🤖 AI Summary
研究通过分析和优化tau-leaping方法中的调度策略，减少因子化误差，提高masked离散扩散模型的采样效率。
📝 Abstract
Masked discrete diffusion models are commonly accelerated using the so-called tau-leaping discretization method, which reveals several coordinates in parallel at each sampling step. The sampler replaces the joint conditional law of each revealed block by a product distribution, incurring a factorization error $\varepsilon_\text{fact}$ present even with perfectly learned predictors. We analyze the standard sampler on $N$ coordinates with $K$ sampling steps, whose random block sizes depend on a denoising schedule. Our analysis uses an exact integral representation of $\varepsilon_\text{fact}$ in terms of a distribution-dependent dependence density $ρ$, which records how conditional dependence evolves as the revealed fraction of coordinates grows. We develop estimators for this profile and quantify how estimation errors affect schedule selection. We derive recursive stationarity equations for the finite-$K$ optimization problem and, under a monotonicity condition, characterize its unique optimizer. In the joint limit $N,K\to\infty$, we obtain an explicit characterization of the optimal limiting smooth schedule and quantify the cost of random block sizes relative to a deterministic planner. When $ρ_N$ converges uniformly to a strictly positive continuous profile, optimizing over fixed smooth schedules can improve the leading constant but not the $N/K$ scaling of $\varepsilon_\text{fact}$. By contrast, if $ρ_N$ degenerates, suitable schedules can improve the asymptotic order relative to the uniform schedule. Examples based on stationary processes and exchangeable mixtures illustrate these two regimes.