# Global Optimization via Schr"odinger-F"ollmer Diffusion

arXiv: https://arxiv.org/abs/2111.00402 · HTML: https://mlsanity.com/paper/2111.00402/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Oct 2021.

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

- [Noise-Free Sampling Algorithms via Regularized Wasserstein Proximals](https://mlsanity.com/paper/2308.14945/) (2023)
- [Path Integral Optimiser: Global Optimisation via Neural Schr"odinger-F"ollmer Diffusion](https://mlsanity.com/paper/2506.06815/) (2025)
- [Gradient-Free Score-Based Sampling Methods with Ensembles](https://mlsanity.com/paper/2401.17539/) (2024)
- [Connections between the F"ollmer process and the denoising diffusion probabilistic model](https://mlsanity.com/paper/2605.18040/) (2026)

## Abstract (arXiv)

We study the problem of finding global minimizers of V(x):ℝdrightarrowℝ approximately via sampling from a probability distribution μσ with density pσ(x)=dfracexp(-V(x)/σ)intmathbb Rd exp(-V(y)/σ) dy  with respect to the Lebesgue measure for σ ∈ (0,1] small enough. We analyze a sampler based on the Euler-Maruyama discretization of the Schr"odinger-F"ollmer diffusion processes with stochastic approximation under appropriate assumptions on the step size s and the potential V. We prove that the output of the proposed sampler is an approximate global minimizer of V(x) with high probability at cost of sampling O(d3) standard normal random variables. Numerical studies illustrate the effectiveness of the proposed method and its superiority to the Langevin method.