Search papers, labs, and topics across Lattice.
This paper unifies diffusion and autoregressive models as paths on a corruption lattice, defining schedule cost by discarded parallel step dependencies. The minimum steps for zero-cost schedules are dictated by data geometry, specifically the treedepth for Markovian data, offering a universal principle for discrete and continuous generation. Pairwise dependence estimated from pretrained weights predicts schedule rankings across text, image, and video generation tasks, validating the framework.
Decoding schedules for diffusion and autoregressive models can be ranked by a kernel of pairwise dependence estimated from pretrained weights, predicting performance across modalities before generation.
Diffusion and autoregression (AR) have long been seen as different categories of generative models, with diffusion specialising in continuous fields and AR specialising in discrete tokens. Recent work seeks to combine the advantages of the two models, and each hybrid fixes its decoding schedule by design. In this paper, we ask whether the performance of decoding schedules of one model can be predicted before decoding at a fixed number of steps. We describe diffusion, AR, and models in between as paths on one corruption lattice, and define the cost of a schedule as the dependence its parallel steps discard. The cost shows that the fewest steps of a zero-cost schedule are set by the geometry of the data, in the same way for tokens and for continuous fields. In particular, for data that are Markov on a graph and dependent along its paths, the fewest steps equal the graph's treedepth, which is logarithmic in the length of a sequence and linear in the side length of a grid. With fewer steps than the treedepth, every schedule pays a positive cost, whose ranking we predict before decoding with a kernel of pairwise dependence estimated from pretrained weights. Across text generation, image generation, and video generation, we verify most of the predictions about the rankings of different schedules under different metrics and benchmarks. This work therefore provides a design principle for decoding for future AR models, diffusion models, and anything in between. Our code is available at https://github.com/TSUITUENYUE/The-Lattice-of-Transition-Laws.
