# Learning to Sample Better

arXiv: https://arxiv.org/abs/2310.11232 · HTML: https://mlsanity.com/paper/2310.11232/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 35 references that are in the map.
- First posted on arXiv 17 Oct 2023.

## Builds on (most cited first, 15 of 15)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Flow-based generative models for Markov chain Monte Carlo in lattice field theory](https://mlsanity.com/paper/1904.12072/) (2019)
- [Equivariant flow-based sampling for lattice gauge theory](https://mlsanity.com/paper/2003.06413/) (2020)
- [Flow-based sampling for multimodal and extended-mode distributions in lattice field theory](https://mlsanity.com/paper/2107.00734/) (2021)
- [Local-Global MCMC kernels: the best of both worlds](https://mlsanity.com/paper/2111.02702/) (2021)

## Built on by (most cited first, 4 of 4)

- [Markovian Flow Matching: Accelerating MCMC with Continuous Normalizing Flows](https://mlsanity.com/paper/2405.14392/) (2024)
- [On The Hidden Biases of Flow Matching Samplers](https://mlsanity.com/paper/2512.16768/) (2025)
- [Flow Map Learning via Nongradient Vector Flow](https://mlsanity.com/paper/2607.26398/) (2026)
- [FluxLite: Inference-Time Proposal Control for Discrete Diffusion Models](https://mlsanity.com/paper/2609.35947/) (2026)

## Abstract (arXiv)

These lecture notes provide an introduction to recent advances in generative modeling methods based on the dynamical transportation of measures, by means of which samples from a simple base measure are mapped to samples from a target measure of interest. Special emphasis is put on the applications of these methods to Monte-Carlo (MC) sampling techniques, such as importance sampling and Markov Chain Monte-Carlo (MCMC) schemes. In this context, it is shown how the maps can be learned variationally using data generated by MC sampling, and how they can in turn be used to improve such sampling in a positive feedback loop.