Null-Space Alignment for Inversion-Free Music Editing

Semantic music editing is inherently underdetermined: a text instruction specifies *what* should change, but leaves many musical degrees of freedom in *how* that change is realized. An effective editing system must therefore distinguish between what is explicitly prescribed by the instruction and what remains unspecified for the generative prior to determine. Motivated by this view, we investigate whether the conditional flow difference of a pretrained flow-matching model naturally exhibits such a separation. We discover that projecting this difference onto the local edit trajectory yields two complementary components: a *parallel* component driving the prescribed change, and an *orthogonal null-space* component. Crucially, increasing the strength of the null-space component consistently shifts the output from source-content fidelity toward stronger instruction alignment. This reveals that the null-space is not a uninformative residual to be discarded, but rather a controllable degree of generative freedom. Building on this insight, we propose Null-Space Alignment (NSA), a training-free and inversion-free framework that gates the null-space component at each step based on its directional consistency. Experiments on MelodiaEdit and ZoME-Bench demonstrate that NSA achieves consistent state-of-the-art performance across both quantitative metrics and human evaluations.