Inverse problems aim to determine parameters from observations, a crucial task in engineering and science. Lately, generative models, especially diffusion models, have gained popularity in this area for their ability to produce realistic solutions and their good mathematical properties. Despite their success, an important drawback of diffusion models is their sensitivity to the choice of variance schedule, which controls the dynamics of the diffusion process. Fine-tuning this schedule for specific applications is crucial but time-costly and does not guarantee an optimal result. We propose a novel approach for learning the schedule as part of the training process. Our method supports probabilistic conditioning on data, provides high-quality solutions, and is flexible, proving able to adapt to different applications with minimum overhead. This approach is tested in two unrelated inverse problems: super-resolution microscopy and quantitative phase imaging, yielding comparable or superior results to previous methods and fine-tuned diffusion models. We conclude that fine-tuning the schedule by experimentation should be avoided because it can be learned during training in a stable way that yields better results.

翻译：逆问题旨在从观测中确定参数，这是工程与科学领域的一项关键任务。近年来，生成模型（尤其是扩散模型）因其能够生成逼真解并具备良好的数学特性而在此领域广受关注。然而，扩散模型的一个显著缺陷是其对方差调度（控制扩散过程动态的机制）的选择高度敏感。针对特定应用微调该调度虽然关键，但耗时且无法保证最优结果。我们提出了一种新方法，在训练过程中学习该调度。该方法支持基于数据的概率条件建模，提供高质量解，且具有灵活性，能够以最小开销适应不同应用。本方法在两个不相关的逆问题（超分辨率显微镜和定量相位成像）中进行了测试，其结果与先前方法及精细调优的扩散模型相比表现出相当或更优的性能。我们得出结论：应避免通过实验手动微调调度，因为可在训练过程中以稳定方式习得该调度并获得更优结果。