  Adapting large-scale pre-trained generative models in a parameter-efficient
manner is gaining traction. Traditional methods like low rank adaptation
achieve parameter efficiency by imposing constraints but may not be optimal for
tasks requiring high representation capacity. We propose a novel spectrum-aware
adaptation framework for generative models. Our method adjusts both singular
values and their basis vectors of pretrained weights. Using the Kronecker
product and efficient Stiefel optimizers, we achieve parameter-efficient
adaptation of orthogonal matrices. We introduce Spectral Orthogonal
Decomposition Adaptation (SODA), which balances computational efficiency and
representation capacity. Extensive evaluations on text-to-image diffusion
models demonstrate SODA's effectiveness, offering a spectrum-aware alternative
to existing fine-tuning methods.
