OrthoMotion:Disentangling Camera and Subject Motion via Geometry Semantics Orthogonal Attention

Abstract: Controllable video generation demands independent command of the camera and the subject, yet 2D conditioning entangles them: camera- and object-induced optical flow share the same inverse-depth (1/Z) scaling and cannot be separated from image evidence alone. We first prove that this entanglement is representational, not architectural -- the 2D camera/object split is a non-identifiable inverse problem -- and therefore reframe decoupling as a question of operator design. We resolve it at the level of the attention operator. OrthoMotion routes camera motion into a geometric channel, a norm-preserving rotation of the rotary position embedding (RoPE) phase, and subject motion into a semantic channel, a gated value injection in cross-attention. Because these sub-operators are algebraically complementary -- a rotation versus a translation of the affine action on tokens -- a lightweight decoupling regularizer provably drives their response subspaces to orthogonality, so the two controls stop interfering. To our knowledge OrthoMotion is the first method to guarantee disentanglement by construction rather than hope for it to emerge. It attains state-of-the-art camera and subject accuracy at once while minimizing cross-talk, which we quantify with a new Cross-Talk Error (CTE) metric, cutting cross-talk by more than 2.4x with no loss in fidelity and generalizing across backbones.