3 accepted papers
We consider a class of conditional forward-backward diffusion models for conditional generative modeling, that is, generating new data given a covariate (or control variable). To formally study the theoretical properties of these conditional generative models, we adopt a statistical framework of dis…
Empirical studies have demonstrated the effectiveness of (score-based) diffusion models in generating high-dimensional data, such as texts and images, which typically exhibit a low-dimensional manifold nature. These empirical successes raise the theoretical question of whether score-based diffusion…
In this paper, we consider the problem of two-sample hypothesis testing that aims at detecting the difference between two probability densities based on finite samples. The proposed test statistic is constructed by first truncating a sample version of a negative Besov norm and then normalizing it. H…