For Gaussian mixture targets, diffusion discretization error and step complexity are controlled by latent entropy rather than ambient dimension.
IEEE Transactions on Information Theory51(4), 1261–1282 (2005)
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Latent diffusability is quantified by decomposing the MMSE rate along diffusion trajectories into Fisher Information and Fisher Information Rate, with three geometric penalties (dimensional compression, tangential distortion, curvature injection) identified as sources of failure.
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When Diffusion Model Can Ignore Dimension: An Entropy-Based Theory
For Gaussian mixture targets, diffusion discretization error and step complexity are controlled by latent entropy rather than ambient dimension.
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Understanding Latent Diffusability via Fisher Geometry
Latent diffusability is quantified by decomposing the MMSE rate along diffusion trajectories into Fisher Information and Fisher Information Rate, with three geometric penalties (dimensional compression, tangential distortion, curvature injection) identified as sources of failure.