We propose a novel diffusion-based framework for automatic colorization of Anime-style facial sketches. Our method preserves the structural fidelity of the input sketch while effectively transferring stylistic attributes from a reference image. Unlike traditional approaches that rely on predefined noise schedules - which often compromise perceptual consistency -- our framework builds on continuous-time diffusion models and introduces SSIMBaD (Sigma Scaling with SSIM-Guided Balanced Diffusion). SSIMBaD applies a sigma-space transformation that aligns perceptual degradation, as measured by structural similarity (SSIM), in a linear manner. This scaling ensures uniform visual difficulty across timesteps, enabling more balanced and faithful reconstructions. Experiments on a large-scale Anime face dataset demonstrate that our method outperforms state-of-the-art models in both pixel accuracy and perceptual quality, while generalizing to diverse styles. Code is available at github.com/Giventicket/SSIMBaD-Sigma-Scaling-with-SSIM-Guided-Balanced-Diffusion-for-AnimeFace-Colorization