# Global Optimization By Gradient From Hierarchical Score-Matching Spaces

arXiv: https://arxiv.org/abs/2601.11639 · HTML: https://mlsanity.com/paper/2601.11639/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- First posted on arXiv 14 Jan 2026.

## Abstract (arXiv)

Gradient-based methods are widely used to solve various optimization problems, however, they are either constrained by local optima dilemmas, simple convex constraints, and continuous differentiability requirements, or limited to low-dimensional simple problems. This work solve these limitations and restrictions by unifying all optimization problems with various complex constraints as a general hierarchical optimization objective without constraints, which is optimized by gradient obtained through score matching. The proposed method is verified through simple-constructed and complex-practical experiments. Even more importantly, it reveals the profound connection between global optimization and diffusion based generative modeling.