Score Estimation for Generative Modeling
Abstract
Recent advances in score-based (diffusion) generative models have achieved state-of-the-art sample quality across standard benchmarks. Building on the remarkable property of these models in estimating scores, this thesis presents three core contributions: 1) new objectives to reduce score estimation error, 2) a novel Bayesian-inspired optimization framework for solving inverse problems, and 3) a fast one-step generative modeling framework that is based on a novel amortized score estimation framework. In the first part of this thesis, we introduce two new score estimation objectives with applications to both implicit and diffusion-based generative models. To improve spectralbased non-parametric estimators, we propose a theoretically optimal parametric framework that learns the score by projecting it onto its top-L principal directions. Additionally, inspired by matrix-valued kernel methods, we present a second approach that lifts the score into the space of outer products, and minimizes the distance between the estimated and true scores in this higher-order space. In the second part, we shift focus from score estimation to leveraging diffusion models as data-driven priors for solving inverse problems. Centering our development around the problem of source separation, we introduce a novel algorithm inspired by maximum a posteriori estimation. This approach combines multiple levels of Gaussian smoothing with an α-posterior, enabling effective signal separation using only…
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