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Sampling, Diffusions, and Stochastic Localization

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arxiv 2305.10690 v2 pith:OIIBZ4K7 submitted 2023-05-18 cs.LG

Sampling, Diffusions, and Stochastic Localization

classification cs.LG
keywords localizationstochasticdiffusionssamplealgorithmicconstructiondiffusiondistribution
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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Diffusions are a successful technique to sample from high-dimensional distributions. The target distribution can be either explicitly given or learnt from a collection of samples. They implement a diffusion process whose endpoint is a sample from the target distribution. The drift of the diffusion process is typically represented as a neural network. Stochastic localization is a successful technique to prove mixing of Markov Chains and other functional inequalities in high dimension. An algorithmic version of stochastic localization was recently proposed in order to sample from certain statistical mechanics models. This expository article has three objectives: $(i)$~Generalize the algorithmic construction to other stochastic localization processes. This construction is both simple and broadly applicable; $(ii)$~Clarify the connection between diffusions and stochastic localization. This allows to derive several known sampling schemes in a unified fashion; $(iii)$~Describe the insights that follow from this unified viewpoint.

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Cited by 9 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

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