Generative modeling has drawn much attention in creative and scientific data generation tasks. Score-based Diffusion Models, a type of generative model that iteratively learns to denoise data, have shown state-of-the-art results on tasks such as image generation, multivariate time series forecasting, and robotic trajectory planning. Using score-based diffusion models, this work implements a novel generative framework to generate ballistic transfers from Earth to Mars. We further analyze the model's ability to learn the characteristics of the original dataset and its ability to produce transfers that follow the underlying dynamics. Ablation studies were conducted to determine how model performance varies with model size and trajectory temporal resolution. In addition, a performance benchmark is designed to assess the generative model's usefulness for trajectory design, conduct model performance comparisons, and lay the groundwork for evaluating different generative models for trajectory design beyond diffusion. The results of this analysis showcase several useful properties of diffusion models that, when taken together, can enable a future system for generative trajectory design powered by diffusion models.

翻译：生成建模在创意和科学数据生成任务中备受关注。基于评分的扩散模型是一类通过迭代学习去噪的生成模型，在图像生成、多元时间序列预测和机器人轨迹规划等任务中展现出最先进的性能。本研究利用基于评分的扩散模型，提出了一种新颖的生成框架，用于生成从地球到火星的弹道转移轨道。我们进一步分析了该模型学习原始数据集特征的能力及其生成遵循底层动力学特性的转移轨道的能力。通过消融研究，确定了模型性能随模型规模和轨迹时间分辨率的变化规律。此外，设计了一个性能基准测试，以评估该生成模型在轨迹设计中的实用性，开展模型性能比较，并为评估除扩散模型之外的其他生成模型在轨迹设计中的应用奠定基础。分析结果展示了扩散模型的若干有用特性，这些特性共同为未来基于扩散模型的生成式轨迹设计系统提供了可能。