The paper establishes the first polynomial lower bounds on the number of parallel rounds required for diffusion sampling with approximate scores. It proves a “~Ω(d^{1/3})” lower bound for sampling smooth, near‑isotropic Gaussian mixtures in ℝ^d, and an Ω(d) lower bound for uniform sampling from anisotropic axis‑aligned boxes inside the unit ball. These bounds apply to any randomized algorithm that can make polynomially many queries per round at arbitrary locations and noise levels, while maintaining inverse‑polynomial score error and constant total variation accuracy.
arXiv:2604.10857v2 Announce Type: replace-cross Abstract: Diffusion models generate samples by iteratively querying learned score estimates. A rapidly growing literature focuses on accelerating sampl...
arXiv:2512. 24152v2 Announce Type: replace-cross Abstract: Sampling based on score diffusions has led to striking empirical results, and has attracted considerable attention from various research communities.
arXiv:2602. 15008v2 Announce Type: replace Abstract: Diffusion models over discrete spaces have recently shown striking empirical success, yet their theoretical foundations remain incomplete.
arXiv:2004. 05813v3 Announce Type: replace-cross Abstract: Suppose that we are given independent, identically distributed random samples $x_1,\cdots,x_n$ from a mixture at most $k$ many $d$-dimensional spherical Gaussian distributions $\mu_1,\cdots,\mu_{k_0}$ of identical and known variance $\sigma^2$ in each coordinate, such that the minimum $\ell^2$ distance between two distinct centers $y_l$ and $y_j$ is greater than $2\Delta\sigma \min\{\sqrt{d},\sqrt k\}$, where $\Delta>C_0$, and $C_0$ is a sufficiently large universal constant.
arXiv:2610.19925v1 Announce Type: cross Abstract: Efficient global optimization aims to identify a global optimum of an expensive black-box function within a limited evaluation budget $N$. We investi...
The paper introduces random walks on graphs as a controllable sandbox for studying parallel sampling strategies in masked diffusion models (MDMs). It shows that common parallel unmasking methods, such as lowest‑entropy scoring, are not universally superior to random sampling and that performance depends on the graph’s conditional dependence structure. The authors also propose training‑free bisection samplers that are provably exact for random walks and demonstrate their effectiveness on both graph‑walk tasks and pretrained MDMs for language generation and reasoning benchmarks.
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:2607.06644v2 Announce Type: replace Abstract: Determinantal point processes (DPPs) have recently emerged as a kernel-based alternative to standard independent sampling for constructing efficien...
arXiv:2607. 00773v1 Announce Type: new Abstract: Discrete diffusion models are widely used for learning and generating discrete distributions.
The paper investigates how many spectral directions a truncated diffusion sampler must retain when data exhibit power‑law covariance spectra. For Gaussian data compared to a smoothed target, it establishes matching upper and lower bounds on the necessary number of retained directions, assuming a sufficiently large ambient dimension. The analysis shows that truncation error depends on the combined Wiener gains of omitted directions, meaning that even weak individual directions can collectively contribute significant error, and it provides practical guidelines for selecting the retained subspace and diffusion noise level.
arXiv:2608. 13520v1 Announce Type: cross Abstract: We study masking diffusion for discrete sampling and introduce a path-resolved measure of data geometry called the \emph{unmasking growth complexity} ({\textsf{UGC}\xspace}).
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.