High-speed quantitative phase imaging enables non-intrusive visualization of transient compressible gas flows and energetic phenomena. However, phase maps reconstructed via the transport of intensity equation (TIE) suffer from spatially correlated low-frequency artifacts introduced by the inverse Laplacian solver, which obscure meaningful flow structures such as jet plumes, shockwave fronts, and density gradients. Conventional filtering approaches fail because signal and noise occupy overlapping spatial frequency bands, and no paired ground truth exists since every frame represents a physically unique, non-repeatable flow state. We address this by developing a physics-informed synthetic training dataset where clean targets are procedurally generated using physically plausible gas flow morphologies, including compressible jet plumes, turbulent eddy fields, density fronts, periodic air pockets, and expansion fans, and passed through a forward TIE simulation followed by inverse Laplacian reconstruction to produce realistic noisy phase maps. A U-Net-based convolutional denoising network trained solely on this synthetic data is evaluated on real phase maps acquired at 25,000 fps, demonstrating zero-shot generalization to real parallel TIE recordings, with a 13,260% improvement in signal-to-background ratio and 100.8% improvement in jet-region structural sharpness across 20 evaluated frames.