arXiv Machine Learning
Beyond the Semicircle: Free Diffusion Models with Prescribed Equilibria
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Free Denoising Diffusion Models
arXiv:2510. 22778v3 Announce Type: replace-cross Abstract: We develop a free-probabilistic framework for denoising diffusion, in which the data is a self-adjoint operator and its law a spectral distribution.
arXiv Machine Learning
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Recursively Trained Diffusion Models: Limiting Collapse Distribution and Spectral Characterization
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.
arXiv Machine Learning
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Foundations of Diffusion Models in General State Spaces: A Self-Contained Introduction
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 AI
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A Random Matrix Theory Perspective on the Consistency of Diffusion Models
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arXiv Machine Learning
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Dimension-Free Convergence of Discrete Diffusion Models: Adjoint Equations Induce the Right Space
arXiv:2605. 17232v2 Announce Type: replace Abstract: Discrete diffusion has become a leading framework for generative modeling in various applications including language, vision, and biology.
arXiv Machine Learning
Oct 9
Diffusion Removes Langevin's Conditioning Dependence: A Sharp Gaussian Analysis
arXiv:2610. 12052v1 Announce Type: cross Abstract: Despite their empirical success, why diffusion models overcome the bottlenecks of classical score-based samplers remains unclear.