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Generative Diffusion From An Action Principle
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Generative diffusion models synthesize new samples by reversing a diffusive process that converts a given data set to generic noise. This is accomplished by training a neural network to match the gradient of the log of the probability distribution of a given data set, also called the score. By casting reverse diffusion as an optimal control problem, we show that score matching can be derived from an action principle, like the ones commonly used in physics. We use this insight to demonstrate the connection between different classes of diffusion models.
Forward citations
Cited by 2 Pith papers
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The Quantum Mechanics of Rare Events: From Quantum Walks to Stochastic Inflation
Rare fluctuations in quantum walks are ruled by a measurement-induced relative entropy, and applying this to stochastic inflation yields a steady state that violates detailed balance.
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A Unified Kullback--Leibler Divergence Analysis of Generative Diffusion Models via Entropy Production Rate
Diffusion model generation error is decomposed through an entropy-production-rate identity that claims O(h²) Euler–Maruyama KL bounds and unifies score SDE, PF-ODE, flow matching, and stochastic interpolant analyses.
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