(1D) Ordered Tokens Enable Efficient Test-Time Search

Tokenization is a key component of autoregressive generative models, converting raw data into more manageable units for modeling. Commonly, tokens describe local information, such as regions of pixels in images or word pieces in text, and autoregressive generation commonly predicts these tokens in a fixed order. A worthwhile question is whether token structures affect the ability to steer the generation through test-time search, where multiple candidate generations are explored and evaluated by a verifier. Using image generation as our testbed, we hypothesize that recent 1D ordered tokenizers with coarse-to-fine structure can be more amenable to search than classical 2D grid structures. This is rooted in the fact that the intermediate states in coarse-to-fine sequences carry semantic meaning that verifiers can reliably evaluate, enabling effective steering during generation. We find that autoregressive models trained on coarse-to-fine ordered tokens exhibit improved test-time scaling behavior compared to grid-based counterparts. Moreover, we demonstrate that, thanks to the ordered structure, pure test-time search over token sequences (i.e., without training an autoregressive model) can perform training-free text-to-image generation when guided by an image-text verifier. Beyond this, we also systematically study how classical search algorithms (best-of-N, beam search, lookahead search) interact with different token structures, as well as the role of different verifiers and autoregressive priors in guiding the generation.