White Noise, by definition, works by defining parameters in which data is ensured to be random, unrelated, and have zero mean.
Modifications made for generating new data should be learnable. Simply adding white noise will not help. Note that white noise is not learnable.
Gaussian Noise
Reference
https://www.amazon.in/Hands-Machine-Learning-Scikit-Learn-TensorFlow/dp/1491962291
https://deepai.org/machine-learning-glossary-and-terms/white-noise
https://nanonets.com/blog/data-augmentation-how-to-use-deep-learning-when-you-have-limited-data-part-2/