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This project develops generative diffusion and flow matching frameworks that operate natively in discrete state spaces via continuous-time Markov chains. By bypassing continuous relaxations, the research addresses the algorithmic challenges of efficient sampling and transition dynamics. Crucially,
High-Dimensional Optimization with Diffusion Models investigates the use of diffusion-based generative models as optimization mechanisms in high-dimensional search spaces. The project explores how reverse diffusion processes can be conditioned on objective functions to iteratively generate candidate solutions that concentrate
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