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.
arXiv:2607. 04113v2 Announce Type: replace Abstract: Diffusion and Gaussian-interpolant flow-matching samplers approach data through a terminal noise floor $\varepsilon$, a singular limit for manifold-supported or rank-deficient data.
By Shiheng Zhang
arXiv:2607. 07665v1 Announce Type: new Abstract: Classifier-free guidance (CFG) is the standard way to strengthen class-conditioning in diffusion and flow-matching samplers, yet at large guidance it oversaturates and destabilizes, symptoms practitioners suppress with more steps or limited-interval schedules.
By Shiheng Zhang
arXiv:2608. 00675v1 Announce Type: cross Abstract: Autoregressive models accumulate error over long rollouts, yet at deployment there is no ground truth to measure it against.
By Alexander Scheinker
arXiv:2608.23094v1 Announce Type: new
Abstract: One implicit DDIM inversion step is the cheapest probe of whether a pretrained diffusion model encodes local manifold geometry. It is the stationarity...
By Gordei Verbii
The paper proves that for discrete diffusion models using uniform or remasking forward processes, an adaptive sampler based on a leave‑one‑out denoiser can achieve sampling error proportional to the score‑estimation error plus a small tolerance. The required number of discretization steps scales with the dual total correlation of the target distribution, not directly with the ambient dimension. This result shows that sampling complexity is governed by the intrinsic dependence structure of the distribution, and the authors provide an information‑theoretic analysis linking discretization error to mutual information between coordinates.
By Daniil Dmitriev, Zhihan Huang, Yuting Wei
arXiv:2607. 24507v1 Announce Type: cross Abstract: Existing methods mainly adapt pretrained autoregressive (AR) language models to masked diffusion, whereas we directly adapt them to uniform-noise diffusion, where every token remains editable during sampling.
By Xiaoyi Jiang, Jingyuan Li, Yixuan Jiang, Wei Liu, Yi Zhu, Zuoqiang Shi, Pipi Hu
Classifier-free guidance (CFG) is the standard way to strengthen class-conditioning in diffusion and flow-matching samplers, yet at large guidance it oversaturates and destabilizes, symptoms practitioners suppress with more steps or limited-interval schedules. We analyze CFG through an asymptotic-preserving, numerical-analysis lens.
arXiv:2607. 24741v2 Announce Type: replace-cross Abstract: Positive two-marginal entropic optimal transport is solved by a nonlinear, positive, order-preserving, homogeneous Sinkhorn map.
By Xinyang Wen
The paper introduces the Latent Generative Solver (LGS), a neural PDE solver that combines a Physics VAE, a Pyramidal Flow-Forcing Transformer, and input noising to achieve generalization across twelve PDE families and stable long-term rollouts. LGS matches or surpasses deterministic baselines on one-step predictions, outperforms them on 5- and 10-step rollouts, and significantly reduces long-horizon error while cutting compute costs. It also adapts efficiently to unseen higher-resolution systems, demonstrating strong empirical performance on 2D regular-grid PDE simulations.
By Zituo Chen, Sili Deng
arXiv:2606. 01078v1 Announce Type: new Abstract: Transport MCMC trains a normalizing flow to precondition Metropolis--Hastings proposals, achieving high empirical efficiency on challenging posteriors; yet no prior work produces a numerically non-vacuous, rigorous spectral-gap bound for such samplers.
By Jun Hu
arXiv:2606. 03820v1 Announce Type: cross Abstract: We develop a quantitative approximation framework for diffusion distillation, viewing few-step sampling as error propagation under compositions of learned flow maps.
By Weiguo Gao, Ming Li, Lei Shi, Hanfei Zhou