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Generative modelling involves two complementary tasks: learning a probabilistic approximation of an unknown data distribution from observations, and designing a tractable mechanism for sampling from this approximation. We present a stochastic-analysis perspective on score-based generative models, connecting ideas from...
Matching problems are ubiquitous in data science as they enable the alignment of structured objects and distributions. While existing solvers are often tailored to specific matching formulations, we unify a broad class of such problems within a common mathematical and optimization framework based on duality theory. The...
This analysis quantifies the role of the reweighting factor in the score approximation error, providing theoretical guidance for weighting choices used in practice, and develops a Neural Tangent Kernel analysis tailored to diffusion training with stochastic gradients.
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