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Score based approaches to sampling have shown much success as a generativealgorithm to produce new samples from a target density given a pool of initialsamples. In this work, we consider if we have no initial samples from thetarget density, but rather $0^{th}$ and $1^{st}$ order oracle access to the loglikelihood. Such problems may arise in Bayesian posterior sampling, or inapproximate minimization of non-convex functions. Using this knowledge alone,we propose a Monte Carlo method to estimate the score empirically as aparticular expectation of a random variable. Using this estimator, we can thenrun a discrete version of the backward flow SDE to produce samples from thetarget density. This approach has the benefit of not relying on a pool ofinitial samples from the target density, and it does not rely on a neuralnetwork or other black box model to estimate the score.

Proposal of a Score Based Approach to Sampling Using Monte Carlo Estimation of Score and Oracle Access to Target Density