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.
By Yizhu Wang, Mu Niu, Xiaochen Yang
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.
By Rongyao Cai, Yuxi Wan, Kexin Zhang, Ming Jin, Zhiqiang Ge, Qingsong Wen, Yong Liu
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.
By Vincent Pauline, Tobias H\"oppe, Kirill Neklyudov, Alexander Tong, Stefan Bauer, Andrea Dittadi
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.
By Na\"il B. Khelifa, Richard E. Turner, Ramji Venkataramanan
arXiv:2209. 14125v3 Announce Type: replace-cross Abstract: Diffusion models have proven to be a flexible and effective framework for modelling probability distributions on finite-dimensional spaces.
By Angus Phillips, Thomas Seror, Michael Hutchinson, Valentin De Bortoli, Arnaud Doucet, Emile Mathieu
arXiv:2606. 04324v1 Announce Type: new Abstract: One of the primary challenges in Bayesian inference on the parameters of a diffusion model from discrete observations is the unavailability of an analytical expression for the transition density function between consecutive observation times, which is needed to derive the likelihood function.
By Riccardo Saporiti, Fabio Nobile
arXiv:2605. 00161v2 Announce Type: replace Abstract: Diffusion language models (DLMs) are an attractive alternative to autoregressive models because they promise sublinear-time, parallel generation, yet practical gains remain elusive as high-quality samples still demand hundreds of refinement steps.
By Hasan Amin, Yuan Gao, Yaser Souri, Subhojit Som, Ming Yin, Rajiv Khanna, Xia Song
FlowSGS introduces a flow-based posterior sampling method that combines Split Gibbs Sampling (SGS) with Langevin dynamics for the likelihood step and Stochastic Interpolants (SI) for the prior step. By integrating a pretrained flow model into the prior step via SI's reverse-time SDE and a novel timestep correction, FlowSGS reduces the number of network evaluations compared to plug‑and‑play diffusion samplers. Experiments demonstrate state‑of‑the‑art performance on various inverse problems, including the first flow‑based solution to a nonlinear inverse problem (Fourier phase retrieval).
By Tianao Li, Xinhui Qian, Emma Alexander
One of the primary challenges in Bayesian inference on the parameters of a diffusion model from discrete observations is the unavailability of an analytical expression for the transition density function between consecutive observation times, which is needed to derive the likelihood function. Extending previous studies that solve Fokker-Planck (FP) type partial differential equations with Normalizing Flows, we propose a new Normalizing Flow architecture to learn the transition density function of the diffusion process between two observation times.
arXiv:2606. 08953v1 Announce Type: new Abstract: Modern generative models often define an entire probability path from a simple prior to the data law, rather than only an endpoint map.
By Lei Luo, Yingzhen Zhang, Jian Yang