Denoising Diffusion Probabilistic Models, Jonathan Ho, Ajay Jain, Pieter Abbeel, 2020Advances in Neural Information Processing Systems (NeurIPS) 33DOI: 10.48550/arXiv.2006.11239 - This foundational paper introduced the modern formulation of Denoising Diffusion Probabilistic Models (DDPMs) and extensively details the forward diffusion process, including the direct sampling formula from x0.
Deep Unsupervised Learning using Nonequilibrium Thermodynamics, Jascha Sohl-Dickstein, Eric A. Weiss, Niru Maheswaranathan, Surya Ganguli, 2015Proceedings of the 32nd International Conference on Machine Learning (ICML)DOI: 10.48550/arXiv.1503.03585 - The original paper that introduced the concept of diffusion models for generative AI, establishing the framework for the forward and reverse processes.
Diffusion Models: A Unified Perspective, Jonathan Timcheck, Sumit Bam Shrestha, Daniel Ben Dayan Rubin, Adam Kupryjanow, Garrick Orchard, Lukasz Pindor, Timothy Shea, Mike Davies, 2023arXiv preprint arXiv:2303.09503DOI: 10.48550/arXiv.2303.09503 - A comprehensive survey providing a unified view of various diffusion models, including detailed explanations of the forward process and its mathematical underpinnings.