This is a beautiful clear explanation of diffusion models. The cool thing is they are actually really easy to understand if you know molecular simulation. There is a direct analog for almost every concept. 1/n
New blog post about the geometry of diffusion guidance:
This complements my previous blog post on the topic of guidance, but it has a lot of diagrams which I was too lazy to draw back then! Guest-starring Bundle, the cutest bunny in ML 🐇
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The “score” Is just the forcefield, the log of the probability is just a free energy. The “sampling” is just running the dynamics where the different algorithms correspond to different thermostats and different choices for the equations of motion. 2/n
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The amount of noise you add during the sampling corresponds to the temperature of the simulation. If you turn the noise down as you sample ie annealing you will eventually end up at points of maximum probability: de blurred images or minimum energy structures in a simulation. 3/n
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Assuming Gaussian noise just corresponds to assuming a harmonic potential about all of your initial samples, as a harmonic potential gives you a Gaussian distribution when you use it in the Boltzmann factor. 4/n
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“Guidance” just corresponds to adding an external potential to bias your simulation towards certain regions of phase space. Something we do all the time in molecular simulation. 5/n
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The only difference is that in traditional molecular simulation we use an analytic function to approximate the real force field. In diffusion models we use a neural network to estimate the forces of a fictional smooth potential energy landscape. 6/n
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This has significant implications, one is that diffusion models should be very useful for predicting new stable molecules, but of course we already know that from the fantastic work on protein design. 7/n
Aaaaand we're live! Excited that our paper "De novo design of protein structure and function with RFdiffusion" is available online
@Nature
Check out the accompanying news article for how it's being used already, and for a few hints at where this story might be going next 😉
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The other implication though is that molecular simulators have developed a whole bag of tricks over the decades which should be useful for diffusion models as well. 8/n
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A nice example of this is metadynamics where you add Gaussian hills to your potential energy surface to bias your simulation away from well sampled regions of phase space that you may not be interested in. 9/n
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A really nice paper just came out that does exactly this in the context of drug design from
@j0hnparkhill
: 10/n
Do you want to map: molecule
vector
available drug-like molecule? Do you want to do calculus on molecules to optimize them? Are you wracked by doubts about how expressive your molecular embedding is? Want to make your own drug generator? Some open science for you🧵 (1/n)
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