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：反问题旨在从观测数据中推断参数，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）因其生成逼真解决方案的能力及其良好的数学性质，在该领域日益受到青睐。尽管取得了成功，扩散模型的一个重要缺陷是其对方差调度（控制扩散过程动态特性）选择的敏感性。为特定应用微调解耦过程耗时费力，且无法保证最优结果。我们提出一种将调度学习融入训练过程的新方法。该方法支持基于数据的概率条件约束，提供高质量解决方案，具有灵活性，能以最小开销适应不同应用场景。该方案在两个不同领域的反问题（超分辨率显微成像与定量相位成像）中进行了测试，取得了与先前方法及精调扩散模型相当或更优的结果。我们得出结论：通过实验微调解耦过程应予以避免，因为可在训练过程中以更稳定方式自主学习达到更优效果。