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

• URL: http://arxiv.org/abs/2606.16257v1
• Date: Mon, 15 Jun 2026 06:01:05 GMT
• Title: Variance Reduction for Non-Log-Concave Sampling with Applications to Inverse Problems
• Abstract summary: We show that we can approximate gradients that exhibit high variance under a fixed-reduction iteration.<n>We extend our theory to solve inverse priors problems in twodimensional imaging.
• Score: 7.041502953437834
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 Poincaré 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.

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