Large Language Models (LLMs) have revolutionized the world, impacting everything from education and law to coding and even academic peer reviews. At the heart of these powerful models lies the Transformer architecture, and within the Transformer, the softmax function plays a critical role. But why is softmax so important? This research delves into the inner workings of softmax, exploring its learning dynamics in two-layer neural networks. Using the Neural Tangent Kernel (NTK) framework, the study reveals that softmax's normalization effect creates a smoother, more predictable 'landscape' for the model to learn in. This leads to faster and more stable training, allowing the model to effectively 'fit' the data it's given. The research goes beyond theory, applying these findings to diffusion models, a cutting-edge technique for generating images and other data. The results show that softmax-powered networks can learn complex patterns with provable accuracy, even when the data is noisy. This work opens doors to understanding the power of softmax not just in simple networks, but also in the more complex self-attention mechanisms that drive LLMs. It suggests that the principles uncovered here could lead to even more powerful and efficient AI models in the future, pushing the boundaries of natural language processing and generative modeling.