# Global Convergence of Sampling-Based Nonconvex Optimization through Diffusion-Style Smoothing

arXiv: https://arxiv.org/abs/2605.16520 · HTML: https://mlsanity.com/paper/2605.16520/

## 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 20 of its 66 references that are in the map.
- First posted on arXiv 15 May 2026.

## Placed in

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

## Builds on (most cited first, 20 of 20)

- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Models](https://mlsanity.com/paper/1805.12114/) (2018)
- [Analyzing and Improving the Training Dynamics of Diffusion Models](https://mlsanity.com/paper/2312.02696/) (2023)
- [Entropy-SGD: Biasing Gradient Descent Into Wide Valleys](https://mlsanity.com/paper/1611.01838/) (2016)
- [Simplifying, Stabilizing and Scaling Continuous-Time Consistency Models](https://mlsanity.com/paper/2410.11081/) (2024)
- [Optimal rates for zero-order convex optimization: the power of two function evaluations](https://mlsanity.com/paper/1312.2139/) (2013)
- [Non-convex Optimization for Machine Learning](https://mlsanity.com/paper/1712.07897/) (2017)
- [Zeroth-Order Stochastic Variance Reduction for Nonconvex Optimization](https://mlsanity.com/paper/1805.10367/) (2018)
- [Information Theoretic Model Predictive Control: Theory and Applications to Autonomous Driving](https://mlsanity.com/paper/1707.02342/) (2017)
- [Stochastic Zeroth-order Optimization in High Dimensions](https://mlsanity.com/paper/1710.10551/) (2017)
- [Zeroth-order Nonconvex Stochastic Optimization: Handling Constraints, High-Dimensionality and Saddle-Points](https://mlsanity.com/paper/1809.06474/) (2018)
- [Model-Based Diffusion for Trajectory Optimization](https://mlsanity.com/paper/2407.01573/) (2024)
- [Full-Order Sampling-Based MPC for Torque-Level Locomotion Control via Diffusion-Style Annealing](https://mlsanity.com/paper/2409.15610/) (2024)
- [Understanding and Mitigating Memorization in Generative Models via Sharpness of Probability Landscapes](https://mlsanity.com/paper/2412.04140/) (2024)
- [Learning to Solve Hard Minimal Problems](https://mlsanity.com/paper/2112.03424/) (2021)
- [DROP: Dexterous Reorientation via Online Planning](https://mlsanity.com/paper/2409.14562/) (2024)
- [Escaping the Local Minima via Simulated Annealing: Optimization of Approximately Convex Functions](https://mlsanity.com/paper/1501.07242/) (2015)
- [Towards Tight Convex Relaxations for Contact-Rich Manipulation](https://mlsanity.com/paper/2402.10312/) (2024)
- [Combining Homotopy Methods and Numerical Optimal Control to Solve Motion Planning Problems](https://mlsanity.com/paper/1703.07546/) (2017)
- [A Cross Entropy based Optimization Algorithm with Global Convergence Guarantees](https://mlsanity.com/paper/1801.10291/) (2018)

## Abstract (arXiv)

Sampling-based optimization (SBO), like cross-entropy method and evolutionary algorithms, has achieved many successes in solving non-convex problems without gradients, yet its convergence is poorly understood. In this paper, we establish a non-asymptotic convergence analysis for SBO through the lens of smoothing. Specifically, we recast SBO as gradient descent on a smoothed objective, mirroring noise-conditioned score ascent in diffusion models. Our first contribution is a landscape analysis of the smoothed objective, demonstrating how smoothing helps escape local minima and uncovering a fundamental coverage-optimality trade-off: smoothing renders the landscape more benign by enlarging the locally convex region around the global minimizer, but at the cost of introducing an optimality gap. Building on this insight, we establish non-asymptotic convergence guarantees for SBO algorithms to a neighborhood of the global minimizer. Furthermore, we propose an annealed SBO algorithm, Diffusion-Inspired Dual-Annealing (DIDA), which is provably convergent to the global optimum. We conduct extensive numerical experiments to verify our landscape results and also demonstrate the compelling performance of DIDA compared to other gradient-free optimization methods. Lastly, we discuss implications of our results for diffusion models.