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Time warping finds use in many fields of time series analysis, and it has been effectively implemented in many different application areas. Rather than focusing on a particular application area we approach the general problem definition, and employ principal curves, a powerful machine learning tool, to improve the noise robustness of existing time warping methods. The increasing noise level is the most important problem that leads to unnatural alignments. Therefore, we tested our approach in low signal-to-noise ratio (SNR) signals, and obtained satisfactory results. Moreover, for the signals denoised by principal curve projections we propose a differential equation-based time warping method, which has a comparable performance with lower computational complexity than the existing techniques.