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：逆问题旨在从观测数据中确定参数，这是工程与科学领域的关键任务。近年来，生成模型（尤其是扩散模型）因其能够生成逼真解且具有良好的数学性质，在该领域备受关注。尽管取得了成功，扩散模型的一个重要缺陷是对控制扩散过程动态特性的方差调度方案的选择高度敏感。针对特定应用微调该调度方案至关重要，但既耗时又无法保证最优结果。我们提出一种在训练过程中学习调度方案的新方法。该方法支持基于数据的概率条件化，可提供高质量解，且灵活性强，能以最小开销适应不同应用。该方案在超分辨率显微成像与定量相位成像两个不相关的逆问题中进行了测试，结果优于或等同于先前方法与微调后的扩散模型。我们得出结论：应避免通过实验手动微调调度方案，因其可在训练过程中以稳定方式学习，从而获得更优结果。