Discretized Föllmer processes supply hyper-parameter settings for DDPM samplers that recover state-of-the-art sampling error bounds with slight improvements.
Central limit theorem for high temperature spin models via martingale embedding
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abstract
We use martingale embeddings to prove a central limit theorem (CLT) for one-dimensional projections of high-dimensional random vectors in $\{-1,1\}^n$ satisfying a Poincar\'e inequality. We obtain a non-asymptotic error bound involving two-point and three-point functions for the CLT in 2-Wasserstein distance. We present three illustrative applications: Ising model with finite-range interactions, ferromagnetic Ising model under the Dobrushin condition, and the Sherrington-Kirkpatrick spin glass model at sufficiently high temperature. In all the examples, we allow heterogeneous external fields.
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A note on connections between the F\"ollmer process and the denoising diffusion probabilistic model
Discretized Föllmer processes supply hyper-parameter settings for DDPM samplers that recover state-of-the-art sampling error bounds with slight improvements.