# Path Integral Optimiser: Global Optimisation via Neural Schr"odinger-F"ollmer Diffusion

arXiv: https://arxiv.org/abs/2506.06815 · HTML: https://mlsanity.com/paper/2506.06815/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 30 references that are in the map.
- First posted on arXiv 7 Jun 2025.

## Builds on (most cited first, 13 of 13)

- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [On the Expressive Power of Deep Neural Networks](https://mlsanity.com/paper/1606.05336/) (2016)
- [Path Integral Sampler: a stochastic control approach for sampling](https://mlsanity.com/paper/2111.15141/) (2021)
- [On the Convergence of Stochastic Gradient Descent with Adaptive Stepsizes](https://mlsanity.com/paper/1805.08114/) (2018)
- [Denoising Diffusion Samplers](https://mlsanity.com/paper/2302.13834/) (2023)
- [Adding Gradient Noise Improves Learning for Very Deep Networks](https://mlsanity.com/paper/1511.06807/) (2015)
- [Improving Generalization Performance by Switching from Adam to SGD](https://mlsanity.com/paper/1712.07628/) (2017)
- [On Empirical Comparisons of Optimizers for Deep Learning](https://mlsanity.com/paper/1910.05446/) (2019)
- [Theoretical guarantees for sampling and inference in generative models with latent diffusions](https://mlsanity.com/paper/1903.01608/) (2019)
- [Bayesian Learning via Neural Schr"odinger-F"ollmer Flows](https://mlsanity.com/paper/2111.10510/) (2021)
- [Convergence guarantees for RMSProp and ADAM in non-convex optimization and an empirical comparison to Nesterov acceleration](https://mlsanity.com/paper/1807.06766/) (2018)
- [A consensus-based global optimization method for high dimensional machine learning problems](https://mlsanity.com/paper/1909.09249/) (2019)
- [Global Optimization via Schr"odinger-F"ollmer Diffusion](https://mlsanity.com/paper/2111.00402/) (2021)

## Built on by (most cited first, 1 of 1)

- [Connections between the F"ollmer process and the denoising diffusion probabilistic model](https://mlsanity.com/paper/2605.18040/) (2026)

## Abstract (arXiv)

We present an early investigation into the use of neural diffusion processes for global optimisation, focusing on Zhang et al.'s Path Integral Sampler. One can use the Boltzmann distribution to formulate optimization as solving a Schr"odinger bridge sampling problem, then apply Girsanov's theorem with a simple (single-point) prior to frame it in stochastic control terms, and compute the solution's integral terms via a neural approximation (a Fourier MLP). We provide theoretical bounds for this optimiser, results on toy optimisation tasks, and a summary of the stochastic theory motivating the model. Ultimately, we found the optimiser to display promising per-step performance at optimisation tasks between 2 and 1,247 dimensions, but struggle to explore higher-dimensional spaces when faced with a 15.9k parameter model, indicating a need for work on adaptation in such environments.