$\sigma$: Sigmoid Modulation for Ultra High Resolution Diffusion

摘要

Diffusion Transformers (DiTs) can synthesize high-fidelity images, but training at ultra-high resolutions is expensive, making inference-time extrapolation essential. Existing methods are typically \textit{scale-agnostic}, applying the same positional-modulation schedule regardless of target resolution. We show that this misses a scale-sensitive property of denoising: resizing shifts a fixed semantic pattern toward lower \emph{normalized} spatial frequencies while enlarging the spatial support over which global structure must be coordinated. The latter delays structural lock-in at high resolutions, so schedules may either relax guidance before global layout has stabilized, causing \textit{structural collapse}, or retain excessive intervention into late denoising, causing \textit{textural degradation}. We introduce \textbf{SigMa ($\sigma$)}, a training-free framework that uses Sigmoid Modulation for \textit{scale-adaptive} extrapolation through two scaling laws: \textit{Decoupled Geometric Center Alignment} and \textit{Iso-Variance Rate Adaptation}. Experiments show that SigMa reduces this mismatch, enabling training-free extrapolation up to 16 megapixels and achieving the best or competitive performance among the tested training-free extrapolation baselines. Code is available at \href{https://github.com/bxuanz/SigMa.git}{github.com/bxuanz/SigMa}.