High-throughput single-cell profiling provides an unprecedented ability to uncover the
molecular states of millions of cells. These technologies are, however, destructive to cells …

Solving transport problems, ie finding a map transporting one given distribution to another,
has numerous applications in machine learning. Novel mass transport methods motivated …

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 …

The dynamical formulation of the optimal transport can be extended through various choices
of the underlying geometry ($\textit {kinetic energy} $), and the regularization of density …

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

We propose a novel generative model for time series based on Schr {\" o} dinger bridge (SB)
approach. This consists in the entropic interpolation via optimal transport between a …

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

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

The momentum Schr\" odinger Bridge (mSB) has emerged as a leading method for
accelerating generative diffusion processes and reducing transport costs. However, the lack …

Practitioners often aim to infer an unobserved population trajectory using sample snapshots
at multiple time points. Eg, given single-cell sequencing data, scientists would like to learn …