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Computer Science > Machine Learning

arXiv:2511.00124 (cs)
[Submitted on 31 Oct 2025]

Title:Cross-fluctuation phase transitions reveal sampling dynamics in diffusion models

Authors:Sai Niranjan Ramachandran, Manish Krishan Lal, Suvrit Sra
View a PDF of the paper titled Cross-fluctuation phase transitions reveal sampling dynamics in diffusion models, by Sai Niranjan Ramachandran and 1 other authors
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Abstract:We analyse how the sampling dynamics of distributions evolve in score-based diffusion models using cross-fluctuations, a centered-moment statistic from statistical physics. Specifically, we show that starting from an unbiased isotropic normal distribution, samples undergo sharp, discrete transitions, eventually forming distinct events of a desired distribution while progressively revealing finer structure. As this process is reversible, these transitions also occur in reverse, where intermediate states progressively merge, tracing a path back to the initial distribution. We demonstrate that these transitions can be detected as discontinuities in $n^{\text{th}}$-order cross-fluctuations. For variance-preserving SDEs, we derive a closed-form for these cross-fluctuations that is efficiently computable for the reverse trajectory. We find that detecting these transitions directly boosts sampling efficiency, accelerates class-conditional and rare-class generation, and improves two zero-shot tasks--image classification and style transfer--without expensive grid search or retraining. We also show that this viewpoint unifies classical coupling and mixing from finite Markov chains with continuous dynamics while extending to stochastic SDEs and non Markovian samplers. Our framework therefore bridges discrete Markov chain theory, phase analysis, and modern generative modeling.
Comments: Accepted at NeurIPS 2025. 10 pages, camera-ready version. appendices included
Subjects: Machine Learning (cs.LG); Statistical Mechanics (cond-mat.stat-mech); Artificial Intelligence (cs.AI)
Cite as: arXiv:2511.00124 [cs.LG]
  (or arXiv:2511.00124v1 [cs.LG] for this version)
  https://doi.org/10.48550/arXiv.2511.00124
arXiv-issued DOI via DataCite

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From: Sai Niranjan Ramachandran [view email]
[v1] Fri, 31 Oct 2025 09:40:59 UTC (7,311 KB)
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