Introduction
Hi ! I was going to publish this content on ArXiv but I decided to write a blog post this time so I can write it a bit more informally =)
It is not a secret that Diffusion models have become the workhorses of high-dimensionality generation: start with a Gaussian noise and, through a learned denoising trajectory, you get high-fidelity images, molecular graphs, or robot trajectories that look (uncannily) real. I wrote extensively about diffusion and its connection with the data manifold metric tensor recently as well, so if you are interested please take a look on it.
Now, for many engineering and practical tasks we care less about “looking real” and more about maximising a task-specific score or a reward from a simulator, a chemistry docking metric, a CLIP consistency score, human preference, etc. Even though we can use guidance or do a constrained sampling from the model, we often require differentiable functions for that. Evolution-style search methods (CEM, CMA-ES, etc), however, can shine in that regime, but naively applying them in the raw object space wastes most samples on absurd or invalid candidates and takes a lot of time to converge to a reasonable solution.
