The Inversion-Denoising Paradigm, which is based on diffusion models, excels in diverse image editing and restoration tasks. We revisit its mechanism and reveal a critical, overlooked factor in reconstruction degradation: the approximate noise error . This error stems from approximating the noise at step $t$ with the prediction at step $t\!-\!1$, resulting in severe error accumulation throughout the inversion process. We introduce Projection-Orthogonal Least Squares for Robust and Adaptive Inversion (POLARIS), which reformulates inversion from an error-compensation problem into an error-origin problem. Rather than optimizing embeddings or latent codes to offset accumulated drift, POLARIS treats the guidance scale $\omega$ as a step-wise variable and derives a mathematically grounded formula to minimize inversion error at each step. Remarkably, POLARIS improves inversion latent quality with just one line of code. With negligible performance overhead, it substantially mitigates noise approximation errors and consistently improves the accuracy of downstream tasks.
POLARIS Method
(A) Existing CFG-based DDIM methods introduce and accumulate errors at each step of the inversion process, eventually leading to the distribution shift of downstream tasks. (B) Our method actively seeks a mathematically invertible path to obtain a latent variable that is closer to the ideal one. During generation, the recorded ωt sequence is replayed, enabling high-fidelity reconstruction. (C) Shows our optimization goal from a geometric point of view to minimize the inversion error.
Position of our work
POLARIS reframes inversion from an error-compensation problem to an error-origin problem. Instead of optimizing embeddings or latents to counteract drift, we treat the guidance scale as a step-wise variable and derive a mathematically grounded rule that minimizes inversion error at each step. Concretely, we obtain a closed-form, per-timestep scale from an orthogonality condition between conditional/unconditional noise-change vectors, yielding a robust, plug-and-play dynamic schedule that can be dropped into standard DDIM inversion. POLARIS is thus complementary to prior pipelines: it preserves their modularity while replacing a brittle, fixed hyperparameter with an adaptive, theoretically justified control law.