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Subpolynomial-Query Proximal Sampling Beyond Log-Concavity

We study the gradient query complexity of sampling from a density $\pi(x)\propto\mathrm{e}^{-V(x)}$ on $\mathbb{R}^d$, where $V$ has a $\beta$-Lipschitz gradient but need not be convex. Our approach uses the proximal sampler, which alternates Gaussian perturbation with sampling a position conditional on the noisy obser...