# Transfer Learning of Multiobjective Indirect Low-Thrust Trajectories Using Diffusion Models and Markov Chain Monte Carlo

arXiv: https://arxiv.org/abs/2605.09125 · HTML: https://mlsanity.com/paper/2605.09125/

## Key facts

- Cited by 1 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 11 of its 53 references that are in the map.
- First posted on arXiv 9 May 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, 11 of 11)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Aligning Text-to-Image Models using Human Feedback](https://mlsanity.com/paper/2302.12192/) (2023)
- [A Conceptual Introduction to Hamiltonian Monte Carlo](https://mlsanity.com/paper/1701.02434/) (2017)
- [DiffuSolve: Diffusion-based Solver for Non-convex Trajectory Optimization](https://mlsanity.com/paper/2403.05571/) (2024)
- [Amortized Global Search for Efficient Preliminary Trajectory Design with Deep Generative Models](https://mlsanity.com/paper/2308.03960/) (2023)
- [Global Search for Optimal Low Thrust Spacecraft Trajectories using Diffusion Models and the Indirect Method](https://mlsanity.com/paper/2501.07005/) (2025)
- [Learning Optimal Control and Dynamical Structure of Global Trajectory Search Problems with Diffusion Models](https://mlsanity.com/paper/2410.02976/) (2024)
- [Global Search of Optimal Spacecraft Trajectories using Amortization and Deep Generative Models](https://mlsanity.com/paper/2412.20023/) (2024)

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

- [Complexity Bounds and Approaches to Learning Projected Gradient Descent Solver Iterates](https://mlsanity.com/paper/2607.22467/) (2026)

## Abstract (arXiv)

Preliminary low-thrust spacecraft mission design is a global search problem characterized by a complex solution landscape, multiple objectives, and numerous local minima. During this phase, mission parameters are often not yet fully defined, requiring new solutions to be generated at a high cadence across varying parameter values. When combined with the indirect approach to optimal control, diffusion models can accelerate this search by learning distributions that represent high-quality initial costates. However, generating training data remains expensive, and opportunities exist to better exploit past data. We propose a transfer-learning framework that combines homotopy in a mission parameter with Markov chain Monte Carlo (MCMC) to generate training data more efficiently. The approach reformulates a multiobjective optimization problem as sampling from an unnormalized target distribution in costate space. We compare three MCMC algorithms on a planar multi-revolution transfer in the circular restricted three-body problem, with homotopy in the system mass parameter. The results show that gradient-based MCMC variants achieve the best trade-off between sample quality and computational cost. For the test transfer, the proposed framework generates 40 % more feasible solutions and achieves a higher-quality Pareto front than a state-of-the-art indirect approach based on adjoint control transformations and gradient-based optimization. Finally, the MCMC-generated samples are used to fine-tune a diffusion model conditioned on the mass parameter, enabling it to learn a global representation of the underlying solution distribution and efficiently generate new solutions. These findings establish the transfer-learning framework as a practical method for efficiently solving indirect trajectory optimization problems with varying parameters.