De novo protein backbone generation by SE(3) diffusion over rigid-body frames. Samples designable monomers up to 500 residues without pretraining.
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A protein backbone is not a cloud of points. Each residue carries a rigid triad of N, C-alpha and C atoms whose internal geometry is fixed by chemistry, so the object a generative model has to place is a set of rigid bodies — a frame per residue, an element of SE(3) — and the distribution over them must not care where in space the protein sits or how it is turned. That invariance is harder to obtain than it looks: no invariant probability measure over translations in three dimensions exists, so a diffusion process on N frames cannot be made SE(3) invariant by construction.
FrameDiff, from MIT CSAIL with collaborators at Columbia, CNRS, Cambridge and Oxford, supplies the missing theory and the model that follows from it. The paper derives Brownian motion and denoising score matching on SE(3), obtains the rotation score in closed form from the heat kernel on SO(3), and shows that pinning the center of mass at the origin — working in a centered subgroup where only SO(3) invariance remains to be enforced — recovers what was otherwise unavailable. The practical payoff is what the model does not need: earlier backbone diffusion models, RFdiffusion most prominently, were initialized from a pretrained structure prediction network, while FrameDiff trains from scratch on the Protein Data Bank and still generates designable monomers up to 500 residues.
Published at ICML 2023, it is the direct predecessor of FrameFlow, which swaps diffusion for flow matching on the same frame representation.
The score network, FramePred, stacks four layers of Invariant Point Attention borrowed
from AlphaFold 2 with a transformer over the sequence dimension, updating node embeddings,
edge embeddings and frames at every layer; self-conditioning on a binned C-alpha distance
matrix feeds each step's prediction into the next. Training used 20,312 monomer backbones
filtered from the PDB and took one week on two A100 GPUs. Backbones are evaluated by
self-consistency: ProteinMPNN designs sequences at temperature 0.1,
ESMFold refolds them, and agreement is scored by TM-score (scTM) and
C-alpha RMSD. At noise scale 0.1 with 500 sampling steps, 75% of samples clear the
scTM > 0.5 designability bar used by Chroma, rising to 84% when 100
sequences are designed per backbone, with 28% under the stricter 2 Angstrom scRMSD
threshold and diversity above 0.5. Cutting to 100 steps costs little: a 100-residue
backbone then samples in 4.4 seconds on an A100. A later repository update fixed a
torch.bucketize call that silently blocked gradients through the rotation score and
added training on PDB clusters at 30% sequence identity, raising designability from 0.29
to 0.34 and diversity from 0.43 to 0.61; both checkpoints ship in the repository.
FrameDiff produces unconditional monomer backbones, the first step of a de novo design campaign: the sampled fold goes to an inverse folding model for sequences, is refolded for validation, and reaches expression only if it survives. Needing no pretrained folding network and running in seconds per backbone, it makes large candidate libraries practical on modest hardware — and its FoldSeek comparisons identify samples that are both designable and structurally distant from anything in the PDB, the regime protein engineers care about.
The theory is what has traveled furthest: FrameDiff's SE(3) diffusion framework, its frame parameterization and the FramePred network recur as the base architecture or the comparison baseline across much of the protein backbone generation literature that followed, including the flow-matching successors from the same group. The model is honest about its ceiling. RFdiffusion, with four times the weights and structure prediction pretraining, remains ahead on designability; this release does no conditional generation such as motif scaffolding; and the authors decline to make state-of-the-art claims given how differently these methods are trained and evaluated. Weights are committed to the MIT-licensed repository rather than a model hub, and development has moved to successor work.
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