Diffusion models have revolutionized generative modeling, yet their extensive denoising trajectories present significant computational hurdles in resource-constrained environments. Conventional sampling strategies rely on fixed-step solvers and uniform model depth, failing to leverage the signal inherent in the evolving score function, which exhibits substantial redundancy across the denoising path. We introduce ADSF, a scheduler-driven framework that conditions computation on a single geometric quantity, that is, the local curvature of the score field, estimated at negligible cost via a Hutchinson trace estimator. By analyzing the magnitude and structural trajectory of score updates between consecutive timesteps, our scheduler dynamically modulates resource allocation. This per-sample, score-aware scheduling mechanism allows for efficient navigation of the denoising process with minimal fidelity loss. Comprehensive experiments demonstrate that ADSF achieves competitive image quality (FID 2.11 on CIFAR-10) while reducing total inference MACs by up to 40% relative to strong baselines such as EDM. Our results demonstrate that a single scalar signal suffices to guide adaptive, per-timestep computation in unconditional diffusion sampling.