Sampling, Diffusions, and Stochastic Localization

• URL: http://arxiv.org/abs/2305.10690v1
• Date: Thu, 18 May 2023 04:01:40 GMT
• Title: Sampling, Diffusions, and Stochastic Localization
• Authors: Andrea Montanari
• Abstract summary: Diffusions are a successful technique to sample from high-dimensional distributions. localization is a technique to prove mixing of Markov Chains and other functional inequalities in high dimension. An algorithmic version of localization was introduced in [EAMS2022] to obtain an algorithm that samples from certain statistical mechanics models.
• Score: 10.368585938419619
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Diffusions are a successful technique to sample from high-dimensional distributions 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 and whose drift 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 introduced in [EAMS2022], to obtain an algorithm that samples from certain statistical mechanics models. This notes have three objectives: (i) Generalize the construction [EAMS2022] to other stochastic localization processes; (ii) Clarify the connection between diffusions and stochastic localization. In particular we show that standard denoising diffusions are stochastic localizations but other examples that are naturally suggested by the proposed viewpoint; (iii) Describe some insights that follow from this viewpoint.

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