The book "The Principles of Diffusion Models" outlines the foundational concepts behind diffusion models, tracing their evolution from a forward process that corrupts data into noise to a reverse process that reconstructs data. It presents three complementary perspectives—variational, score-based, and flow-based—each describing how a time-dependent velocity field transports a simple prior to the data distribution. The text also covers practical guidance for controllable generation, efficient solvers, and diffusion-inspired flow-map models, providing a mathematically grounded framework for readers with basic deep‑learning knowledge.
By Chieh-Hsin Lai, Yang Song, Dongjun Kim, Yuki Mitsufuji, Stefano Ermon
arXiv:2605. 12764v3 Announce Type: replace-cross Abstract: This paper introduces a physics-informed generative framework that resolves the fundamental conflict between the statistical flexibility of deep learning and the rigorous theoretical constraints of fixed-income modeling.
By Fusheng Luo, H'elyette Geman
arXiv:2609.37435v1 Announce Type: new
Abstract: Neural Koopman autoencoder models have been shown to successfully build a latent embedding with linear dynamics for arbitrary dynamical systems, enabli...
By Anthony Frion, Lucas Drumetz, Guillaume Tochon, Mauro Dalla Mura, Ali Can Bekar, Abdeldjalil A\"issa El Bey
arXiv:2606. 25900v1 Announce Type: new Abstract: Variational Autoencoders (VAEs) belong to a family of autoencoders with probabilistic properties, making them well suited for generating data by producing a smooth and continuous latent space.
By Gananath R
Variational Autoencoders (VAEs) belong to a family of autoencoders with probabilistic properties, making them well suited for generating data by producing a smooth and continuous latent space. Despite being introduced over a decade ago, the method continues to be widely adopted in both research and industry for diverse applications.
arXiv:2606. 30384v1 Announce Type: new Abstract: Training in artificial neural networks can be viewed as a trajectory evolving through a high-dimensional loss landscape.
By Pedro Jim\'enez-Gonz\'alez, Miguel C. Soriano, Lucas Lacasa