7 accepted papers
The population dynamics of molecules, cells, and organisms are governed by a number of unknown internal and external forces. In the last decade, population dynamics have predominately been modeled with Wasserstein gradient flows. However, since gradient flows minimize free energy, they fail to captu…
Modeling the transport dynamics of natural processes from population-level observations is a ubiquitous problem in the natural sciences. Such models rely on key assumptions about the underlying process in order to enable faithful learning of governing dynamics that mimic the actual system behavior.…
Numerous biological and physical processes can be modeled as systems of interacting entities evolving continuously over time, e.g. the dynamics of communicating cells or physical particles. Learning the dynamics of such systems is essential for predicting the temporal evolution of populations across…
The Cambrian explosion of easily accessible pre-trained diffusion models suggests a demand for methods that combine multiple different pre-trained diffusion models without incurring the significant computational burden of re-training a larger combined model. In this paper, we cast the problem of com…
The dynamical formulation of the optimal transport can be extended through various choices of the underlying geometry (*kinetic energy*), and the regularization of density paths (*potential energy*). These combinations yield different variational problems (*Lagrangians*), encompassing many variation…
We present simulation-free score and flow matching ([SF]$^2$M), a simulation-free objective for inferring stochastic dynamics given unpaired samples drawn from arbitrary source and target distributions. Our method generalizes both the score-matching loss used in the training of diffusion models and…
One of the grand challenges of cell biology is inferring the gene regulatory network (GRN) which describes interactions between genes and their products that control gene expression and cellular function. We can treat this as a causal discovery problem but with two non-standard challenges: (1) regul…