Cross-Fluctuation Phase Transitions Reveal Sampling Dynamics in Diffusion Models

MCML Authors

Sai Niranjan Ramachandran

→ Group Suvrit Sra
 Resource Aware Machine Learning

Manish Krishan Lal

Dr.

→ Group Suvrit Sra
 Resource Aware Machine Learning

Suvrit Sra

Prof. Dr.

Principal Investigator

Resource Aware Machine Learning

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 nth-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.

inproceedings RLS+25

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NeurIPS 2025

39th Conference on Neural Information Processing Systems. San Diego, CA, USA, Nov 30-Dec 07, 2025. To be published. Preprint available.

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Authors

S. N. Ramachandran • M. K. Lal • S. Sra

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Links

URL

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Research Area

 A2 | Mathematical Foundations