掩码离散扩散中 tau-leaping 的调度优化

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Abstract:Masked diffusions are popular generative models for discrete distributions. Unlike standard autoregressive sampling, they reveal several coordinates in parallel, approximating each block's joint conditional law by a product of one-coordinate conditionals. The resulting procedure, usually called tau-leaping, reduces computational cost but introduces a factorization error ($\varepsilon_\text{fact}$), even with perfectly learned predictors. We study the resulting tradeoff between generative accuracy and computational cost, focusing on how to choose a denoising schedule to minimize $\varepsilon_\text{fact}$ for a fixed sampling budget. To do so, we establish an exact integral representation of $\varepsilon_\text{fact}$ separating the schedule from the target's dependence structure, summarized by a dependence density $\rho$. This representation yields recursive stationarity equations for optimal schedules and allows us to quantify how estimation errors in $\rho$ affect schedule selection. As the dimension $N$ and sampling budget grow, we characterize the optimal schedule and quantify the cost of random block sizes relative to a deterministic planner. We highlight a fundamental dichotomy: if $\rho$ converges uniformly to a strictly positive continuous profile as $N\to\infty$, schedule optimization can only improve the leading constant of $\varepsilon_\text{fact}$, while if $\rho$ degenerates, schedule optimization can improve the asymptotic order. Examples based on stationary processes and exchangeable mixtures illustrate these regimes.

Subjects:	Statistics Theory (math.ST); Machine Learning (cs.LG); Machine Learning (stat.ML)
Cite as:	arXiv:2609.21960 [math.ST]
	(or arXiv:2609.21960v2 [math.ST] for this version)
	https://doi.org/10.48550/arXiv.2609.21960 arXiv-issued DOI via DataCite

Submission history

From: Cecilia Secchi [view email]
[v1] Fri, 18 Sep 2026 16:18:26 UTC (817 KB)
[v2] Mon, 5 Oct 2026 19:58:19 UTC (821 KB)