Introduction

In the world of computational structural biology you might have heard of diffusion models as the current big thing in generative modelling. Diffusion models are great because primarily they look cool when you visualise the denoising process to generate a protein structure (checkout RFdiffusion Colab notebook), but also because they are state of the art at diverse and designable protein backbone structure generation.

Originally emerging from computer vision, a lot of work has been built up around their application to macromolecules – especially exciting is their harmonious union with geometric deep learning in the case of SE(3) equivariance (see FrameDiff). I don’t know about you but I get particularly excited about geometric deep learning, mostly because it involves objectively dope words like “manifold” and “Riemannian”, better yet “Riemannian manifolds” – woah! (see Bronstein’s geometric deep learning for more fun vocabulary to add to your vernacular- like “geodesic”, Geometric Deep Learning).

But we’re getting side tracked. Diffusion is a square to rectangle case of score-based generative models with the clause that diffusion refers explicitly to the learning of a time-dependent score function that is typically learned via a denoising process. Checkout Jakub Tomczak’s blog for more on diffusion and score-based generative models. Flow matching, although technically different to score-based generative models, also makes use of transformations to gaussian but is generally faster and not constrained to discrete time steps (or even Gaussian priors). So the big question is, how does one flow match?