发表机构
School of Mathematics and Statistics, University of Glasgow（格拉斯哥大学数学与统计学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出ILDM框架，将概率降维与未知流形几何感知扩散结合，通过混合扩散与近似去噪得分匹配方法，在三类数据集上实现生成质量提升，降低了FID和LPIPS分数。
AI 中文摘要
我们提出了内在混合隐式扩散模型（Intrinsic Hybrid Latent Diffusion Model，ILDM），这是一种将概率降维与未知流形上的几何感知扩散相结合的生成框架。扩散模型（Diffusion Models，DMs）在高维数据合成中取得了最先进的成果，但依赖大型训练数据集且忽略内在几何结构。隐式扩散模型（Latent Diffusion Models，LDMs）通过学习隐空间解决了高维问题，但通常采用欧氏结构，无法捕捉底层流形几何，这在数据稀疏 regime 中尤为突出。ILDM 将隐空间解释为未知黎曼流形的一个图，通过概率解码器量化几何与不确定性；前向过程是混合扩散，根据局部不确定性在黎曼与欧氏动力学间切换，其中黎曼分量由解码器推导的概率度量张量控制。为学习生成动力学，我们引入了适配混合扩散场景的近似去噪得分匹配方法，实现了由混合朗之万动力学定义的反向过程。在 COIL-100、MNIST 和心脏 MRI 数据集上的实验表明，ILDM 显著提升了生成质量，相比标准扩散模型和隐式扩散模型，其 FID 和 LPIPS 分数更低。
英文摘要
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.
