Generating DDPM-based Samples from Tilted Distributions

ArXi:2604.03015v1 Announce Type: new Given $n$ independent samples from a $d$-dimensional probability distribution, our aim is to generate diffusion-based samples from a distribution obtained by tilting the original, where the degree of tilt is parametrized by $\theta \in \mathbb{R}^d$. We define a plug-in estimator and show that it is minimax-optimal. We develop Wasserstein bounds between the distribution of the plug-in estimator and the true distribution as a function of $n$ and $\theta$, illustrating regimes where the output and the desired true distribution are close.