This study discusses the spatial resolution of a forward stimulated Brillouin scattering (F-SBS) sensing system based on phase demodulation. A theoretical analysis of this resolution is conducted, and numerical simulations confirm that inadequate signal-to-noise ratios in the original data lead to a noticeable degradation of the system's spatial resolution. To mitigate the impact of an insufficient signal-to-noise ratio, this study proposes the utilization of an attention-guided denoising convolutional neural network algorithm for data post-processing. The signal-to-noise ratio of the zero-order sideband of the reading pulse increases from 47.05 dB to 64.23 dB when this algorithm is applied. As a result, the system's spatial resolution is restored from 15 m to its theoretical value of 3 m. This approach effectively enhances the spatial resolution without introducing additional complexity to the measurement apparatus, thereby contributing to the practical implementation of phase-demodulated F-SBS sensors.