Diffusion and flow-matching samplers integrate a learned probability-flow ODE from a large noise scale down to a small terminal floor $σ_{\min}$, at which the score is stiff and the flow develops a boundary layer. We treat $σ_{\min}$ as a singular-perturbation parameter and determine which fixed-step samplers are asymptotic-preserving (AP), that is, stable and uniformly accurate as $σ_{\min}\to0$, casting the criteria as an a posteriori audit: residual functionals with $σ_{\min}$-uniform coefficients, computable on a pretrained checkpoint without ground-truth scores or exact trajectories.
GeoSPRINT is a training‑free framework that constructs non‑uniform sampling schedules for diffusion model inference by detecting geometrically redundant steps in denoising trajectories. It uses a hyperplanarity test in latent space, implemented via QR factorization, to allocate more steps to high‑curvature regions, and introduces the trajectory projection score α_traj as a model‑free diagnostic for flow quality. Across CIFAR‑10, LSUN Church, and Stable Diffusion v1.5, GeoSPRINT consistently outperforms uniform DDIM schedules at matched NFE budgets, improving FID scores by up to 1.93 points.
By Arpita Joshi
arXiv:2607. 26285v1 Announce Type: cross Abstract: Two central challenges in diffusion-based sampling are the theoretical one of understanding their remarkable effectiveness even in high-dimensional settings, and the practical one of designing algorithms with certified performance guarantees.
By Martin J. Wainwright
arXiv:2607. 04113v1 Announce Type: new Abstract: Diffusion and flow-matching samplers integrate a learned probability-flow ODE from a large noise scale down to a small terminal floor $\sigma_{\min}$, at which the score is stiff and the flow develops a boundary layer.
By Shiheng Zhang
Spectral-Guided Diffusion introduces a method to accelerate diffusion inference by identifying and reusing residual branches that need not be recomputed during the trajectory. The approach uses a Spectral Concentration Ratio (SCR) combined with Frobenius magnitude to create an offline sensitivity proxy and deterministic lifetime for each scheduled unit, eliminating the need for routers or input-dependent searches. Experiments on models such as LLaDA-8B, DiT-XL/2, U-ViT-L, and SDXL show that this scheduling preserves quality better than several baselines and achieves up to a 3.0× wall‑clock speedup over eager inference.
By Ibne Farabi Shihab, Abu Sa-Adat Mohamed Moon-Im Al Ahsan, Anuj Sharma
arXiv:2607. 06546v1 Announce Type: cross Abstract: Denoising graphs is a fundamental problem in graph learning and the core operation of graph diffusion models.
By Shervin Khalafi, Igor Krawczuk, Sergio Rozada, Charilaos Kanatsoulis, Antonio G Marques, Alejandro Ribeiro
arXiv:2607. 06833v1 Announce Type: new Abstract: Sampling stochastic signals supported on a graph underlies many graph machine learning tasks, including recommender systems, forecasting in financial markets, and wireless network optimization.
By Yi\u{g}it Berkay Uslu, Samar Hadou, Sergio Rozada, Shirin Saeedi Bidokhti, Alejandro Ribeiro
arXiv:2606. 18186v1 Announce Type: cross Abstract: Finite-dimensional (FD) diffusion policies exhibit temporal drift owing to discretization artifacts that degrade long-horizon performance (when deployed on physical systems).
By Lekan Molu
arXiv:2606. 14636v1 Announce Type: new Abstract: Control-function instrumental variable estimators need a first-stage residual, not merely a first-stage prediction.
By Rui Wu, Zongyuan Chen, Hong Xie, Defu Lian, Enhong Chen
Denoising graphs is a fundamental problem in graph learning and the core operation of graph diffusion models. Attention-based architectures like graph transformers have recently shown promise in denoising graphs.
arXiv:2606. 13796v1 Announce Type: cross Abstract: Recursive training of generative models on their own outputs can lead to model collapse, a compounding drift away from the true data distribution.
By Na\"il B. Khelifa, Richard E. Turner, Ramji Venkataramanan
arXiv:2609.35947v1 Announce Type: new
Abstract: Many inference-time tasks for pretrained discrete diffusion models and diffusion language models reduce to drawing samples from a tilted version of the...
By Yinuo Ren, Haoxuan Chen, Grant M. Rotskoff, Jiequn Han, Lexing Ying