Generative modeling and scalable test-time optimization using diffusion and flow models
Abstract
This thesis develops a principled framework for generative modeling and scalable test-time optimization, grounded in posterior sampling, stochastic optimal control, and structured anchoring. Modern diffusion-based generative models achieve remarkable quality, yet their use in inverse problems, personalization, editing, and structured generation remains limited by inefficient inference, heuristic guidance, and poor utilization of informative structure. This dissertation addresses these challenges by reinterpreting generative models as stochastic dynamical systems and designing theoretically grounded, training-free algorithms that enable controllable and efficient inference at test time. We first introduce Posterior Sampling with Latent Diffusion (PSLD), the first framework to solve linear inverse problems using pretrained latent diffusion models. We provide theoretical recovery guarantees in linear settings and demonstrate strong empirical performance across a broad class of inverse problems, including inpainting, deblurring, destriping, and super-resolution. Building on this foundation, we identify fundamental limitations of first-order Tweedie-based samplers and propose the \emph{Second-order Tweedie from Surrogate Loss} (STSL), which enables tractable second-order posterior sampling using only $\mathcal{O}(1)$ additional computation. STSL substantially reduces neural function evaluations while improving reconstruction quality, and further enables text-guided image editing…
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