We present BrainODE, a neural ordinary differential equation (ODE)-based framework for modeling continuous longitudinal deformations of brain shapes. BrainODE learns a deformation space over anatomically meaningful brain regions to facilitate early prediction of neurodegenerative disease progression. Addressing inherent challenges of longitudinal neuroimaging data-such as limited sample sizes, irregular temporal sampling, and substantial inter-subject variability-we propose a conditional neural ODE architecture that models shape dynamics with subject-specific age and cognitive status. To enable autoregressive forecasting of brain morphology from a single observation, we propose a pseudo-cognitive status embedding that allows progressive shape prediction across intermediate time points with predicted cognitive decline. Experiments show that BrainODE outperforms time-aware baselines in predicting future brain shapes, demonstrating strong generalization across longitudinal datasets with both regular and irregular time intervals.

Spatial control methods using additional modules on pretrained diffusion models have gained attention for enabling conditional generation in natural images. These methods guide the generation process with new conditions while leveraging the capabilities of large models. They could be beneficial as training strategies in the context of 3D medical imaging, where training a diffusion model from scratch is challenging due to high computational costs and data scarcity. However, the potential application of spatial control methods with additional modules to 3D medical images has not yet been explored. In this paper, we present a tailored spatial control method for 3D medical images with a novel lightweight module, Volumetric Conditioning Module (VCM). Our VCM employs an asymmetric U-Net architecture to effectively encode complex information from various levels of 3D conditions, providing detailed guidance in image synthesis. To examine the applicability of spatial control methods and the effectiveness of VCM for 3D medical data, we conduct experiments under single-and multimodal conditions scenarios across a wide range of dataset sizes, from extremely small datasets with 10 samples to large datasets with 500 samples. The experimental results show that the VCM is effective for conditional generation and efficient in terms of requiring less training data and computational resources. We further investigate the potential applications for our spatial control method through axial super-resolution for medical images. Our code is available at https://github.com/SSTDV-Project/VCM.git