# Diffusion-Based Multiple-Shooting Indirect Optimal Control for Fuel-Optimal Spacecraft Trajectory Generation

arXiv: https://arxiv.org/abs/2609.13990 · HTML: https://mlsanity.com/paper/2609.13990/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models.
- Builds on 12 of its 27 references that are in the map.
- First posted on arXiv 12 Sep 2026.

## 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, 12 of 12)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [On Neural Differential Equations](https://mlsanity.com/paper/2202.02435/) (2022)
- [Policy-Guided Diffusion](https://mlsanity.com/paper/2404.06356/) (2024)
- [Global Search for Optimal Low Thrust Spacecraft Trajectories using Diffusion Models and the Indirect Method](https://mlsanity.com/paper/2501.07005/) (2025)
- [Comparison of control regularization techniques for minimum-fuel low-thrust trajectory design using indirect methods](https://mlsanity.com/paper/2409.01490/) (2024)
- [Co-state Neural Network for Real-time Nonlinear Optimal Control with Input Constraints](https://mlsanity.com/paper/2503.00529/) (2025)
- [Gradient-Informed Monte Carlo Fine-Tuning of Diffusion Models for Low-Thrust Trajectory Design](https://mlsanity.com/paper/2512.08705/) (2025)

## Abstract (arXiv)

Diffusion-based generative models (DMs) have found applications in control problems, and in particular robotics, where the DMs enable exploration of possible control solutions. A critical shortcoming of these applications is that they have lacked optimality guarantees. This is a problem for their potential use in fuel-optimal spacecraft trajectories that are characterized with long time-horizons and bang-bang profiles. Alternatively, indirect optimal control methods ensure explicit satisfaction of necessary conditions, but are highly sensitive to the initial costate estimation needed to solve the resulting Hamiltonian boundary-value problems (HBVPs). To alleviate this sensitivity and enlarge the convergence domain of HBVPs, advanced indirect methods have been developed that use smoothing approaches and continuation. We propose a diffusion-based multiple shooting indirect control method that combines the exploration capability of DMs with indirect method to generate fuel-optimal spacecraft trajectories. We benchmark our method against an advanced indirect method on a fuel-optimal Earth-Mars low-thrust transfer problem, showing higher convergence robustness than the advanced indirect method that is based on random costate initialization. Code and visualizations are available at https://saeidtafazzol.github.io/Diffusion_Indirect_Control/.