The authors treat diffusion models, autoregressive (AR) models, and intermediate hybrids as trajectories on a shared corruption lattice, where each decoding schedule incurs a cost defined by the dependence discarded among its parallel steps. They show that the minimum number of steps required for a zero‑cost schedule is dictated by the geometry of the data: for data that form a Markov process on a graph and exhibit dependence along graph paths, this minimum equals the graph’s treedepth, which scales logarithmically with sequence length for tokens and linearly with the side length of spatial grids for images or videos. When a schedule uses fewer steps than the treedepth, it inevitably incurs a positive cost, yet the relative ranking of such costs across different schedules can be predicted a priori using a kernel of pairwise dependence derived from pretrained model weights. Empirical validation across text, image, and video generation benchmarks confirms that these predicted rankings align with observed performance under various metrics. Consequently, the work furnishes a principled method for selecting decoding schedules in future AR, diffusion, or hybrid generative models, and the accompanying code is released to facilitate adoption.