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反演参数，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）因其能生成逼真解决方案及良好的数学性质而在此领域广受关注。尽管取得了成功，但扩散模型的一个显著缺陷是其对方差调度（控制扩散过程动态变化）的敏感依赖。针对特定应用微调该调度至关重要，但耗时且无法保证最优结果。我们提出了一种在训练过程中学习调度参数的新方法。该方法支持基于数据的概率条件约束，可生成高质量解，且灵活性强，能以最小额外开销适应不同应用场景。我们将此方法应用于两个不相关的逆问题——超分辨率显微成像与定量相位成像，取得了与先前方法及精细调谐扩散模型相当或更优的结果。实验表明，应避免通过实验手动微调调度参数，因为该参数可在训练过程中以稳定方式自动学习，并取得更优成效。