In the previous chapter, we examined the forward diffusion process, where we systematically added Gaussian noise to data over a series of timesteps until only noise remained. Now, we focus on the inverse operation: the reverse diffusion process. This is the generative part, where we aim to start from pure noise and progressively denoise it to produce a sample that resembles the original data distribution.

This chapter explains how this reversal is achieved. Since calculating the true reverse probability $p(x_{t-1}|x_t)$ directly is often intractable, we will learn how to approximate it.

You will learn about:

• The objective of the reverse process: estimating the transition probability $p(x_{t-1}|x_t)$.
• Why a direct calculation is difficult and how neural networks are used for approximation.
• How we parameterize the reverse process, often by training a network to predict the noise $\epsilon$ added at timestep $t$.
• The mathematical formulation that defines a single denoising step, allowing us to move from $x_t$ to an estimate of $x_{t-1}$.

By the end of this chapter, you will understand the core mechanics of how a diffusion model learns to generate data by systematically reversing the noising process.