# Learning Optimal Control and Dynamical Structure of Global Trajectory Search Problems with Diffusion Models

arXiv: https://arxiv.org/abs/2410.02976 · HTML: https://mlsanity.com/paper/2410.02976/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models.
- Builds on 5 of its 27 references that are in the map.
- First posted on arXiv 3 Oct 2024.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)

## Builds on (most cited first, 5 of 5)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Amortized Global Search for Efficient Preliminary Trajectory Design with Deep Generative Models](https://mlsanity.com/paper/2308.03960/) (2023)

## Built on by (most cited first, 6 of 6)

- [Global Search for Optimal Low Thrust Spacecraft Trajectories using Diffusion Models and the Indirect Method](https://mlsanity.com/paper/2501.07005/) (2025)
- [Aligning Diffusion Model with Problem Constraints for Trajectory Optimization](https://mlsanity.com/paper/2504.00342/) (2025)
- [Self-supervised diffusion model fine-tuning for costate initialization using Markov chain Monte Carlo](https://mlsanity.com/paper/2510.02527/) (2025)
- [Gradient-Informed Monte Carlo Fine-Tuning of Diffusion Models for Low-Thrust Trajectory Design](https://mlsanity.com/paper/2512.08705/) (2025)
- [Transfer Learning of Multiobjective Indirect Low-Thrust Trajectories Using Diffusion Models and Markov Chain Monte Carlo](https://mlsanity.com/paper/2605.09125/) (2026)
- [GLENS: Global Search via Learning from Solver Iterates with Diffusion Models](https://mlsanity.com/paper/2606.00366/) (2026)

## Abstract (arXiv)

Spacecraft trajectory design is a global search problem, where previous work has revealed specific solution structures that can be captured with data-driven methods. This paper explores two global search problems in the circular restricted three-body problem: hybrid cost function of minimum fuel/time-of-flight and transfers to energy-dependent invariant manifolds. These problems display a fundamental structure either in the optimal control profile or the use of dynamical structures. We build on our prior generative machine learning framework to apply diffusion models to learn the conditional probability distribution of the search problem and analyze the model's capability to capture these structures.