SLIM-Diff: Shared Latent Image-Mask Diffusion with Lp loss for Data-Scarce Epilepsy FLAIR MRI

Focal cortical dysplasia (FCD) lesions in epilepsy FLAIR MRI are subtle and scarce, making joint image--mask generative modeling prone to instability and memorization. We propose SLIM-Diff, a compact joint diffusion model whose main contributions are (i) a single shared-bottleneck U-Net that enforces tight coupling between anatomy and lesion geometry from a 2-channel image+mask representation, and (ii) loss-geometry tuning via a tunable $L_p$ objective. As an internal baseline, we include the canonical DDPM-style objective ($ε$-prediction with $L_2$ loss) and isolate the effect of prediction parameterization and $L_p$ geometry under a matched setup. Experiments show that $x_0$-prediction is consistently the strongest choice for joint synthesis, and that fractional sub-quadratic penalties ($L_{1.5}$) improve image fidelity while $L_2$ better preserves lesion mask morphology. Our code and model weights are available in https://github.com/MarioPasc/slim-diff