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. 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.
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.
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.
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: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.
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.
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.
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.
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.
arXiv:2607. 05381v1 Announce Type: cross Abstract: What does a discrete diffusion model learn: a denoiser, a score ratio, or a bridge plug-in predictor?
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.
arXiv:2606. 16620v1 Announce Type: cross Abstract: Inference-time scaling has become the dominant lever for improving language-model reasoning, but existing methods derive rollout diversity from a single source: stochastic token-level sampling.