A Mathematical Introduction to Diffusion Models

Error Bounds for a Diffusion Model-Based Drift Estimator

Parameter estimation in stochastic differential equations is a classical statistical problem of much importance in many scientific fields. Recent work of Tapia Costa et al.

Error Bounds for a Diffusion Model-Based Drift Estimator

arXiv:2606. 02115v1 Announce Type: cross Abstract: Parameter estimation in stochastic differential equations is a classical statistical problem of much importance in many scientific fields.

Diffusion Models Live Event

The Annotated Diffusion Model

Self-Regulating Annealing in Heavy-Tailed Diffusion Models

arXiv:2606. 01645v1 Announce Type: cross Abstract: Diffusion models have emerged as a leading framework for deep generative modeling.

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.