Diffusion-based generative models have recently achieved state-of-the-art empirical performance across a wide range of applications. Despite this success, their theoretical understanding remains limited, particularly under weak assumptions on the target distribution. In this talk, I will present recent quantitative convergence guarantees for several classes of diffusion-based generative methods, including Score-based Generative Models (SGMs), Diffusion Flow Matching models (DFMs), and Iterative Markovian Fitting (IMF). The focus will be on quantifying the discrepancy between the generated distribution and the target distribution through non-asymptotic bounds either in Kullback–Leibler divergence and/or Wasserstein distance. The results discussed were obtained during my PhD in collaboration with G. Conforti, A. Durmus, and A. Ocello.
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