Entropy Can Flow, or It Can Guide. Be Entropy. LEDFlow: Introducing Entropy-guided Generation Order into Uniform Discrete Flow

Tung Sum Thomas Kwok, Yidong Ouyang, Yingjia Wan, Ying Nian Wu, Zhijiang Guo +1

Uniform discrete flow permits repeated updates at every generation position. While continued revision supports correction of wrong tokens, it also exposes correct intermediate predictions to later errors. An experiment on Sudoku puzzles shows that 9.4% of generated cells are correct at an intermediate step but incorrect in the final output. We introduce generation order into uniform discrete flow through selective absorption, which fixes chosen predictions while preserving the uniform flow velocity at active positions. To prioritize reliable predictions for absorption, we propose Low-Entropy Discrete Flow (LEDFlow), a training-free sampler that adaptively orders absorption by local entropy. By decomposing absorption error into joint dependence and conditional prediction terms, we show that, under entropy-error regularity, selecting the lowest-entropy positions under a fixed absorption count minimizes an upper bound on the conditional term. We further analyze sensitivity of global lookahead, whose worst-case decision-error bound grows with lookahead window under an imperfect denoiser. Across reasoning benchmarks, LEDFlow attains 0.845 Nikoli Sudoku solve accuracy, with largest…