The paper argues that the concrete random noise used in diffusion models is not merely a passive perturbation but a learnable input that can be exploited by the model. By analyzing how clean data and realized noise jointly form the noisy input, the authors show that the model can learn regularities in the data or in the noise structure, and that these two routes can interact. Experiments on MNIST and CIFAR‑10 using pseudorandom streams demonstrate that structured‑noise training can reduce prediction loss, but this advantage disappears when test noise is replaced with IID noise, indicating that the learned dependence is tied to the specific noise structure.
By Shengzhi Deng, Chenqi Ye, Yanze Guo
arXiv:2609.37080v1 Announce Type: new
Abstract: Latent Diffusion Models (LDMs) typically adopt a two-stage pipeline: an auto-encoder (AE) is first pre-trained to define a latent space, then a diffusi...
By Zhengqiang Zhang, Lingchen Sun, Rongyuan Wu, Qiaosi Yi, Xiangtao Kong, Chaodong Xiao, Lei Zhang
arXiv:2512.12749v3 Announce Type: replace-cross
Abstract: Learning surrogate models for physical systems with latent uncertainty remains challenging in data-scarce regimes: deterministic neural opera...
By Sahil Bhola, Karthik Duraisamy
arXiv:2606. 08953v1 Announce Type: new Abstract: Modern generative models often define an entire probability path from a simple prior to the data law, rather than only an endpoint map.
By Lei Luo, Yingzhen Zhang, Jian Yang
arXiv:2605. 00161v2 Announce Type: replace Abstract: Diffusion language models (DLMs) are an attractive alternative to autoregressive models because they promise sublinear-time, parallel generation, yet practical gains remain elusive as high-quality samples still demand hundreds of refinement steps.
By Hasan Amin, Yuan Gao, Yaser Souri, Subhojit Som, Ming Yin, Rajiv Khanna, Xia Song
arXiv:2607. 15693v1 Announce Type: cross Abstract: We describe a model of perceptual inference in primary visual cortex (V1) equivalent to a minimal diffusion model whose function can be readily understood from its parameters.
By Zeyu Yun, Alexander Belsten, Dasheng Bi, Zahra Kadkhodaie, Yubei Chen, Bruno A. Olshausen
arXiv:2512. 20963v3 Announce Type: replace Abstract: Diffusion models excel at generating high-quality, diverse samples, yet they risk memorizing training data when overfit to the training objective.
By Zekai Zhang, Xiao Li, Xiang Li, Lianghe Shi, Meng Wu, Molei Tao, Qing Qu
Neural operators learn mappings between function spaces, but are typically developed with dense input-output training fields and fully observed inputs at inference. Many scientific problems require instead predicting solution fields from sparse, irregular, or partial observations under uncertainty.
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:2606. 03119v1 Announce Type: cross Abstract: Guidance methods, such as classifier-free guidance (CFG) and auto-guidance (AG), have advanced noise-to-data generation in diffusion models.
By Zehua Chen, Yucheng Yang, Binjie Yuan, Kaiwen Zheng, Jun S. Liu, Jun Zhu
arXiv:2606. 08672v1 Announce Type: cross Abstract: Diffusion and flow generative models sample by integrating a learned ODE, but high quality still requires many sequential model evaluations.
By Sihyeon Kim, Seunghun Lee, Vikas Singh, Hyunwoo J. Kim
arXiv:2606. 14283v1 Announce Type: cross Abstract: Deep learning has driven many recent advances in process analytics, especially for predictive and prescriptive monitoring.
By Johannes De Smedt, Jari Peeperkorn, Artem Polyvyanyy, Jochen De Weerdt