectories, drastically reducing inter-sample diversity. By enforcing Optimal Transport coupling, OT-CFM globally disentangles probability paths, minimizing the variance of the regression target. Quantitative metrics, including Fréchet Inception Distance (FID), Maximum Mean Discrepancy (MMD), and Voxel-wise Variance, confirm that OT-CFM is the only formulation capable of preserving true patient-to-patient anatomical diversity without requiring massive architectural scaling. Ultimately, this work establishes Optimal Transport as an indispensable prerequisite for efficient, high-fidelity 3D medical generation in resource-constrained settings.