# Total Variation Guarantees for Sampling with Stochastic Localization

arXiv: https://arxiv.org/abs/2603.29555 · HTML: https://mlsanity.com/paper/2603.29555/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 28 of its 53 references that are in the map.
- First posted on arXiv 31 Mar 2026.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 28 of 28)

- [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)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions](https://mlsanity.com/paper/2209.11215/) (2022)
- [Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localization](https://mlsanity.com/paper/2308.03686/) (2023)
- [Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptions](https://mlsanity.com/paper/2211.01916/) (2022)
- [Convergence of score-based generative modeling for general data distributions](https://mlsanity.com/paper/2209.12381/) (2022)
- [Convergence for score-based generative modeling with polynomial complexity](https://mlsanity.com/paper/2206.06227/) (2022)
- [Stochastic Normalizing Flows](https://mlsanity.com/paper/2002.06707/) (2020)
- [Denoising Diffusion Samplers](https://mlsanity.com/paper/2302.13834/) (2023)
- [An optimal control perspective on diffusion-based generative modeling](https://mlsanity.com/paper/2211.01364/) (2022)
- [User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradient](https://mlsanity.com/paper/1710.00095/) (2017)
- [Improved sampling via learned diffusions](https://mlsanity.com/paper/2307.01198/) (2023)
- [KL Convergence Guarantees for Score diffusion models under minimal data assumptions](https://mlsanity.com/paper/2308.12240/) (2023)
- [Beyond ELBOs: A Large-Scale Evaluation of Variational Methods for Sampling](https://mlsanity.com/paper/2406.07423/) (2024)
- [Score-Based Diffusion meets Annealed Importance Sampling](https://mlsanity.com/paper/2208.07698/) (2022)
- [Sampling from the Sherrington-Kirkpatrick Gibbs measure via algorithmic stochastic localization](https://mlsanity.com/paper/2203.05093/) (2022)
- [Metropolis-Hastings Generative Adversarial Networks](https://mlsanity.com/paper/1811.11357/) (2018)
- [Reverse Diffusion Monte Carlo](https://mlsanity.com/paper/2307.02037/) (2023)
- [Variational Refinement for Importance Sampling Using the Forward Kullback-Leibler Divergence](https://mlsanity.com/paper/2106.15980/) (2021)
- [Stochastic Localization via Iterative Posterior Sampling](https://mlsanity.com/paper/2402.10758/) (2024)
- [Zeroth-Order Sampling Methods for Non-Log-Concave Distributions: Alleviating Metastability by Denoising Diffusion](https://mlsanity.com/paper/2402.17886/) (2024)
- [A theoretical perspective on mode collapse in variational inference](https://mlsanity.com/paper/2410.13300/) (2024)
- [Improving the evaluation of samplers on multi-modal targets](https://mlsanity.com/paper/2504.08916/) (2025)
- [Balanced Training of Energy-Based Models with Adaptive Flow Sampling](https://mlsanity.com/paper/2306.00684/) (2023)
- [Joint stochastic localization and applications](https://mlsanity.com/paper/2505.13410/) (2025)
- [Diffusion approximations and control variates for MCMC](https://mlsanity.com/paper/1808.01665/) (2018)

## Abstract (arXiv)

Motivated by the success of score-based generative models, a number of diffusion-based algorithms have recently been proposed for the problem of sampling from a probability measure whose unnormalized density can be accessed. Among them, Grenioux et al. introduced SLIPS, a sampling algorithm based on Stochastic Localization. While SLIPS exhibits strong empirical performance, no rigorous convergence analysis has previously been provided. In this work, we close this gap by establishing the first guarantee for SLIPS in total variation distance. Under minimal assumptions on the target, our bound implies that the number of steps required to achieve an varepsilon-guarantee scales linearly with the dimension, up to logarithmic factors. The analysis leverages techniques from the theory of score-based generative models and further provides theoretical insights into the empirically observed optimal choice of discretization points.