Tag: diffusion

Machine Learning

Diffusion Elites: surprisingly good, simple and embarrassingly parallel

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.

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Machine Learning, Math

Thoughts on Riemannian metrics and its connection with diffusion/score matching [Part I]

Different gaussian curvature surfaces. Image by Nicoguaro.

We are so used to Euclidean geometry that we often overlook the significance of curved geometries and the methods for measuring things that don’t reside on orthonormal bases. Just as understanding physics and the curvature of spacetime requires Riemannian geometry, I believe a profound comprehension of Machine Learning (ML) and data is also not possible without it. There is an increasing body of research that integrates differential geometry into ML. Unfortunately, the term “geometric deep learning” has predominantly become associated with graphs. However, modern geometry offers much more than just graph-related applications in ML.

I was reading the excellent article from Sander Dieleman about different perspectives on diffusion, so I thought it would be cool to try to contribute a bit with a new perspective.

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