Proves global GD convergence on reverse Fisher divergence for GMM score matching to single-Gaussian targets from arbitrary init and to separated GMM targets under random init.
Learning mixtures of gaussians using diffu- sion models.arXiv preprint arXiv:2404.18869,
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Recasting diffusion noise schedule design as optimal control on Fisher information yields sufficient conditions for O(d/n) sampling error and parametric closed-form schedules that generalize exponential/sigmoid ones and improve empirical performance.
Coupled initial noises in diffusion models, with designed dependence but unchanged marginal Gaussians, improve generated image diversity on Stable Diffusion variants while preserving quality and alignment.
Generative models learn rules before memorizing data, creating an innovation window whose width depends on dataset size and rule complexity, observed in both diffusion and autoregressive architectures.
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Global Convergence of Gradient Descent for Score Matching in Gaussian Mixtures via Reverse Fisher Divergence
Proves global GD convergence on reverse Fisher divergence for GMM score matching to single-Gaussian targets from arbitrary init and to separated GMM targets under random init.
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Noise Schedule Design for Diffusion Models: An Optimal Control Perspective
Recasting diffusion noise schedule design as optimal control on Fisher information yields sufficient conditions for O(d/n) sampling error and parametric closed-form schedules that generalize exponential/sigmoid ones and improve empirical performance.
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Couple to Control: Joint Initial Noise Design in Diffusion Models
Coupled initial noises in diffusion models, with designed dependence but unchanged marginal Gaussians, improve generated image diversity on Stable Diffusion variants while preserving quality and alignment.
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The two clocks and the innovation window: When and how generative models learn rules
Generative models learn rules before memorizing data, creating an innovation window whose width depends on dataset size and rule complexity, observed in both diffusion and autoregressive architectures.
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