Having established the mathematical framework for the forward and reverse diffusion processes, we now address how to implement the reverse (denoising) step. This requires a trainable model that can learn to estimate the noise added at a specific timestep $t$, given the noisy data $x_t$.

This chapter concentrates on the architecture and training procedure for this core model. We will cover:

• The U-Net Architecture: Examining the structure of the U-Net, a convolutional network frequently employed for its ability to handle image-like data and preserve spatial information, which is essential for noise prediction.
• Timestep Integration: Methods for providing the diffusion timestep $t$ as input to the network, enabling it to condition its predictions accordingly.
• The Training Objective: Defining the loss function, typically the Mean Squared Error (MSE) between the actual noise added and the noise predicted by the network. We will touch upon its connection to the overall probabilistic objective.
• The Training Algorithm: Outlining the step-by-step process for training the noise prediction network using batches of data.
• Practical Setup: Discussing key aspects of implementing the U-Net and timestep embeddings in code.

Upon completing this chapter, you will understand the design principles of the neural network used within diffusion models and the procedure for training it to perform the denoising task.