PhysFlow

Generative models for protein backbones — diffusion and flow-matching methods such as RFdiffusion, Chroma, FrameDiff, FrameFlow, and FoldFlow — almost all share the same forward process: a linear noising schedule that scatters a folded structure into a soup of disconnected residues. That schedule is chosen for mathematical convenience, not physical plausibility. Along the way it breaks the peptide backbone and lets residues pass straight through one another, and because the generative model is trained to reverse exactly this trajectory, the resulting inductive bias offers no protection against steric clashes or broken geometry in the samples.

PhysFlow, introduced in September 2025 by Yogesh Verma, Markus Heinonen, and Vikas Garg at Aalto University and YaiYai, replaces that schedule with a forward process derived from Hamiltonian dynamics. Instead of dissolving a protein into noise, the process unfolds it: a damped simulation drives the backbone toward a target state made of isolated secondary-structure elements — alpha helices and extended beta strands — under a quadratic target potential plus a Coulomb-like repulsion barrier. Bonds stay intact throughout, and the repulsion term keeps residues from colliding.

The reverse of this trajectory is then learned with conditional flow matching on SE(3), the group of rigid rotations and translations that parameterizes protein backbone frames. Because the model also ingests sequence information, a single trained network serves two tasks: unconditional generation of novel backbones and sequence-conditioned folding of monomers.

#Key Features

• Physics-derived noising: The forward process is a Hamiltonian simulation with a target potential and a Coulomb repulsion barrier, so it degrades structures into secondary-structure elements while preserving covalent bonds and avoiding steric collisions.
• Dual angular and frame representation: Unfolding is simulated in dihedral/bond-angle space and mapped to Cartesian coordinates with the differentiable mp-NeRF algorithm, while the generative model operates on SE(3) backbone frames.
• Unified generation and folding: Sequence conditioning is randomly masked half the time during training, letting one checkpoint perform both unconditional backbone design and sequence-to-structure folding.
• Look-ahead training objective: An auxiliary loss penalizes the network for mispredicting future states along the trajectory, which is what makes the non-linear unfolding path learnable by a flow-matching model.
• Tunable clash control: Raising the weight on the Coulombic repulsion term measurably reduces residue–residue collisions across the forward trajectory.

#Technical Details

PhysFlow uses an invariant point attention (IPA) transformer as its structure encoder and a second IPA transformer as the decoder that predicts SE(3) velocity fields, each with four blocks, eight attention heads, and 256-dimensional node embeddings. Sequence information comes from the frozen 650M-parameter ESM-2 protein language model, and the two representation streams are merged by a combiner module using triangular self-attention before decoding. Training used 24,003 PDB monomers of 60–512 residues at better than 5 Å resolution, filtered with DSSP to exclude structures with more than 50% loop content, spanning 4,532 clusters at 40% sequence identity — the same corpus used by FrameDiff and FoldFlow — on a single NVIDIA H200 GPU.

On unconditional monomer generation, PhysFlow reaches 0.81 designability (fraction of backbones that ProteinMPNN sequences refold to within 2 Å scRMSD), against 0.77 for FoldFlow-OT, 0.65 for FoldFlow-CFM, 0.60 for FrameFlow, 0.55 for Genie, and 0.40 for FrameDiff on the same training data. It also improves novelty (0.197 TM-fraction below 0.3) over those baselines. On sequence-conditioned folding of held-out clusters it reaches 11.08 Å RMSD for proteins under 200 residues and 15.11 Å above, versus 13.52 Å and 17.88 Å for FoldFlow-2 and 17.41 Å and 20.63 Å for MultiFlow retrained on the same set. ESMFold, trained on roughly 65 million UniRef sequence–structure pairs, remains far more accurate at 1.64 Å and 2.82 Å.

#Applications

The primary use is de novo protein backbone design, where samples are passed to an inverse folding model for sequence assignment and then screened for self-consistency — the standard pipeline for scaffolds, binders, and enzyme frameworks. Because the physics-derived forward process suppresses clashes by construction, generated backbones need less geometric cleanup before downstream design. The clash-free unfolding formulation is also of independent interest to method developers building generative models over other bonded molecular structures.

#Impact

PhysFlow's contribution is conceptual as much as empirical: it demonstrates that the forward noising process in a protein generative model is a design choice with real consequences, and that grounding it in classical mechanics improves designability and novelty without extra data, pretraining, or fine-tuning. Comparisons to RFdiffusion, Proteína, and ESM-3 are not like-for-like, since those models draw on larger or different corpora with pretraining. The work remains an arXiv preprint awaiting peer review, evaluation is entirely in silico, coverage is limited to single-chain monomers, and no code or weights have been released.