Initial experimentation. Consider the manifold hypothesis, along with the fact that diffusion is a continuous ode. It would be desirable to have a prior distribution that has an arbitrary topology, which can then be mapped to the data manifold.
Here, is an initial experiment testing to see if a simple 2d gaussian prior distribution can be mapped to a 2d data manifold using flow matching. Initial results appear promising, however difficulties arise when attempting this with the swiss roll dataset...
Initial Data Manifold
Learned Reverse Process