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.
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.
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.
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.
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.
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...
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.
arXiv:2505. 22839v2 Announce Type: replace-cross Abstract: Recent studies suggest that diffusion models significantly improve the empirical adversarial robustness of deep neural network models.
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.
Neural Bridge Processes (NBPs) replace the input‑independent forward kernel of Neural Diffusion Processes with an input‑anchored bridge trajectory, allowing conditioning inputs to influence the noisy training states. When input and output dimensions differ, NBPs learn an output‑space anchor that guides the generative path without altering the denoising backbone. Theoretical analysis shows that this anchoring yields pathwise input distinguishability, injects input information into noisy states, and provides a direct gradient pathway, leading to consistent performance gains across synthetic regression, EEG, CylinderFlow, and image regression tasks.
arXiv:2610.14136v2 Announce Type: new Abstract: Iterative sampling in diffusion models can lead to error accumulation due to exposure bias. The denoiser is trained on real images interpolated with no...
arXiv:2606. 09718v1 Announce Type: new Abstract: Diffusion models have demonstrated remarkable generative capabilities and have also emerged as powerful self-supervised representation learners, yet the connection between these two abilities remains less explored.
The paper investigates why Diffusion Transformers perform well when predicting clean data but poorly when predicting noise or velocity. It introduces the concept of *residual-stream burden*, explaining that noisy targets force the residual stream to carry noise-dependent variation through the network, limiting representation flexibility. Experiments show that spectral concentration of clean targets reduces this burden, and the authors propose Spatially Indexed Hyper-Connections (SiHC) to expand residual bandwidth, achieving state‑of‑the‑art FID on ImageNet.