Recent text-to-video (T2V) models have demonstrated strong capabilities in producing high-quality, dynamic videos. To improve the visual controllability, recent works have considered fine-tuning pre-trained T2V models to support image-to-video (I2V) generation. However, such adaptation frequently suppresses motion dynamics of generated outputs, resulting in more static videos compared to their T2V counterparts. In this work, we analyze this phenomenon and identify that it stems from the premature exposure to high-frequency details in the input image, which biases the sampling process toward a shortcut trajectory that overfits to the static appearance of the reference image. To address this, we propose adaptive low-pass guidance (ALG), a simple training-free fix to the I2V model sampling procedure to generate more dynamic videos without compromising per-frame image quality. Specifically, ALG adaptively modulates the frequency content of the conditioning image by applying a low-pass filter at the early stage of denoising. Extensive experiments show ALG significantly improves the temporal dynamics of generated videos, while preserving or even improving image fidelity and text alignment. For instance, on the VBench test suite, ALG achieves a 33% average improvement across models in dynamic degree while maintaining the original video quality. For additional visualizations and source code, see the project page.