Diffusion models on manifold-supported data admit score decompositions whose statistical rates are controlled by intrinsic dimension and curvature.
Score-based diffusion models via stochastic differential equations– a technical tutorial.arXiv preprint arXiv:2402.07487
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Diffusion, score-based, and flow matching models are unified as instances of learning time-dependent vector fields inducing marginal distributions governed by continuity and Fokker-Planck equations.
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Diffusion Model for Manifold Data: Score Decomposition, Curvature, and Statistical Complexity
Diffusion models on manifold-supported data admit score decompositions whose statistical rates are controlled by intrinsic dimension and curvature.
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A Unified Measure-Theoretic View of Diffusion, Score-Based, and Flow Matching Generative Models
Diffusion, score-based, and flow matching models are unified as instances of learning time-dependent vector fields inducing marginal distributions governed by continuity and Fokker-Planck equations.