Spectral Steering: Local Inverse Geometry for Frozen Diffusion Generators

A frozen diffusion generator may need to change several output properties while preserving others. We study when guidance faithfully realizes such a structured request and whether local inverse correction improves its direction. Our account links this benefit to the interaction between the request and the objective-specific remaining-sampler Jacobian: conditioning alone is insufficient. Spectral steering combines a request-specific cosine-gain predictor with damped inverse correction and fixed-time relinearization for finite edits. Scalar nulls and matched-movement controls test the predicted mechanism. Across 8,923 instances in a retrospectively identified local regime, predicted and realized gains correlate at Spearman $0.79$, versus $-0.11$ for condition number. Experiments span images, audio, robotics, and control and planning, including complex character motion generation. On 50 paired inpainting cases, four corrections improve unobserved-pixel PSNR over Adam by 3.25 dB at equal total derivative traversals. Together, the analysis and controls connect request-dependent geometry to directional gains and establish where these gains translate into downstream performance.