arXiv:2606. 09816v1 Announce Type: cross Abstract: Standard diffusion models typically use a single time-homogeneous Gaussian terminal distribution as the reference law for generation.
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Standard diffusion models typically use a single time-homogeneous Gaussian terminal distribution as the reference law for generation. While this choice is analytically convenient and empirically powerful, it provides little explicit structure for data concentrated near low-dimensional manifolds, where different regions of the data distribution may correspond to distinct local geometric or semantic factors.
arXiv:2608. 04827v1 Announce Type: cross 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.
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.
arXiv:2602. 17706v2 Announce Type: replace Abstract: Diffusion models learn data distributions indirectly through denoising, making the difficulty of generative modeling closely tied to the dependency structure of data.
The article "Foundations of Diffusion Models in General State Spaces: A Self-Contained Introduction" presents a unified primer on diffusion models that applies to both continuous Euclidean data and discrete categorical structures. It develops discrete-time forward noising via Markov kernels and learned reverse dynamics, and connects these to continuous-time limits such as stochastic differential equations in ρ^d and continuous-time Markov chains on finite alphabets, deriving the corresponding Fokker–Planck and master equations. The work also shows how different forward corruption choices—Gaussian processes for continuous spaces and structured categorical transition kernels for discrete spaces—affect reverse dynamics and the evidence lower bound used in training, offering a layered exposition for newcomers, practitioners, and experts alike.
arXiv:2606. 13796v1 Announce Type: cross Abstract: Recursive training of generative models on their own outputs can lead to model collapse, a compounding drift away from the true data distribution.