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

arXiv: https://arxiv.org/abs/2212.03325 · HTML: https://mlsanity.com/paper/2212.03325/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 11 references that are in the map.
- First posted on arXiv 6 Dec 2022.

## Builds on (most cited first, 9 of 9)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [Score-Based Generative Modeling with Critically-Damped Langevin Diffusion](https://mlsanity.com/paper/2112.07068/) (2021)
- [Convergence for score-based generative modeling with polynomial complexity](https://mlsanity.com/paper/2206.06227/) (2022)
- [Score-Based Diffusion meets Annealed Importance Sampling](https://mlsanity.com/paper/2208.07698/) (2022)
- [Stein Point Markov Chain Monte Carlo](https://mlsanity.com/paper/1905.03673/) (2019)
- [Simulated Tempering Langevin Monte Carlo II: An Improved Proof using Soft Markov Chain Decomposition](https://mlsanity.com/paper/1812.00793/) (2018)

## Built on by (most cited first, 3 of 3)

- [Particle Denoising Diffusion Sampler](https://mlsanity.com/paper/2402.06320/) (2024)
- [Inflationary Flows: Calibrated Bayesian Inference with Diffusion-Based Models](https://mlsanity.com/paper/2407.08843/) (2024)
- [Value Gradient Sampler: Learning Invariant Value Functions for Equivariant Diffusion Sampling](https://mlsanity.com/paper/2502.13280/) (2025)

## Abstract (arXiv)

Score based approaches to sampling have shown much success as a generative algorithm to produce new samples from a target density given a pool of initial samples. In this work, we consider if we have no initial samples from the target density, but rather 0th and 1st order oracle access to the log likelihood. Such problems may arise in Bayesian posterior sampling, or in approximate minimization of non-convex functions. Using this knowledge alone, we propose a Monte Carlo method to estimate the score empirically as a particular expectation of a random variable. Using this estimator, we can then run a discrete version of the backward flow SDE to produce samples from the target density. This approach has the benefit of not relying on a pool of initial samples from the target density, and it does not rely on a neural network or other black box model to estimate the score.