# SE(3) Flow Matching

Protein conformational ensemble generation has treated coordinated motion between residues as implicit in the learned distribution, which limits direct control. CoMoFlow builds protein-specific collective modes from the equilibrium structure, learns the distribution of their coefficients across the molecular dynamics ensemble, and uses sampled collective displacements to guide SE(3) flow matching through feature conditioning and prior recentering. On ATLAS and de novo proteins it raises DCCM correlation over BBFlow from 0.87/0.83 to 0.93/0.89 and lowers PCA distance from 1.33/0.67 to 1.21/0.59, while allowing generated conformations to be steered along a chosen mode in direction and magnitude.

Protein conformational ensemble generation has treated coordinated motion between residues as implicit in the learned distribution, which limits direct control. CoMoFlow builds protein-specific collective modes from the equilibrium structure, learns the distribution of their coefficients across the molecular dynamics ensemble, and uses sampled collective displacements to guide SE(3) flow matching through feature conditioning and prior recentering. On ATLAS and de novo proteins it raises DCCM correlation over BBFlow from 0.87/0.83 to 0.93/0.89 and lowers PCA distance from 1.33/0.67 to 1.21/0.59, while allowing generated conformations to be steered along a chosen mode in direction and magnitude.

Protein motif scaffolding usually fixes both where a motif sits along the chain and the relative pose of several rigid fragments, yet many applications supply neither. NomadFlow takes each motif group as a condition, holds each group's internal geometry exactly with a group projection, and lets the groups move independently through the first half of generation before locking them as conditioning to complete the scaffold. On 21 multi-group tasks adapted from Protpardelle, 19 reach unique success; against the same residue set fixed as one rigid body, the median ratio is 0.57 in yield and 1.00 in unique successes.

Protein motif scaffolding usually fixes both where a motif sits along the chain and the relative pose of several rigid fragments, yet many applications supply neither. NomadFlow takes each motif group as a condition, holds each group's internal geometry exactly with a group projection, and lets the groups move independently through the first half of generation before locking them as conditioning to complete the scaffold. On 21 multi-group tasks adapted from Protpardelle, 19 reach unique success; against the same residue set fixed as one rigid body, the median ratio is 0.57 in yield and 1.00 in unique successes.