Diffusion posterior samplers produce biased outputs that can be expressed as an Ornstein-Uhlenbeck path expectation via a surrogate Gaussian path and Feynman-Kac representation, with STSL flattening the spatially varying bias term.
arXiv preprint arXiv:2602.04404 , year=
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Pattern formation in trained diffusion models emerges from out-of-equilibrium phase transitions driven by instabilities in low-frequency denoising modes linked to data symmetries and architectural constraints.
Discrete diffusion models on Ising-like data exhibit analytically predictable speciation and collapse transitions in backward dynamics via high-temperature expansion and Random Energy Model condensation, with scaling matching continuous cases when noise varies with time.
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Diffusion-Based Posterior Sampling: A Feynman-Kac Analysis of Bias and Stability
Diffusion posterior samplers produce biased outputs that can be expressed as an Ornstein-Uhlenbeck path expectation via a surrogate Gaussian path and Feynman-Kac representation, with STSL flattening the spatially varying bias term.
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How Out-of-Equilibrium Phase Transitions can Seed Pattern Formation in Trained Diffusion Models
Pattern formation in trained diffusion models emerges from out-of-equilibrium phase transitions driven by instabilities in low-frequency denoising modes linked to data symmetries and architectural constraints.
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Dynamical Regimes of Discrete Diffusion Models
Discrete diffusion models on Ising-like data exhibit analytically predictable speciation and collapse transitions in backward dynamics via high-temperature expansion and Random Energy Model condensation, with scaling matching continuous cases when noise varies with time.