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Diffusion model for de novo protein backbone design that learns a 32-dimensional latent code for global fold geometry and generates conditioned on it.
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Ask a backbone diffusion model for "a two-layer beta sandwich, roughly 120 residues" and there is nowhere to put the request. The conditioning handles that RFdiffusion and Chroma expose are residue-wise — secondary-structure strings, block adjacency matrices, motif coordinates — so a whole shape must be spelled out one position at a time by someone who already knows what the answer looks like. It shows in the results: validated de novo designs are dominated by mainly-alpha and alpha-beta proteins, while the mainly-beta class stays underrepresented.
TopoDiff adds the missing channel. A structure encoder compresses a backbone into a 32-dimensional latent vector capturing its global geometry, and a diffusion decoder is trained jointly with that encoder to reconstruct coordinates conditioned on the vector — a diffusion-VAE arrangement in which the low dimensionality and a KL penalty force the encoder to keep only the handful of degrees of freedom that separate one fold from another. A second-stage latent diffusion model then learns the distribution of those vectors, so generation becomes two steps: sample a global geometry, then denoise a backbone that realizes it. Because the latent is 32 numbers rather than a residue-length tensor, steering it is cheap — interpolate between two folds, perturb around a reference, or reweight the sampler toward regions predicted to be designable or beta-rich.
TopoDiff comes from Haipeng Gong's group at Tsinghua University, with collaborators at the National Institute of Biological Sciences, Beijing and UC San Diego. A first version appeared at the NeurIPS 2023 GenBio workshop; the expanded work, adding the latent sampler and wet-lab validation, was preprinted in October 2024 and published in Nature Machine Intelligence in June 2025.
Backbones are represented as sequences of SE(3) rigid frames. The structure diffusion module was first trained alone on a PDB monomer set to learn a generative prior, then trained jointly with a randomly initialized SE(3)-equivariant encoder on the CATH-60 set built from the S60 non-redundant domain list of CATH 4.3. The full model is small: 19,466,970 parameters in the structure module and 217,696 in the latent module, against 4.1M for Genie, 17.4M for FrameDiff, 32.4M for Chroma and 59.8M for RFdiffusion. Benchmarking used 500 samples at each of nine lengths from 50 to 250 residues — 22,500 backbones per model — with designability scored by threading eight ProteinMPNN sequences and refolding with ESMFold. TopoDiff leads coverage at every length tested, holds median maxTM near 0.6 against CATH-40, and trails only RFdiffusion on designability while sampling at least three times faster. Twenty-one mainly-beta designs went to the bench: nine expressed solubly in E. coli, four gave separable monomers with beta-sheet circular dichroism spectra, two stayed folded to 95 °C, and the crystal structure of design B10 matches its generated backbone to 1.31 Å Cα-RMSD.
TopoDiff suits design campaigns that begin with a shape rather than a functional site — building a scaffold library that spans fold space instead of clustering on helical bundles, generating variants around a topology that already works, or reaching classes such as mainly-beta that other generators rarely produce. The trained encoder is also useful alone, as a continuous embedding of protein global geometry for organizing structure databases, measuring distances between fold categories, or flagging entries whose classification sits oddly beside their structural neighbours. Outputs are backbones, so sequence design follows downstream.
The contribution most likely to outlast the benchmark table is the framing: a generative model of protein structure can learn its own continuous account of fold space without annotations, and that account is a usable control surface. The coverage metric lets the field see mode collapse that designability and diversity scores hide, and the solved mainly-beta design shows broader coverage translating into real proteins. Scope is bounded — single-chain backbones of 50 to 250 residues, with control over overall geometry rather than functional detail. Code is on GitHub under an MIT licence, with weights, training data and the validated designs on Zenodo.
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