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}). Its local increments directly control Kullback–Leibler (KL) discretization error, yielding a unified analysis of Bernoulli-subset and fixed-cardinality unmasking schemes. In log-reveal-odds coordinates, this structure yields optimized single-block and multi-block schedules, and quantifies the gains from adapting computational effort to data geometry. Crucially, we show how {textsf{UGC}xspace} increments can be estimated from samples via KL increments along coupled reveal trajectories. This leads to emph{certified-optimal} samplers that achieve a prescribed KL error with high probability and iteration complexity within a constant factor of the corresponding oracle procedure. Collapsing the ugc path yields the aggregate {textsf{UGC}xspace} mass, which connects to classical multivariate dependence measures and complexity measures from previous analyses of discrete diffusion. In the fine-partition limit, the squared integral of the square-root {textsf{UGC}xspace} density determines the sharp leading-order optimal Euler discretization error. Examples exhibit substantial dimension-dependent gains over coarse schedules, including $widetilde{Omega}(sqrt{d})$ improvements achievable with a constant number of adaptively placed blocks.