# Variance Reduction for Non-Log-Concave Sampling with Applications to Inverse Problems

arXiv: https://arxiv.org/abs/2606.16257 · HTML: https://mlsanity.com/paper/2606.16257/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 67 references that are in the map.
- First posted on arXiv 15 Jun 2026.

## Builds on (most cited first, 3 of 3)

- [fastMRI: An Open Dataset and Benchmarks for Accelerated MRI](https://mlsanity.com/paper/1811.08839/) (2018)
- [A Fast Stochastic Plug-and-Play ADMM for Imaging Inverse Problems](https://mlsanity.com/paper/2006.11630/) (2020)
- [Zeroth-Order Non-Log-Concave Sampling with Variance Reduction and Applications to Inverse Problems](https://mlsanity.com/paper/2605.30573/) (2026)

## Abstract (arXiv)

Sampling from high-dimensional, non-log-concave distributions with unnormalized densities is a fundamental challenge in machine learning, particularly when the exact gradient of the potential is unavailable and must be approximated via stochastic gradients that exhibit high variance under a fixed budget of gradient computations per iteration. Although variance reduction techniques such as SGD with momentum, STORM, and PAGE have demonstrated improved convergence properties in non-convex optimization, their implications for sampling from non-log-concave distributions remain largely unexplored. In this work, we develop the first unified analysis of these estimators for sampling from non-log-concave distributions. We establish improved non-asymptotic convergence rates in varepsilon-relative Fisher information and, under a Poincar'e inequality assumption, in squared total variation distance, and further prove weak convergence to the target distribution. We extend our analysis to solving inverse problems with score-based generative priors. We empirically validate our theory and demonstrate that, under a fixed gradient computations per iteration, variance-reduction techniques consistently improve sample quality in two standard imaging applications.