How do you implement a basic diffusion model using PyTorch?

To implement a basic diffusion model in PyTorch, start by defining the core components: the forward process (adding noise to data), the reverse process (removing noise), and the neural network that predicts the noise. The forward process gradually corrupts input data (like images) over multiple timesteps using a predefined noise schedule. For example, you can define a linear schedule for beta values (noise levels) that increase from 1e-4 to 0.2 across 1,000 steps. Each step computes the noisy sample using x_t = sqrt(alpha_bar[t]) * x_0 + sqrt(1 - alpha_bar[t]) * epsilon, where alpha_bar is the cumulative product of 1 - beta.

Next, build the U-Net model to predict the noise in the reverse process. A minimal U-Net might include convolutional blocks with residual connections, attention layers, and downsampling/upsampling steps. For example, use PyTorch’s nn.Module to create a network with encoder and decoder blocks. The encoder reduces spatial dimensions while increasing channels, and the decoder does the inverse. Include time embedding layers to inject timestep information into the network, often done using sinusoidal positional encoding or learned embeddings. The model takes the noisy image and timestep as input, outputting the predicted noise.

For training, sample a batch of data, generate random timesteps, add noise to the data, and train the model to predict the added noise. Use an Adam optimizer with a mean squared error (MSE) loss between the predicted and actual noise. During inference (sampling), start with pure noise and iteratively denoise it by predicting and subtracting the noise at each timestep. Use the ddpm_sampler function to apply the reverse diffusion steps, adjusting the sample using the predicted noise and the noise schedule. Keep the code modular, separating the model, training loop, and sampling logic for clarity.