Algorithms and Representations for Learning and Inference with Diffusion Models
Abstract
Diffusion models have emerged as a scalable paradigm to learn rich high-dimensional data distributions and generate new samples from them. However, many practical problems require more than generating samples from the learned distribution: inverse problems require samples that explain measurements, visual editing demands control over what changes, large-scale applications demand efficiency. This thesis extends diffusion models to meet these demands, organized around two complementary questions: (1) Can diffusion models provide an effective new route to solving scientific inverse problems, and how? (2) How can diffusion models be made more efficient and controllable for practical generation? For the first, diffusion models offer what classical priors cannot — a rich, learned prior over high-dimensional solution spaces; we test whether this translates into an effective route by curating five benchmark problems across distinct scientific domains. The results reveal their promise but also clear gaps, motivating algorithms that handle challenging forward models, numerical stability, and uncertainty. We then develop an inference algorithm that balances between two dynamics, one for the diffusion prior and one for measurement consistency. It produces samples that resolve structure the measurements leave undetermined, while still explaining those measurements with calibrated uncertainty. For the second, the standard diffusion formulation leaves usable structure untapped; we reshape…
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