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

Summary

A new arXiv paper observes that while uniform discrete flow allows repeated updates at every generation position, that same continued revision can overwrite correct intermediate predictions. A Sudoku experiment found 9.4% of generated cells were correct mid-trajectory but wrong in the final output. The authors propose LEDFlow, a training-free sampler that introduces generation order via selective absorption, fixing chosen predictions while preserving uniform-flow velocity at still-active positions, and ordering absorption by local entropy. LEDFlow reaches 0.845 Nikoli Sudoku solve accuracy and improves text-to-image and multimodal understanding results at inference cost comparable to standard flow sampling.

SourcearXiv Machine LearningAuthor: Tung Sum Thomas Kwok, Yidong Ouyang, Yingjia Wan, Ying Nian Wu, Zhijiang Guo, Oscar Leong
Entropy Can Flow, or It Can Guide. Be Entropy. LEDFlow: Introducing Entropy-guided Generation Order into Uniform Discrete Flow
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[Submitted on 20 Sep 2026]

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

View a PDF of the paper titled Entropy Can Flow, or It Can Guide. Be Entropy. LEDFlow: Introducing Entropy-guided Generation Order into Uniform Discrete Flow, by Tung Sum Thomas Kwok and Yidong Ouyang and Yingjia Wan and Ying Nian Wu and Zhijiang Guo and Oscar Leong

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Abstract: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 prevent absorbing incorrect predictions, 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 selecting the lowest-entropy positions under a fixed absorption budget minimizes an upper bound on the conditional term. We further support the choice of local entropy by showing that the decision-error bound of global lookahead grows with the lookahead window under an imperfect denoiser. Across reasoning benchmarks, LEDFlow attains 0.845 Nikoli Sudoku solve accuracy, with the largest gains on strongly constrained tasks. On text-to-image generation it attains the best overall score, and on multimodal understanding it improves over the native sampler on all six benchmarks, at an inference cost comparable to standard flow sampling.

Subjects:

Machine Learning (cs.LG)

Cite as: arXiv:2609.25131 [cs.LG]

(or arXiv:2609.25131v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.25131

arXiv-issued DOI via DataCite

Submission history

From: Tung Sum Thomas Kwok [view email] [v1] Sun, 20 Sep 2026 19:34:30 UTC (825 KB)

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Key points and analysis

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Key points

  • A Sudoku experiment shows 9.4% of generated cells are correct at an intermediate step but incorrect in the final output.
  • LEDFlow introduces generation order through selective absorption, fixing chosen predictions while preserving uniform-flow velocity at active positions.
  • Decomposing absorption error into joint dependence and conditional prediction terms shows that, under a fixed absorption budget, absorbing the lowest-entropy positions minimizes an upper bound on the conditional term.
  • The method attains 0.845 Nikoli Sudoku accuracy, the best overall text-to-image score, and gains on all six multimodal understanding benchmarks at comparable inference cost.

Highlights and analysis are generated automatically and may contain errors. Check the original source.

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