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

翻译：癫痫FLAIR MRI中的局灶性皮质发育不良（FCD）病灶既细微又稀少，这使得联合图像-掩码生成建模容易不稳定和产生记忆效应。我们提出了SLIM-Diff，一个紧凑的联合扩散模型，其主要贡献在于：（i）一个单共享瓶颈U-Net，它从一个双通道的“图像+掩码”表示中强制实现解剖结构与病灶几何形态之间的紧密耦合；（ii）通过可调的$L_p$目标函数进行损失几何形态调优。作为内部基线，我们包含了经典的DDPM风格目标（$ε$预测与$L_2$损失），并在匹配的设置下分离了预测参数化和$L_p$几何形态的影响。实验表明，对于联合合成任务，$x_0$预测始终是最强的选择，并且分数阶次二次惩罚项（$L_{1.5}$）能提高图像保真度，而$L_2$则能更好地保留病灶掩码的形态。我们的代码和模型权重可在 https://github.com/MarioPasc/slim-diff 获取。