Watermarking is a viable approach for safeguarding the proprietary rights of digital media. This study introduces an innovative fast Fourier transform (FFT)-based phase modulation (PM) scheme that facilitates efficient and effective blind audio watermarking at a remarkable rate of 508.85 numeric values per second while still retaining the original quality. Such a payload capacity makes it possible to embed a full-color image of 64 × 64 pixels within an audio signal of just 24.15 s. To bolster the security of watermark images, we have also implemented the Arnold transform in conjunction with chaotic encryption. Our comprehensive analysis and evaluation confirm that the proposed FFT–PM scheme exhibits exceptional imperceptibility, rendering the hidden watermark virtually undetectable. Additionally, the FFT–PM scheme shows impressive robustness against common signal-processing attacks. To further enhance the visual rendition of the recovered color watermarks, we propose using residual neural networks to perform image denoising and super-resolution reconstruction after retrieving the watermarks. The utilization of the residual networks contributes to noticeable improvements in perceptual quality, resulting in higher levels of zero-normalized cross-correlation in cases where the watermarks are severely damaged.