SSA and DA extract barrier-sensitive mode separation from the autocovariance matrix of a unique constant-coefficient diffusion with the given density as stationary distribution.
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A plug-in estimator for tilted distributions is minimax-optimal, with Wasserstein closeness bounds to the true tilted distribution and TV-accuracy guarantees when running diffusion on the estimated samples.
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Measuring and Decomposing Mode Separation via the Canonical Diffusion
SSA and DA extract barrier-sensitive mode separation from the autocovariance matrix of a unique constant-coefficient diffusion with the given density as stationary distribution.
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Generating DDPM-based Samples from Tilted Distributions
A plug-in estimator for tilted distributions is minimax-optimal, with Wasserstein closeness bounds to the true tilted distribution and TV-accuracy guarantees when running diffusion on the estimated samples.