Small-time score-mixed diffusion dynamics are governed by the geometric potential Φ_λ = λ d1² + (1-λ) d2², reducing the problem to Clarke subgradient inclusions with convergence guarantees in the Dirac-mixture case.
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A PDE framework using Li-Yau inequalities proves well-posedness and sharp stability for score-based Fokker-Planck dynamics, with reverse-time trajectories concentrating on compactly supported data manifolds at rate sqrt(t).
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Geometric Asymptotics of Score Mixing and Guidance in Diffusion Models
Small-time score-mixed diffusion dynamics are governed by the geometric potential Φ_λ = λ d1² + (1-λ) d2², reducing the problem to Clarke subgradient inclusions with convergence guarantees in the Dirac-mixture case.
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A PDE Perspective on Generative Diffusion Models
A PDE framework using Li-Yau inequalities proves well-posedness and sharp stability for score-based Fokker-Planck dynamics, with reverse-time trajectories concentrating on compactly supported data manifolds at rate sqrt(t).