Diffusion concepts occupy provably-separate, editable score subspaces

Wang et al. treat the diffusion score function as the representation and prove (Theorem 3.2) that if the generation is "causally separable" in two concepts, the centered score is arithmetically composable, each concept occupying its own additive subspace [wang-etal-2023-concept-algebra] The concept subspace is estimable from contrastive prompt pairs alone (e.g. "a man" vs "a woman") [wang-etal-2023-concept-algebra] Concept algebra edits generations by projecting and swapping score-subspace components; on Stable Diffusion, 10 raters judged it most faithful to target content and style 47.6% of the time vs ~16% for prompting and naive composition [wang-etal-2023-concept-algebra] A demonstrated failure case (gender transfer on "nurse") arises exactly when the causal-separability hypothesis is violated, linking the theorem's precondition to a practical limit [wang-etal-2023-concept-algebra]