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

2026-08-05 · 13:28 UTC ·Yizhu Wang, Mu Niu, Xiaochen Yang ·1 min read

Brief

The paper introduces ILDM, which integrates probabilistic dimensionality reduction with geometry-aware diffusion by treating the latent space as a manifold chart and deriving a probabilistic metric from a decoder. A hybrid forward diffusion switches between Riemannian and Euclidean dynamics by local uncertainty, trained via approximate denoising score matching and reversed with hybrid Langevin dynamics, yielding lower FID and LPIPS on COIL-100, MNIST and cardiac MRI versus standard diffusion and latent diffusion models.

Why it matters

ILDM (Intrinsic Hybrid Latent Diffusion Model) treats the learned latent as a chart on an unknown Riemannian manifold and uses a probabilistic decoder to produce a metric tensor; the forward process is a hybrid diffusion that switches between Riemannian and Euclidean dynamics according to local uncertainty.

Key details

The paper develops an approximate denoising score matching training objective and a hybrid Langevin backward process; experiments on COIL-100, MNIST, and cardiac MRI report improved generation quality, achieving lower FID and LPIPS than standard diffusion and latent diffusion baselines.

Abstract

We introduce the Intrinsic Hybrid Latent Diffusion Model (ILDM), a generative framework that integrates probabilistic dimensionality reduction with geometry-aware diffusion on unknown manifolds. While diffusion models (DMs) have achieved state-of-the-art results in high-dimensional data synthesis, they rely on large training datasets and ignore intrinsic geometric structure. Latent diffusion models (LDMs) address the high dimensionality by learning a latent space, but they typically impose a Euclidean structure, failing to capture the underlying manifold geometry, especially problematic in data-sparse regimes. ILDM addresses these limitations by interpreting the latent space as a chart of an unknown Riemannian manifold, with geometry and uncertainty quantified through a probabilistic decoder. The forward process is a hybrid diffusion that switches between Riemannian and Euclidean dynamics based on local uncertainty, where the Riemannian component is governed by a probabilistic metric tensor derived from the decoder. To learn the generative dynamics, we introduce an approximate denoising score matching method tailored to the hybrid diffusion setting, enabling a backward process defined by hybrid Langevin dynamics. Experiments on COIL-100, MNIST, and cardiac MRI datasets demonstrate that ILDM significantly improves generation quality, achieving lower FID and LPIPS scores compared to standard diffusion and latent diffusion models.