Continuous 3-D Latent Diffusion for Medical Image Generation and Reconstruction
High-resolution three-dimensional (3-D) medical diffusion models remain constrained by the cost of processing full volumes, even when denoising is performed in a compact latent space. We introduce a continuous 3-D latent diffusion model (LDM) framework for computed tomography (CT) and magnetic resonance imaging (MRI) generation and measurement-guided reconstruction. Its central component is a compact autoencoder (AE) with a coordinate-conditioned local implicit image function (LIIF) decoder that represents a volume as a continuous function of spatial coordinates. By evaluating the convolutional decoder once on the latent grid and restricting repeated computation to a lightweight implicit head, the proposed design avoids overlapping sub-volume decoding while remaining differentiable for inverse-problem optimization. We evaluate the framework on CT volumes of 512^3 voxels and MRI volumes of 256^3 voxels. On high-resolution CT, the proposed AE is approximately x12-32 faster than the evaluated reference autoencoders, achieves the lowest peak graphics processing unit (GPU) memory use, and retains comparable structural fidelity despite a moderate reduction in voxel-level accuracy. The resulting frozen 3-D latent prior generates coherent full volumes without visible patch seams and can be applied, without task-specific retraining, to sparse-view CT and accelerated MRI reconstruction through hard data consistency. Although direct pixel-domain reconstruction remains more accurate, the results demonstrate that a single volumetric latent prior can support both unconditional generation and measurement-conditioned reconstruction on one GPU. Overall, the framework provides a practical trade-off between continuous volumetric decoding, computational efficiency, and fine-detail preservation. Our code will be made available at https://github.com/mellak/.