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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.
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