Diffusion models are built on the central idea of gradual noise corruption:

• You start with a dataset — such as images, audio, or any structured data;
• Random noise is added to your data, step by step, in a slow and systematic way;
• Each step only slightly perturbs the data, so the process is carefully controlled;
• The original structure is gradually destroyed, until it is replaced by pure noise.

This is not random chaos. The process is designed to be reversible: if you can learn to undo each step—starting from noise and iteratively removing it—you can generate new data that looks like your original dataset. This is the core motivation for using diffusion models in generative modeling.

The noise addition process happens gradually, in a series of small, controlled steps. At each step, you add a little more noise to the data. In the early steps, the data still looks familiar and keeps most of its original structure. As you continue, the structure fades and the data appears more and more random. After many steps, the data becomes completely unrecognizable — just noise.

This stepwise transformation follows the Markov property: each new state depends only on the immediately previous state, not on the entire sequence of past steps. This Markovian structure makes the process easier to analyze and model mathematically.