arXiv:2310. 05264v5 Announce Type: replace Abstract: In this work, we investigate an intriguing and prevalent phenomenon of diffusion models which we term as "consistent model reproducibility": given the same starting noise input and a deterministic sampler, different diffusion models often yield remarkably similar outputs.
By Huijie Zhang, Jinfan Zhou, Yifu Lu, Minzhe Guo, Peng Wang, Liyue Shen, Qing Qu
arXiv:2608. 02575v1 Announce Type: new Abstract: Diffusion models rely on stochastic inputs, yet on finite-precision hardware, the "randomness" they consume is realized as deterministic numerical orbits generated by pseudorandom rules.
By Shengzhi Deng, Chenqi Ye, Yanze Guo
The paper investigates why diffusion models, despite their practical success, can fully memorize training data when optimal. It shows that as training proceeds, the denoising objective causes overfitting at intermediate noise levels, creating a gap between validation and training performance. In a 2D toy model, this gap arises from the interplay between model error and the data distribution’s support density, leading to a smooth, generalizing flow field rather than exact recall of training points. The study also reveals that predictions from intermediate inference states become increasingly similar to training data in feature space, even as overall similarity to validation data remains unchanged.
By Tim Kaiser, Markus Kollmann
arXiv:2602. 02908v2 Announce Type: replace-cross Abstract: Diffusion models trained on different, non-overlapping subsets of a dataset often produce strikingly similar outputs when given the same noise seed.
By Binxu Wang, Jacob Zavatone-Veth, Cengiz Pehlevan
arXiv:2605.08144v2 Announce Type: replace-cross
Abstract: Training a diffusion model involves two sources of randomness for each data sample: the timestep and the Gaussian noise realization. The time...
By Haokai Zhao, Da Xing, Hanqun Cao, Tinson Xu, Xinyu Xiang, Yanchao Li, Xiangru Tang, Hongbin Lin, Zehong Wang, Kuan Pang, Peng Xia, Molei Tao, Li Erran Li, Aditya Joshi, Jure Leskovec, Fang Wu
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