Diffusion regulates numerous natural processes and the dynamics of many successful
generative models. Existing models to learn the diffusion terms from observational data rely …

Diffusion models (DMs) represent state-of-the-art generative models for continuous inputs.
DMs work by constructing a Stochastic Differential Equation (SDE) in the input space (ie …

This article considers the generative modeling of the (mixed) states of quantum systems, and
an approach based on denoising diffusion model is proposed. The key contribution is an …

We propose a custom learning algorithm for shallow over-parameterized neural networks,
ie, networks with single hidden layer having infinite width. The infinite width of the hidden …

Accurate modeling of system dynamics holds intriguing potential in broad scientific fields
including cytodynamics and fluid mechanics. This task often presents significant challenges …

In this dissertation, we investigate convex optimization problems over the space of
probability measures, highlighting applications in stochastic control, stochastic modeling …