We address the multiscale singularity in Euclidean diffusion models for manifold-constrained data and propose two novel methods to improve sampling accuracy on complex geometries.

We accelerate border basis computations with a Transformer-based oracle.

We accelerate Taylor mode for practically relevant differential operators by collapsing Taylor coefficients; this can be done automatically with compute graph simplifications

We develop trust region methods for stochastic optimal control to improve sampling from unnormalized densities, transition path sampling, and diffusion model finetuning.

A multi-metric Common Task Framework that standardizes characterization and comparison of modeling methods for dynamic systems.