Intrinsic-Hybrid Latent Diffusion Models for Generative Modeling on Unknown Manifolds

The paper introduces the Intrinsic Hybrid Latent Diffusion Model (ILDM), combining probabilistic dimensionality reduction with geometry-aware diffusion on an unknown Riemannian manifold. Its latent space is treated as a manifold chart, while a probabilistic decoder estimates both local geometry and uncertainty. The forward process switches between Riemannian and Euclidean dynamics according to local uncertainty, and training uses approximate denoising score matching for hybrid diffusion. The authors report lower FID and LPIPS than standard diffusion and latent diffusion baselines on COIL-100, MNIST, and cardiac MRI datasets.